Measurements of the groomed and ungroomed jet angularities in pp collisions at $\sqrt{s} = 5.02$ TeV

ALICE Collaboration

doi:10.1007/JHEP05(2022)061

Measurements of the groomed and ungroomed jet angularities in pp collisions at $\sqrt{s} = 5.02$ TeV

ALICE Collaboration 2021-07-23 00:00:00 The jet angularities are a class of jet substructure observables which characterize the angular and momentum distribution of particles within jets. These observables are sensitive to momentum scales ranging from perturbative hard scatterings to nonperturbative fragmentation into ﬁnal-state hadrons. We report measurements of several groomed and ungroomed jet angularities in pp collisions at s = 5:02 TeV with the ALICE detector. Jets are reconstructed using charged particle tracks at midrapidity (jhj < 0:9). The anti-k algorithm is used with jet resolution parameters R = 0:2 and ch jet R = 0:4 for several transverse momentum p intervals in the 20100 GeV/c range. Using the jet grooming algorithm Soft Drop, the sensitivity to softer, wide-angle processes, as well as the underly- ing event, can be reduced in a way which is well-controlled in theoretical calculations. We report the ungroomed jet angularities, l , and groomed jet angularities, l , to investigate the interplay be- a a ,g tween perturbative and nonperturbative effects at low jet momenta. Various angular exponent param- eters a = 1, 1.5, 2, and 3 are used to systematically vary the sensitivity of the observable to collinear and soft radiation. Results are compared to analytical predictions at next-to-leading-logarithmic ac- curacy, which provide a generally good description of the data in the perturbative regime but exhibit discrepancies in the nonperturbative regime. Moreover, these measurements serve as a baseline for future ones in heavy-ion collisions by providing new insight into the interplay between perturbative and nonperturbative effects in the angular and momentum substructure of jets. They supply crucial guidance on the selection of jet resolution parameter, jet transverse momentum, and angular scaling variable for jet quenching studies. © 2021 CERN for the beneﬁt of the ALICE Collaboration. Reproduction of this article or parts of it is allowed as speciﬁed in the CC-BY-4.0 license. See Appendix B for the list of collaboration members arXiv:2107.11303v2 [nucl-ex] 1 Dec 2022 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 1 Introduction In high-energy particle collisions, jet observables are sensitive to a variety of processes in quantum chro- modynamics (QCD), from the initial hard (high Q ) parton scattering to a scale evolution culminating in hadronization near L . Jets reconstructed with a radius (resolution) parameter near R = 1 and with QCD jet sufﬁciently large transverse momentum p provide a proxy for the dynamics of the initial hard parton jet scattering, whereas those reconstructed with smaller R or at lower p become sensitive to nonperturba- tive effects. In this article, jet substructure observables are deﬁned by clustering particles into a jet and then constructing an observable from its constituents to characterize its internal radiation pattern. Jet substructure techniques have provided one of the key tools to study rare event topologies in pp col- lisions, for example by tagging boosted objects that decay into jets [1]. Moreover, measurements of jet substructure enable stringent tests of perturbative QCD (pQCD) and facilitate studies of nonpertur- bative effects which are not yet under satisfactory theoretical control [2]. Jet substructure observables offer both ﬂexibility and rigor: they can be constructed to be theoretically calculable from ﬁrst-principles pQCD while simultaneously maintaining sensitivity to jet radiation in speciﬁc regions of phase-space. Jet grooming algorithms, such as Soft Drop [3–5], can additionally be used to remove soft, wide-angle radiation via well-controlled approaches, reducing nonperturbative effects. This deﬁnes two families of jet substructure observables: one that can be constructed from all jet constituents and one based on a subset of jet constituents which remain after grooming procedures. One such set of observables are the generalized jet angularities [6, 7]. Expanding upon the jet girth g (also known as the jet radial moment), the generalized jet angularities form a class of jet substructure observables deﬁned by k k a l z q ; (1) a i i where the sum runs over the jet constituents i, and k and a are continuous free parameters. The ﬁrst jet factor z p =p describes the momentum fraction carried by the constituent, and the second factor i T;i q DR =R denotes the separation in rapidity (y) and azimuthal angle (j ) of the constituent from the jet i i 2 2 axis, where DR Dy +Dj and R is the jet resolution parameter. The jet angularities are infrared- i i and collinear- (IRC-)safe for k = 1 and a > 0 [8, 9]. We consider the ungroomed jet angularities, denoted as l , as well as the groomed jet angularities in which the sum runs only over the constituents of the groomed jet, denoted as l . These include the jet girth [10], l , and the jet thrust [11], l , a;g 1 2 jet 2 2 which is related to the jet mass m by l = (m =p ) +O(l ); l , however, is more robust against jet 2 jet 2 nonperturbative effects than m since it does not depend explicitly on the hadron masses. jet The IRC-safe jet angularities offer the possibility to systematically vary the observable deﬁnition in a way that is theoretically calculable and therefore provide a rich opportunity to study both perturbative and nonperturbative QCD [12–15]. This article considers jet angularities constructed from charged-particle jets. While charged-particle jets are IRC-unsafe [16], comparisons to these theoretical predictions can nonetheless be carried out by following a nonperturbative correction procedure, as outlined in Sec. 5.1. Jet angularities were recently calculated in pp collisions both in the ungroomed [9] and groomed [17] cases, as well as for jets produced in association with a Z boson [18]. These calculations use all-order resummation of large logarithms up to next-to-leading-logarithmic (NLL ) accuracy [19]. Measurements of l and l will serve to test these analytical predictions, in particular the role of resummation effects a a;g and power corrections. Moreover, by measuring multiple values of a , one can test the predicted scaling of nonperturbative shape functions that are used to model hadronization, which depend only on a single The notation l is employed to represent the jet angularities instead of the commonly-used notation l in order to avoid conﬂict with the letter b , which is also used to denote the angular parameter of the Soft Drop grooming algorithm. 2 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration nonperturbative parameter for all values of a [20, 21]. Several measurements of jet angularities have been performed in hadronic collisions. The ungroomed jet angularity l has been measured in pp collisions by the ATLAS, CMS, and ALICE Collaborations [22– 24] in addition to pp collisions by the CDF Collaboraiton [25]. The ungroomed jet angularity l has also been measured in pp collisions by the CMS Collaboration [24]. The closely related ungroomed and groomed jet mass have been extensively measured in pp collisions by the ATLAS and CMS Collabora- tions [23, 24, 26–35], and the ungroomed mass was also studied in pp collisions by the CDF Collabo- ration [25] and in p–Pb collisions by the ALICE Collaboration [36]. Many of these measurements have focused on using jet substructure for tagging objects at high p , rather than for fundamental studies of QCD, and with the exception of the jet mass there have not yet been comparisons of jet angularities to an- alytical calculations, nor have any such comparisons been made for charged-particle jets. In this article, we perform the ﬁrst measurements of groomed jet angularities in pp collisions, and a systematic scan of jet the IRC-safe ungroomed jet angularities. These measurements focus on low to moderate p , and small to moderate R. Moreover, the measurements are performed in pp collisions at a center-of-mass energy s = 5:02 TeV, the same center-of-mass energy at which ALICE recorded data in heavy-ion collisions during LHC Run 2, and where no jet angularity measurements have been made. These measurements serve as a baseline for future measurements of the jet angularities in heavy-ion col- lisions, in which a deconﬁned state of strongly-interacting matter is produced [37–40]. Measurements of jets and jet substructure in heavy-ion collisions may provide key insight into the physical properties of this deconﬁned state [41–43]. The jet angularities are sensitive both to medium-induced broadening as well as jet collimation [44–46]; by systematically varying the weight of collinear radiation, one may be able to efﬁciently discriminate between jet quenching models. In Pb–Pb collisions, l has been mea- sured for R = 0:2 by the ALICE Collaboration [22], and the ungroomed and groomed jet mass have been measured for R = 0:4 by the ATLAS, CMS, and ALICE Collaborations [30, 34, 36]. The interpreta- tion of previous measurements is unclear, with strong modiﬁcation being observed in Pb–Pb collisions compared to pp collisions for the case when a = 1 and R = 0:2, but little to no modiﬁcation seen for the R = 0:4 jet mass. Future measurements over a range of R and a offer a compelling opportunity to disentangle the roles of medium-induced broadening, jet collimation, and medium response in jet evo- lution. By measuring small to moderate R jets in pp collisions, which are theoretically challenging and involve signiﬁcant resummation effects [47], the ability of pQCD to describe the small-radius jets that are measured in heavy-ion collisions can be tested. This article reports measurements of ungroomed and groomed jet angularities for a = 1, 1.5, 2, and 3 in pp collisions at s = 5:02 TeV. In addition to the standard jet girth (a = 1) and jet mass (related to a = 2) parameters, a = 1:5 and a = 3 are included to test the universality of a nonperturbative shape function by varying effects of soft, wide-angle radiation, as discussed below in Sec. 5.1.2, and to serve as a reference for future jet quenching measurements in heavy-ion collisions. Grooming is performed according to the Soft Drop grooming procedure with z = 0:2 and b = 0 [48]. Charged particle jets were cut reconstructed at midrapidity using the anti-k algorithm with jet resolution (radius) parameters R = 0:2 ch jet and R = 0:4 in four equally-sized p intervals from 20 to 100 GeV=c. The results are compared to NLL pQCD predictions, as well as to the PYTHIA8 [49] and Herwig7 [50, 51] Monte Carlo generators. 2 Experimental setup and data sets A description of the ALICE detector and its performance can be found in Refs. [52, 53]. The pp data used in this analysis were collected in 2017 during LHC Run 2 at s = 5:02 TeV [54]. A minimum bias (MB) trigger was used; this requires a coincidence of hits in the V0 scintillator detectors, which provide full azimuthal coverage and cover the pseudorapidity ranges of 2:8 < h < 5:1 and 3:7 < h < 1:7 [55]. The event selection also requires the location of the primary vertex to be within 10 cm from the nom- 3 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration inal interaction point (IP) along the beam direction and within 1 cm of the IP in the transverse plane. Beam-induced background events were removed using two neutron Zero Degree Calorimeters located at 112:5 m along the beam axis from the center of the detector. Events with multiple reconstructed vertices were rejected, and track quality selection criteria ensured that tracks used in the analysis were from only one vertex. Events were acquired at instantaneous luminosities between approximately 10 31 2 1 and 10 cm s , corresponding to a low level of pileup with approximately 0:004 < m < 0:03 events per bunch crossing. The pp data sample contains 870 million events and corresponds to an integrated luminosity of 18.0(4) nb [56]. This analysis uses charged particle tracks reconstructed from clusters in both the Time Projection Cham- ber (TPC) [57] and the Inner Tracking System (ITS) [58]. Two types of tracks are deﬁned: global tracks and complementary tracks. Global tracks are required to include at least one hit in the silicon pixel de- tector (SPD), comprising the ﬁrst two layers of the ITS, and to satisfy a number of quality criteria [59], including having at least 70 out of a maximum of 159 TPC space points and at least 80% of the geo- metrically ﬁndable space points in the TPC. Complementary tracks do not contain any hits in the SPD, but otherwise satisfy the tracking criteria, and are reﬁt with a constraint to the primary vertex of the event. Including this second class of tracks ensures approximately uniform azimuthal acceptance, while preserving similar transverse momentum p resolution to tracks with SPD hits, as determined from the ﬁt quality. Tracks with p > 0:15 GeV=c are accepted over pseudorapidity jhj < 0:9 and azimuthal T;track angle 0 < j < 2p . All tracks are assigned a mass equal to the p mass. The instrumental performance of the ALICE detector and its response to particles is estimated with a GEANT3 [60] model. The tracking efﬁciency in pp collisions, as estimated by propagating pp events from PYTHIA8 Monash 2013 [49] through the ALICE GEANT3 detector simulation, is approximately 67% at p = 0:15 GeV=c, rises to approximately 84% at p = 1 GeV=c, and remains above T;track T;track 75% at higher p . The momentum resolution s(p )=p is estimated from the covariance matrix of T T T the track ﬁt [53] and is approximately 1% at p = 1 GeV=c. This increases with p , reaching T;track T;track approximately 4% at p = 50 GeV=c. T;track 3 Analysis method 3.1 Jet reconstruction Jets are reconstructed from charged tracks with p > 150 MeV=c using the FastJet package [61]. The anti-k algorithm is used with the E recombination scheme for resolution parameters R = 0:2 and ch jet 0:4 [62]. All reconstructed charged-particle jets in the transverse momentum range 5 < p < 200 GeV=c are analyzed in order to maximize statistics in the unfolding procedure (described below). Each jet axis is required to be within the ﬁducial volume of the TPC, h < 0:9 R. Jets containing a track jet with p > 100 GeV=c are removed from the collected data sample, due to limited momentum resolu- tion. In order to make consistent comparisons between the data and the theoretical calculations, the background due to the underlying event is not subtracted from the data, and instead the underlying event (along with other nonperturbative effects) is included in model corrections, as described in Sec. 5.1. The jet reconstruction performance is studied by comparing jets reconstructed from PYTHIA8-generated events at “truth level” (before the particles undergo interactions with the detector) to those at “detector level” (after the ALICE GEANT3 detector simulation). Two collections of jets are constructed: pp truth level (PYTHIA truth) and pp detector level (PYTHIA with detector simulation). The detector- level jets are then geometrically matched with truth-level jets within DR < 0:6 R while additionally requiring that each match be unique. Table 1 shows approximate values of the mean jet energy scale D E . ch jet ch jet ch jet ch jet ch jet shift, D = p p =p , the jet energy resolution, JER = s p p , and the JES T;det T;truth T;truth T;det T;truth ch jet ch jet jet reconstruction efﬁciency, e , for both R = 0:2 and R = 0:4, where p is the detector-level p , reco T;det 4 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration Table 1: Approximate values characterizing the jet reconstruction performance for R = 0:2 and 0:4 in pp collisions. D is the mean jet energy scale shift, JER is the jet energy resolution, and e is the reconstruction efﬁciency. JES reco R = 0:2 R = 0:4 ch jet p 20 GeV=c 100 GeV=c 20 GeV=c 100 GeV=c D –12% –24% –13% –21% JES JER 22% 21% 21% 21% e 94% 100% 97% 100 reco ch jet ch jet and p is the truth-level p . The jet energy scale shift is a long-tailed asymmetric distribution T;truth T ch jet ch jet due to tracking inefﬁciency [63] with a peak at p = p , and D should be understood only as a JES T;det T;truth rough characterization of this distribution. The ungroomed jet angularities are reconstructed using all of the charged-particle jet constituents ac- cording to Eq. (1). For the groomed jet angularities, Soft Drop grooming [3] is performed, in which the constituents of each jet are reclustered with the Cambridge–Aachen algorithm [64] with resolution parameter R, forming an angularly-ordered tree data structure. Each node corresponds to a constituent 2 2 p Dy +Dj T;subleading DR track, and each edge is a branch splitting deﬁned by z and q . The p +p R R T;leading T;subleading jet tree is then traversed starting from the largest-angle splitting, and the Soft Drop condition, z > z q , cut is recursively evaluated. Here, z is the subleading branch p fraction deﬁned above, and z and b are T cut tunable, free parameters of the grooming algorithm. For this analysis, b = 0 is used to maximize the perturbative calculability [17], while z = 0:2 is chosen (as opposed to the more common z = 0:1) cut cut since higher-accuracy branch tagging can be achieved in future heavy-ion collision analyses [48]. If the Soft Drop condition is not satisﬁed, then the softer subleading branch is discarded and the next splitting in the harder branch is examined in the same way. If, however, the condition is satisﬁed, then the groom- ing procedure is concluded, with all remaining constituents deﬁning the groomed jet. The groomed jet angularity is then deﬁned according to Eq. (1) using the groomed jet constituents, but still with the un- ch jet groomed p and ungroomed jet axis to deﬁne q , since the groomed jet observable is a property of the ch jet ch jet original (ungroomed) jet object. Note that while the ungroomed p is IRC-safe, the groomed p T,g is Sudakov safe [65]. If the jet does not contain a splitting that passes the Soft Drop condition, then the groomed jet contains zero constituents (“untagged”) and does not have a deﬁned groomed jet angularity. 3.2 Corrections ch jet The reconstructed p and l differ from their true values due to tracking inefﬁciency, particle– material interactions, and track p resolution. To account for these effects, PYTHIA8 Monash 2013 [49, 66] and the ALICE GEANT3 detector simulation are used to construct a 4D response matrix that ch jet ch jet ch jet ch jet describes the detector response mapping of p and l to p and l , where p and p a;truth a;det T;truth T;det T;det T;truth are as above, and l and l are the analogous detector- and truth-level l . The truth-level jet was a;det a;truth a constructed from the charged primary particles of the PYTHIA event, deﬁned as all particles with a mean proper lifetime larger than 1 cm/c, and excluding the decay products of these particles [67]. ch jet A 2D unfolding in p and l is then performed using the iterative Bayesian unfolding algorithm [68, 69] implemented in the RooUnfold package [70] to recover the true jet spectrum at the charged- hadron level. This technique utilizes a “prior" distribution (equivalent to the per-bin MC prediction) as a starting point, before iteratively updating the distribution using Bayes’ theorem in conjunction with the calculated response matrix and measured data (see Refs. [68, 69] for details). Since the jet yield in each ch jet ch jet ch jet reported p interval varies widely, with higher-p jets being less probable than lower-p jets, T T T ch jet and since the shape and mean value of the jet angularity distributions also changes with p , a separate ch jet 2D unfolding for each reported p bin is performed in order to optimize the observable binning at both 5 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration truth and detector levels, thus ensuring sufﬁcient jet yield is included in the procedure for all distributions while simultaneously maximizing the number of bins for regions of phase space where higher yield is available. The bin migration in all cases is dominated by a strong diagonal mapping in the response ch jet matrix coupled with a slight smearing along the p and l axes. The smearing in l is roughly a;truth a T;truth ch jet symmetric about the diagonal, whereas the smearing in p tends to be skewed towards lower values ch jet of p due to tracking efﬁciency effects. T;truth In the groomed case, the number of untagged jets in the unfolding procedure is included as an additional bin adjacent to the lower edge of the l distributions. This is done so that the unfolding procedure will correct for detector effects on the groomed jet tagging fraction as well as account for bin migration effects for jets which are groomed away at detector-level but not truth-level, or vice versa. To validate the performance of the unfolding procedure, a set of refolding and closure tests is performed, in which either the response matrix is multiplied by the unfolded data and compared to the original detector-level spectrum, or in which the shape of the input MC spectrum is modiﬁed to account for the fact that the actual distribution may be different than the MC input spectrum. The number of iterations, which sets the strength of regularization, is chosen to be the minimal value such that all unfolding tests succeed. This results in the number of iterations being equal to 3 for all distributions. In all cases, closure is achieved compatible with statistical uncertainties. The distributions after unfolding are corrected for the kinematic efﬁciency, deﬁned as the efﬁciency of ch jet ch jet reconstructing a truth-level jet at a particular p and l value given a reconstructed jet p and a;truth T;truth T;det l range. Kinematic inefﬁciency results from effects including smearing from the Soft Drop threshold a;det ch jet and p -smearing of the jet out of the selected p range. Any “missed” jets, those jets which exist at T;det truth level but not at detector level, are handled by this kinematic efﬁciency correction. In this analysis, minimal detector-level cuts are applied, and the kinematic efﬁciency is therefore greater than 99% in all ch jet cases. Since a wide p range is taken, the effect of “fake” jets, those jets which exist at detector level T;truth but not truth level, is taken to be negligible. 4 Systematic uncertainties The systematic uncertainties in the unfolded results arise from uncertainties in the tracking efﬁciency and unfolding procedure, as well as the model-dependence of the response matrix, and the track mass assumption. Table 2 summarizes the systematic uncertainty contributions. Each of these sources of uncertainty dominate in certain regions of the measured observables, with the exception of the track mass assumption which is small in all cases. The total systematic uncertainty is taken as the sum in quadrature of the individual uncertainties described below. The tracking efﬁciency uncertainty is estimated to be 4% by varying track selection parameters and the ITS–TPC matching requirement. In order to assign a systematic uncertainty to the nominal result, a response matrix is constructed using the same techniques as for the ﬁnal result except that an additional 4% of tracks are randomly rejected before the jet ﬁnding. This response matrix is then used to unfold the distribution in place of the nominal response matrix, and the result is compared to the default result, with the differences in each bin taken as a symmetric uncertainty. This uncertainty constitutes a smaller effect in the groomed jet angularities, where single-particle jets, being the most sensitive to the tracking efﬁciency, are groomed away by the Soft Drop condition. The uncertainty on the track momentum resolution is a sub-leading effect to the tracking efﬁciency and is taken to be negligible. Several variations of the unfolding procedure are performed in order to estimate the systematic uncer- tainty arising from the unfolding regularization procedure: 1. The number of iterations was varied by2 and the average difference with respect to the nominal 6 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration result is taken as the systematic uncertainty. ch jet ch jet 0:5 2. The prior distribution is scaled by a power law in p and a linear scaling in l , (p ) T T [1(l 0:5)]. The average difference between the result unfolded with this prior and the original is taken as the systematic uncertainty. 3. The binning in l was varied to be slightly ﬁner and coarser than the nominal binning, by com- bining (splitting) some adjacent bins with low (high) jet yield, or by shifting the bin boundaries to be between the nominal boundaries. ch jet 4. The lower and upper bounds in the p range were increased to 10 and decreased to 120 GeV=c, T;det respectively. These values are chosen as reasonable values to estimate sensitivity to truncation effects. The total unfolding systematic uncertainty is then the standard deviation of the variations, å s =N, i=1 i where N = 4 and s is the systematic uncertainty due to a single variation, since they each comprise independent measurements of the same underlying systematic uncertainty in the regularization. A systematic uncertainty associated with the model-dependent reliance on the Monte Carlo generator which is used to unfold the spectra is included. We construct a fast simulation to parameterize the tracking efﬁciency and track p resolution, and build response matrices using PYTHIA8 Monash 2013 and Herwig7 (default tune) as generators. Even though a full detector simulation using PYTHIA8 has also been generated, a fast simulation is used for this purpose so that there is complete parity between the two generators in the calculation of this systematic uncertainty. This fast simulation provides agreement within10% of the full detector simulation for R = 0:2 jets, with some larger deviations seen in the tails of the jet angularity distributions for R = 0:4 jets. These two response matrices are then used to unfold the measured data, and the differences between the two unfolded results in each interval are taken as a ch jet symmetric uncertainty. This uncertainty is most signiﬁcant at lower p . In order to assess the uncertainty due to the track mass assumption, K meson and proton masses are randomly assigned to 13% and 5.5% of tracks, respectively, in both the data and the response matrix. These numbers are chosen from the (approximate) inclusive number of each respective particle measured ch jet at midrapidity in pp events by ALICE [71]. Neither the measurement inside the jets nor the p - dependence are considered, so these numbers are taken to constitute a reasonable maximum uncertainty. The bin-by-bin difference of the unfolded result to the nominal result is taken as a symmetric uncertainty. 5 Results and discussion ch jet We report the l and l distributions for a = 1, 1.5, 2, and 3 in four equally-sized intervals of p a a;g between 20 and 100 GeV/c. The distributions are reported as differential cross sections: 1 ds 1 dN 1 ds 1 dN jets gr jets (ungroomed), or (groomed), (2) s dl N dl s dl N dl a jets a inc a;g inc jets a;g ch jet where N is the number of jets within a given p range and s is the corresponding cross section. jets For the groomed case, some jets are removed by the grooming procedure, and therefore two different quantities are deﬁned: N , the number of jets which have at least one splitting satisfying the Soft gr jets Drop condition, and N , the total number of inclusive jets, with both N and N being within inc jets gr jets inc jets ch jet the given p range. s is the cross section corresponding to the latter inclusive quantity. For the un- inc groomed case, N = N and s = s , so the redundant labels are dropped. It is useful to normalize inc jets jets inc the groomed differential cross section by the number of inclusive jets since the groomed jet angularities 7 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet Table 2: Summary of systematic uncertainties for a representative sample of a , R, and p . A moderately high ch jet 60 < p < 80 GeV=c with R = 0:4 is chosen to show the variation with a , and two additional rows show the ch jet trends with smaller p and R. Relative uncertainty ch jet a R p (GeV=c) Trk. eff. Unfolding Generator Mass hypothesis Total 1 0.4 60–80 1–15% 2–7% 1–5% 0–2% 7–16% 2 0.4 60–80 1–10% 1–8% 1–5% 1–3% 4–12% 3 0.4 60–80 1–10% 2–4% 1–4% 0–4% 4–11% 2 0.4 20–40 1–16% 1–4% 1–43% 0–5% 2–44% 2 0.2 60–80 2–12% 2–7% 1–9% 0–2% 3–12% a;g 1 0.4 60–80 1–7% 2–8% 1–6% 0–4% 2–13% 2 0.4 60–80 1–8% 2–9% 1–5% 0–4% 3–12% 3 0.4 60–80 1–6% 2–7% 1–11% 0–7% 4–16% 2 0.4 20–40 1–8% 2–5% 1–40% 0–3% 2–42% 2 0.2 60–80 1–7% 1–8% 1–12% 0–3% 1–15% are a property of the inclusively-measured jet population and are thus typically normalized as such in theoretical calculations [17]. The ungroomed jet angularity distributions are shown in Fig. 1 and Fig. 2 for R = 0:4 and R = 0:2, respec- tively. By the deﬁnitions given in Eq. 2, these distributions are all normalized to unity. As a increases, the distributions skew towards small l , since q is smaller than unity. For larger R, the distributions are a i narrower than for smaller R, as expected due to the collinear nature of jet fragmentation. For small R ch jet and low p there is a visible peak at l = 0, which is due to single particle jets. These distributions are compared to PYTHIA8 Monash 2013 [49, 66] and Herwig7 (default tune) [50, 51] from truth-level projections of the respective response matrices, with jet reconstruction assigning tracks the p meson mass as in the measured data. These comparisons show deviations up to approximately +50%(30%). The largest deviations are for small values of l , where nonperturbative physics becomes signiﬁcant (see Sec. 5.1 for discussion). The groomed jet angularity distributions for z = 0:2 and b = 0 are shown in Fig. 3 for R = 0:4 and cut Fig. 4 for R = 0:2. Note that these distributions are shown on a logarithmic scale due to the distributions being more strongly peaked and falling faster with l as compared to the ungroomed distributions. The groomed jet angularities have signiﬁcantly smaller values than the ungroomed jet angularities, due to the removal of soft wide-angle radiation. The fraction of “untagged” jets, those that do not contain a splitting which passes the Soft Drop condition, ranges from 10 to 12%. Unlike the ungroomed jet angularities, which are normalized to unity, the groomed jet angularities are normalized to the Soft Drop tagging fraction. Since the tagging rate is fairly large, the measured distributions are therefore normalized close to unity. PYTHIA and Herwig describe the groomed jet angularities slightly better than the ungroomed jet angularities, with most deviations seen in the ungroomed distributions improving by 10–20% in the groomed case. Comparing to the two MC generators, the data are in slightly better agreement with Herwig7 than with PYTHIA8, especially for R = 0:4. The data cover a wide range of a and multiple R down to low p , and therefore are subject to vary- ing inﬂuence from nonperturbative effects. Accordingly, these data can be used to study nonpertubative effects. The level and location of the disagreements with PYTHIA and Herwig provide further con- straints on nonperturbative effects in MC event generators. Moreover, the comparison of the groomed 8 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 14 14 α = 1 α = 1 ALICE Syst. uncertainty α = 1.5 α = 1.5 pp s = 5.02 TeV PYTHIA8 Monash 2013 12 12 α = 2 α = 2 charged jets anti-k Herwig7 10 α = 3 (×0.5) 10 α = 3 (×0.5) R = 0.4 |η | < 0.5 jet ch jet ch jet 8 8 20 < p < 40 GeV/c 40 < p < 60 GeV/c T T 6 6 4 4 2 2 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α α = 1 α = 1 9 9 α = 1.5 (×0.7) α = 1.5 (×0.7) 8 8 α = 2 (×0.5) α = 2 (×0.5) 7 7 α = 3 (×0.3) α = 3 (×0.3) 6 6 ch jet ch jet 60 < p < 80 GeV/c 80 < p < 100 GeV/c 5 5 T T 4 4 3 3 2 2 1 1 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α 1.5 1.5 1 1 0.5 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α Figure 1: Comparison of ungroomed jet angularities l in pp collisions for R = 0:4 to MC predictions using ch jet PYTHIA8 and Herwig7, as described in the text. Four equally-sized p intervals are shown, with edges ranging between 20 and 100 GeV=c. The distributions are normalized to unity. dσ 1 dσ Data 1 Data Data Data Herwig7 PYTHIA8 PYTHIA8 Herwig7 σ σ dλ dλ α α dσ dσ Data 1 Data Data 1 Data Herwig7 Herwig7 PYTHIA8 σ PYTHIA8 σ dλ dλ α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 14 14 α = 1 α = 1 ALICE Syst. uncertainty α = 1.5 α = 1.5 pp s = 5.02 TeV PYTHIA8 Monash 2013 12 12 α = 2 α = 2 charged jets anti-k Herwig7 10 α = 3 (×0.5) 10 α = 3 (×0.5) R = 0.2 |η | < 0.7 jet ch jet ch jet 8 8 20 < p < 40 GeV/c 40 < p < 60 GeV/c T T 6 6 4 4 2 2 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α α = 1 α = 1 9 9 α = 1.5 (×0.7) α = 1.5 (×0.7) 8 8 α = 2 (×0.5) α = 2 (×0.5) 7 7 α = 3 (×0.3) α = 3 (×0.3) 6 6 ch jet ch jet 60 < p < 80 GeV/c 80 < p < 100 GeV/c 5 5 T T 4 4 3 3 2 2 1 1 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α 1.5 1.5 1 1 0.5 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α Figure 2: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 to MC predictions using ch jet PYTHIA8 and Herwig7, as described in the text. Four equally-sized p intervals are shown, with edges ranging between 20 and 100 GeV=c. The distributions are normalized to unity. dσ 1 dσ Data 1 Data Data Data Herwig7 PYTHIA8 PYTHIA8 Herwig7 σ σ dλ dλ α α dσ dσ Data 1 Data Data 1 Data Herwig7 Herwig7 PYTHIA8 σ PYTHIA8 σ dλ dλ α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 7 7 10 10 α = 1 α = 1 ALICE 6 6 Syst. uncertainty 10 10 α = 1.5 (×0.5) α = 1.5 (×0.5) pp s = 5.02 TeV PYTHIA8 Monash 2013 5 5 10 10 α = 2 (×0.2) α = 2 (×0.2) charged jets anti-k Herwig7 4 4 10 10 α = 3 (×0.03) α = 3 (×0.03) R = 0.4 |η | < 0.5 3 jet 3 10 10 Soft Drop z = 0.2 β = 0 cut 2 2 10 10 ch jet ch jet 20 < p < 40 GeV/c 40 < p < 60 GeV/c 10 10 T T 1 1 - 1 - 1 10 10 - 2 - 2 10 10 - 3 - 3 10 10 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g α = 1 α = 1 10 10 α = 1.5 (×0.25) α = 1.5 (×0.25) α = 2 (×0.1) α = 2 (×0.1) α = 3 (×0.02) α = 3 (×0.02) 1 1 - 1 - 1 10 10 ch jet ch jet - 2 - 2 60 < p < 80 GeV/c 80 < p < 100 GeV/c 10 10 T T 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 1.5 1.5 1 1 0.5 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g Figure 3: Comparison of groomed jet angularities l in pp collisions for R = 0:4 to MC predictions using a;g ch jet PYTHIA8 and Herwig7, as described in the text. Four equally-sized p intervals are shown between 20 and 100 GeV=c. The distributions are normalized to the groomed jet tagging fraction. dσ dσ 1 1 Data Data Data Data σ σ Herwig7 PYTHIA8 PYTHIA8 Herwig7 dλ dλ inc inc α ,g α ,g dσ 1 dσ Data Data Data Data σ σ Herwig7 Herwig7 PYTHIA8 PYTHIA8 dλ dλ inc inc α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 7 7 10 α = 1 10 α = 1 ALICE Syst. uncertainty 6 6 α = 1.5 (×0.5) α = 1.5 (×0.5) 10 10 pp s = 5.02 TeV PYTHIA8 Monash 2013 5 5 α = 2 (×0.2) α = 2 (×0.2) 10 charged jets anti-k 10 Herwig7 4 4 α = 3 (×0.03) α = 3 (×0.03) R = 0.2 |η | < 0.7 10 10 jet 3 3 10 10 Soft Drop z = 0.2 β = 0 cut 2 2 10 ch jet 10 ch jet 20 < p < 40 GeV/c 40 < p < 60 GeV/c T T 10 10 1 1 - 1 - 1 10 10 - 2 - 2 10 10 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 2 2 10 10 α = 1 α = 1 α = 1.5 (×0.25) α = 1.5 (×0.25) 10 10 α = 2 (×0.1) α = 2 (×0.1) α = 3 (×0.02) α = 3 (×0.02) 1 1 - 1 - 1 10 10 - 2 - 2 10 10 ch jet ch jet - 3 - 3 60 < p < 80 GeV/c 80 < p < 100 GeV/c 10 10 T T 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 1.5 1.5 1 1 0.5 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g Figure 4: Comparison of groomed jet angularities l in pp collisions for R = 0:2 to MC predictions using a;g ch jet PYTHIA8 and Herwig7, as described in the text. Four equally-sized p intervals are shown between 20 and 100 GeV=c. The distributions are normalized to the groomed jet tagging fraction. dσ dσ 1 1 Data Data Data Data σ σ Herwig7 PYTHIA8 PYTHIA8 Herwig7 dλ dλ inc inc α ,g α ,g dσ 1 dσ Data Data Data Data σ σ Herwig7 Herwig7 PYTHIA8 PYTHIA8 dλ dλ inc inc α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration and the ungroomed jet angularities with MC event generators allows direct sensitivity to radiation that was groomed away, which is highly nonperturbative. 5.1 Comparison to analytical calculations The measured ungroomed and groomed jet angularities are compared with analytical calculations [9, 17] which use all-order resummations of large logarithms to next-to-leading logarithmic (NLL ) ac- curacy [19]. In particular, the calculations resum logarithms of l , R, and z . In the case of the a cut n k l logarithms, the cumulant of the cross section includes the complete set of terms of form a ln l a a for k = 2n, 2n 1, and 2n 2. The calculations are valid up to power corrections in l , R, and z , a cut and do not include non-global logarithms [72]. These calculations are based on the framework of Soft Collinear Effective Theory (SCET) [73], in which the jet cross section is factorized into a “hard func- tion" corresponding to the initial scattering, and a “jet function" corresponding to the fragmentation of a hard-scattered parton into a jet. For the calculation of the jet angularities, the jet function is then further factorized into collinear and soft functions. Systematic uncertainties on the analytical predictions are estimated by systematically varying ﬁfteen combinations of scales that emerge in the calculation. For the ungroomed jet angularities, the collinear-soft momentum scale for the factorization formalism becomes nonperturbative for [9] l . ; (3) ch jet p R where L is the energy scale at which a becomes nonperturbative, which is taken to be approximately 1 GeV=c. For the groomed jet angularities with b = 0, this soft factorization scale becomes nonpertur- bative for [17] 1a l . z : (4) a;g cut ch jet p R Accordingly, the analytical predictions are expected to describe the data only at sufﬁciently large l , ch jet which depends on p , R, and z . On the other hand, for l = O(1), power corrections in l become cut a a important, and are not included in the NLL calculations. Note that for l > z , the groomed and a;g cut ungroomed predictions are identical at the parton level. For values of l that are sufﬁciently large to be described by SCET, corrections for nonperturbative effects must still be applied in order to compare these parton-level calculations to our charged-hadron- level measurements. These nonperturbative effects include hadronization, the underlying event, and the selection of charged particle jets. Note that track-based observables are IRC-unsafe. In general, nonperturbative track functions can be used to directly compare track-based measurements to analytical calculations [16, 74, 75]; however, such an approach has not yet been developed for jet angularities. Two techniques are used, described in the following subsections, to apply the nonperturbative corrections. 5.1.1 MC-based hadronization correction The ﬁrst technique relies solely on MC generators to transform the parton-level calculations into the ﬁnal predictions at the charged-hadron level. Two response matrices are constructed, one using PYTHIA 8.244 and the other using Herwig7, which map the jet angularity distributions from jets reconstructed at the ﬁnal-state parton level (after the parton shower) to those from jets reconstructed at the charged-hadron level. This is done by requiring a unique geometrical match between the parton and charged-hadron-level jets of DR < R=2. The PYTHIA8 simulation uses the default Monash 2013 tune, which is tuned to both e e and pp data [66], with the only change being that the minimum shower p (TimeShower:pTmin) is set to 0.2 GeV=c, one half of its default value, in order to better match the NLL predictions at parton level. Herwig7 is also run with the default tune [76]. The response matrix generated with both MC parton jet parton jet ch jet simulations is 4D, mapping p and l to p and l . a;truth b T;truth 13 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet Since the NLL predictions are generated as normalized distributions, each p interval is ﬁrst scaled by jet a value corresponding to the inclusive p cross section, calculated at Next-to-Leading Order (NLO) with NLL resummation of logarithms in the jet radius [77]. The 4D response matrix discussed above is then jet multiplied by these scaled 2D NLL predictions (in both p , ranging from 10 to 200 GeV=c, and l ) to obtain the theoretical predictions at charged-hadron level. To propagate the systematic uncertainty on the original NLL calculations, this “folding" procedure is performed individually for each of ﬁfteen scale variations, from which a total systematic uncertainty is constructed from the minimum and maximum variation in each interval. Note that this procedure introduces a model-dependence to the comparison, and in fact signiﬁcantly reduces the magnitude of the systematic uncertainties compared to the parton level; the repetition of this procedure with both PYTHIA8 and Herwig7 is meant to estimate the size of this model dependence. Although the perturbative accuracy of the MC generators is not clear, by restricting these comparisons ch jet to p > 60 GeV=c, there is adequate matching between the analytical calculations and the MC gen- erators’ ﬁnal-state parton-level predictions to employ the nonperturbative corrections via this mapping procedure. After the folding step, an additional bin-by-bin correction is applied for multi-parton inter- actions in the underlying event using the respective event generator. More speciﬁcally, a ratio is created between the 2D jet angularity distributions generated with multi-parton interactions on versus off at the charged-hadron level, which is then multiplied bin-by-bin by the folded distributions. In all cases, the corrections performed with PYTHIA and those with Herwig are similar in magnitude, indicating that this correction procedure is reasonable. Figure 5 shows comparisons of the measured ungroomed jet angularities to the folded theoretical predic- ch jet tions for 60 < p < 80 GeV=c, for both R = 0:2 (top) and R = 0:4 (bottom) and for a = 1:5 (left), 2 (middle), and 3 (right). Figure 6 shows the corresponding comparisons for the groomed jet angularities. ch jet The comparisons for 80 < p < 100 GeV=c are shown in Appendix A. Predictions for the a = 1 dis- tributions are not currently available due to enhanced sensitivity to soft-recoil, which requires a different factorization [22]. A dashed vertical line is drawn as a rough estimate for the division of perturbative- and nonperturbative- ch jet dominated regions, via Eq. 3 or Eq. 4 with L = 1 GeV=c and the mean p for each interval. Note that the transition from values of l which are dominated by perturbative versus nonperturbative physics is actually smooth, and this vertical line is merely intended as a visual guide. The nonperturbative- NP dominated region of the jet angularities is denoted as l . Since the integral for all of the distributions in Fig. 1 through Fig. 4 is ﬁxed at unity by construction, it is important to note that disagreement in the nonperturbative-dominated region induces disagreement in the perturbative-dominated region. Discrepancy in the nonperturbative region is expected due to the divergence of a and the corresponding signiﬁcance of higher-order terms in the perturbative expansion — and will necessarily induce disagreement in the perturbative-dominated region. Accordingly, for these NP theoretical comparisons, the distributions are normalized such that the integral above l is unity. 5.1.2 Shape function based correction An alternate correction technique is also used, which employs a nonperturbative shape function F(k) [14, 20, 21] to correct for the effects caused by hadronization and the underlying event. The shape function is deﬁned as 4k 2k F(k) = exp ; (5) W W where k is a momentum scale parameter of the shape function, and W is described by a single parameter W = O(1 GeV=c) obeying the scaling relation W = W=(a 1); (6) 14 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet NP ALICE 18 18 18 λ ≤ Λ / (p R) Data pp s = 5.02 TeV Syst. uncertainty 16 16 charged jets anti-k NLL' ⊗ PYTHIA8 R = 0.2 |η | < 0.7 14 14 jet ch jet NLL' ⊗ Herwig7 60 < p < 80 GeV/c 12 12 12 α = 1.5 α = 2 (×0.3) α = 3 (×0.12) 10 10 8 8 8 6 6 4 4 2 2 2 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 10 0.30 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.1 0.2 λ λ λ α α α 24 24 24 ch jet NP ALICE λ ≤ Λ / (p R) Data 22 22 pp s = 5.02 TeV Syst. uncertainty 20 20 20 charged jets anti-k NLL' ⊗ PYTHIA8 R = 0.4 |η | < 0.5 18 18 18 jet ch jet NLL' ⊗ Herwig7 16 60 < p < 80 GeV/c 16 16 14 14 α = 1.5 α = 2 (×0.65) α = 3 (×0.27) 12 12 10 10 8 8 8 6 6 6 4 4 2 2 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure 5: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions with MC hadronization corrections in the range 60 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α 1-α ALICE λ ≤ z (λ ) Data α ,g cut α pp s = 5.02 TeV Syst. uncertainty charged jets anti-k NLL' ⊗ PYTHIA8 3 3 3 10 10 R = 0.2 |η | < 0.7 Soft Drop: z = 0.2, β = 0 cut jet ch jet NLL' ⊗ Herwig7 60 < p < 80 GeV/c 2 2 2 10 10 α = 1.5 α = 2 α = 3 10 10 1 1 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g NP NP α 1-α ALICE λ ≤ z (λ ) Data α ,g cut α pp s = 5.02 TeV Syst. uncertainty 3 charged jets anti-k 3 NLL' ⊗ PYTHIA8 3 10 T 10 10 R = 0.4 |η | < 0.5 Soft Drop: z = 0.2, β = 0 cut jet ch jet NLL' ⊗ Herwig7 60 < p < 80 GeV/c 2 2 2 10 10 α = 1.5 α = 2 α = 3 10 10 1 1 1 10 0 0.2 0.4 10 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g Figure 6: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions with MC hadronization corrections in the range 60 l (to the right of a;g a;g the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration and expected to hold universally for hadronization corrections (but not necessarily for underlying event corrections). To correct the parton-level calculations to the hadron level, this shape function is convolved with the perturbative (parton level) jet angularity distribution via numerical integration over argument k ds ds pert shift = F(k) l l (k) dk; (7) jet jet dp dl dp dl a a T T shift where the shift term l (k) is either [17, 21]: k k shift 1a l (k) = (ungroomed), or z (groomed, with b = 0). (8) a cut jet jet p R p R T T shift The limits of the integral are thus given by the values of k for which the argument l l (k) is between 0 and 1. Since the nonperturbative parameter W is not calculable within perturbation theory, four values (0.2, 0.4, 0.8, and 2 GeV=c) are chosen to observe the different shifting effects. These distributions are then corrected once more using a similar PYTHIA8 folding procedure as described above to account for the effects of only reconstructing charged-particle jets. This correction is dominated by a shift and jet smearing along the p axis. The comparisons to the ungroomed predictions are shown in Fig. 7, and the groomed predictions are shown in Fig. 8. The shape function approach, speciﬁcally the scaling given in Eq. 6, is not fully justiﬁed in the groomed case [78, 79]; nevertheless, reasonable agreement is observed. Since this shape convolution does not require matching to MC at the parton level, the comparisons are extended to the ch jet 40 < p < 60 GeV=c interval, but below this the perturbative accuracy of the parton-level predictions ch jet ch jet is insufﬁcient for rigorous comparisons. The comparisons for 40 < p < 60 GeV=c and 80 < p < T T 100 GeV=c are shown in Appendix A. 5.2 Discussion The l distributions are generally consistent with the calculations within uncertainties when l is suf- a a jet ﬁciently large to be in the pQCD regime. This holds approximately independent of a , R, and p , and whether or not the jets are groomed. In some distributions, however, particularly for R = 0:4, modest disagreement is observed at large l . This disagreement cannot be unambiguously associated with a particular value of l due to the self-normalization of the observable, but rather demonstrates an overall inconsistency in the shape of the distribution. This disagreement could be caused by the unaccounted power corrections in l , or other effects — and suggests a need for further theoretical investigation. Nev- ertheless, the overall agreement with the perturbative calculations is striking, given the low-to-moderate jet p and R considered. NP For a = 1:5, the majority of the distributions can be described perturbatively, as l is conﬁned towards NP the left-hand side of the distributions. As a increases to a = 3, the inﬂuence of the l region grows, and the ungroomed distributions become strongly nonperturbative. Similarly, as R increases from R = 0:2 to ch jet R = 0:4, or as p increases, the size of the perturbative region increases. In the nonperturbative region NP l < l , the l distributions diverge from the calculations. This is expected, since the perturbative a a NP approximations break down for l < l , and neither the MC or shape function corrections are neces- sarily expected to fully correct for missing physics at higher orders or for nonperturbative coupling. In some distributions, the shape-function-based correction is sometimes able to describe the data partially into the nonperturbative regime for suitable values of W. While the overall level of agreement is comparable in both the ungroomed and groomed cases, grooming widens the pQCD regime, as indicated by the location of the dashed blue line in Figures [5-8]. On the other hand, grooming shifts the distributions themselves to signiﬁcantly smaller values of l . Neverthe- less, this highlights the potential beneﬁt of grooming in heavy-ion collisions in order to retain a larger degree of perturbative control in addition to controlling effects of the underlying event. 17 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet NP Data ALICE 20 20 20 λ ≤ Λ / (p R) Ω=0.2 T pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP 18 18 18 Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 16 16 R = 0.2 |η | < 0.7 NLL' ⊗ F ⊗ PYTHIA8 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 14 14 60 < p < 80 GeV/c NP 12 12 α = 1.5 α = 2 (×0.3) α = 3 (×0.12) 10 10 10 8 8 8 6 6 4 4 2 2 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 10 0.30 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.1 0.2 λ λ λ α α α ch jet NP Data ALICE λ ≤ Λ / (p R) 30 30 30 α Ω=0.2 T pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP 25 25 Ω=0.8 R = 0.4 |η | < 0.5 NLL' ⊗ F ⊗ PYTHIA8 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 60 < p < 80 GeV/c NP 20 20 20 α = 1.5 α = 2 (×0.65) α = 3 (×0.27) 15 15 15 10 10 5 5 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure 7: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions using F(k) convolution in the range 60 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α 4 4 Data 4 1-α ALICE 10 10 λ ≤ z (λ ) α ,g cut α Ω=0.2 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 3 R = 0.2 |η | < 0.7 3 3 Soft Drop: z = 0.2, β = 0 NLL' ⊗ F ⊗ PYTHIA8 cut 10 NP 10 jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 60 < p < 80 GeV/c NP 2 α = 1.5 2 α = 2 2 α = 3 10 10 10 10 10 1 1 1 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g NP NP α Data 1-α ALICE λ ≤ z (λ ) α ,g cut α Ω=0.2 4 4 4 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 10 10 10 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.4 |η | < 0.5 NLL' ⊗ F ⊗ PYTHIA8 Soft Drop: z = 0.2, β = 0 cut NP 3 3 3 jet 10 10 Ω=2.0 10 ch jet NLL' ⊗ F ⊗ PYTHIA8 60 < p < 80 GeV/c NP 2 α = 1.5 2 α = 2 2 α = 3 10 10 10 10 10 1 1 10 0 0.2 0.4 10 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g Figure 8: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions using F(k) convolution in the range 60 l (to the right of the dashed a;g a;g vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration The performance of the two nonperturbative correction methods — based entirely on MC generators, or on shape functions — are comparable in the perturbative regime. Comparing different values of W for the ungroomed case, where Eq. 6 is justiﬁed, there is in many cases only a small difference between the calculations with W = 0:2, 0.4, and 0.8 GeV=c. However, for a = 1:5 and a = 2, larger values of W (W = 2 GeV=c) appear to have more tension with the data in the perturbative regime than smaller values. For a = 3, the perturbative region is too small to make any clear statement. One must bear in NP mind, however, that l is only a rough characterization of the regime of validity of the perturbative calculation. Consequently, it is unknown whether this disagreement is due to the value of W or due to the breakdown of the perturbative calculation. For smaller values of W (e.g. W = 0:2 or 0:4 GeV=c), the predicted scaling of Eq. 6 is consistent with the data. Note that the value of W which describes the data is O(1) as expected for hadronization corrections. These smaller values contrast with a previous jet result of W = 3:5 GeV=c for the ungroomed mass of R = 0:4 jets at 200 < p < 300 GeV=c [80], suggesting that the underlying event contribution to W, which is not expected to obey the scaling of jet Eq. 6, may be modiﬁed by jets measured at different p or by the choice to reconstruct jets using only charged-particle tracks. No signiﬁcant R-dependence is observed in the scaling behavior in this analysis, suggesting that any scaling-breaking underlying event contributions, when also combined with hadronization corrections, are small for R = 0:2 and 0.4. 6 Conclusion The generalized jet angularities are reported both with and without Soft Drop grooming, l and l , a;g a respectively, for charged-particle jets in pp collisions at s = 5:02 TeV with the ALICE detector. This measurement of both the ungroomed and, for the ﬁrst time, the groomed jet angularities provides con- straints on models and captures the interplay between perturbative and nonperturbative effects in QCD. Systematic variations of the contributions from collinear and soft radiation of the shower, captured within a given R, are provided by measuring the jet angularities for a selection of a parameters. These results consequently provide rigorous tests of pQCD calculations. The theoretical predictions at NLL in SCET show an overall agreement with the data for jets with values of l in the perturbative regime delimited by a collinear-soft momentum scale in the factorization framework of about 1 GeV=c. The calculations, after accounting for nonperturbative effects by two different methods, are compatible within about 20% or better with the data in the perturbative region for all explored values of R and a . However, larger deviations of up to about 50% are observed in the tails of some distributions, suggesting a need for further theoretical study. By making comparisons solely in the perburbatively-dominated regime, consistency is seen with a predicted universal scaling of the nonperturbative shape function parameter W with value W < 1. A clear breakdown of the agreement is observed for small l , where the perturbative calculation is expected to fail. Such nonperturbative effects include soft splittings and hadronization, and these effects dominate over signiﬁcant regions of the phase space of moderate and low-energy jets. This is corroborated by the comparison of the measured groomed jet angularities to the equivalent theoretical calculations, which demonstrate a wider range of agreement with the perturbative calculations. These comparisons provide critical guidance for measurements in high-energy heavy-ion collisions where the internal structure of jets may undergo modiﬁcations via scatterings of jet fragments with the hot and dense QCD medium. Our measurements demonstrate that any comparison to pQCD must also con- sider the regimes of l and l that are controlled by perturbative processes as opposed to those that a a;g are dominated by nonperturbative processes. This provides guidance for the selections of a , R, and ch jet p , and indicates the importance of capturing the complete spectrum of processes (perturbative and non-perturbative) in theory calculations attempting to explain jet quenching. These measurements further highlight that disagreement between theoretical predictions and data in the 20 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration nonperturbative regime will necessarily induce disagreement in the perturbative regime, when in fact the perturbative accuracy of predictions should only be scrutinized within the perturbative regime. In practice, these measurements give a clear indication that careful inspection is needed when interpreting measurements of jet substructure based on models of jet quenching in heavy-ion collisions for observ- ables including the jet angularity and the jet mass. Future measurements will beneﬁt from the provided guidance demonstrating not only the agreement of jet angularities with pQCD calculations in the per- ch jet turbative regime but also on selecting on jet angularity differentially with a , R, and p in order to maximize theoretical control and interpretation of the perturbative and nonpertubative regimes of jet substructure observables. Acknowledgements We gratefully acknowledge Kyle Lee and Felix Ringer for providing theoretical predictions, and for valuable discussions regarding the comparison of these predictions to our measurements. The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable con- tributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics In- stitute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and National- stiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Cientíﬁco e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientiﬁque (CNRS), France; Bundesmin- isterium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Ofﬁce, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientiﬁc and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tec- nología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Coun- cil of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontiﬁcia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technol- 21 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ogy Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientiﬁc Research, Institute of Atomic Physics and Ministry of Research and Innova- tion and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Rus- sian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technol- ogy (SUT), National Science and Technology Development Agency (NSDTA) and Ofﬁce of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Ofﬁce of Nuclear Physics (DOE NP), United States of America. 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W. Stewart, V. Vaidya, and L. Zoppi, “EFT for Soft Drop Double Differential Cross Section”, JHEP 04 (Apr, 2021) 32, arXiv:2012.15568 [hep-ph]. [80] Z.-B. Kang, K. Lee, X. Liu, and F. Ringer, “The groomed and ungroomed jet mass distribution for inclusive jet production at the LHC”, JHEP 10 (Oct, 2018) 137, arXiv:1803.03645 [hep-ph]. 27 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration A Additional ﬁgures ch jet Figures A.1, A.2 show the groomed and ungroomed angularities for 80 < p < 100 GeV=c using MC generators to apply hadronization corrections. Figures A.3, A.4 and A.5, A.6 show the groomed and ungroomed angularities using the shape function ch jet ch jet to apply hadronization corrections, for 40 < p < 60 GeV=c and 80 < p < 100 GeV=c. T T 25 25 ch jet NP ALICE λ ≤ Λ / (p R) Data pp s = 5.02 TeV Syst. uncertainty charged jets anti-k NLL' ⊗ PYTHIA8 20 20 R = 0.2 |η | < 0.7 jet α = 3 (×0.035) NLL' ⊗ Herwig7 ch jet 80 < p < 100 GeV/c 15 15 15 α = 1.5 α = 2 (×0.42) 10 10 5 5 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 0.1 10 10 10 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 λ λ λ α α α ch jet NP ALICE λ ≤ Λ / (p R) 20 Data 20 20 α pp s = 5.02 TeV Syst. uncertainty 18 18 charged jets anti-k NLL' ⊗ PYTHIA8 16 R = 0.4 |η | < 0.5 16 16 jet NLL' ⊗ Herwig7 ch jet 80 < p < 100 GeV/c 14 14 14 12 12 12 α = 1.5 α = 2 (×0.33) α = 3 (×0.15) 10 10 8 8 6 6 4 4 2 2 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 10 10 10 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure A.1: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions with MC hadronization corrections in the range 80 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α 1-α ALICE λ ≤ z (λ ) Data α ,g cut α pp s = 5.02 TeV 4 4 4 10 10 10 Syst. uncertainty charged jets anti-k NLL' ⊗ PYTHIA8 R = 0.2 |η | < 0.7 Soft Drop: z = 0.2, β = 0 cut jet ch jet NLL' ⊗ Herwig7 80 < p < 100 GeV/c 3 3 3 10 10 10 α = 1.5 α = 2 α = 3 2 2 2 10 10 10 10 10 0 0.1 0.2 0.310 0 0.1 0.2 10 0 0.05 0.1 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 λ λ λ α ,g α ,g α ,g NP NP α 1-α ALICE λ ≤ z (λ ) Data α ,g cut α pp s = 5.02 TeV Syst. uncertainty 3 charged jets anti-k 3 NLL' ⊗ PYTHIA8 3 T 10 10 R = 0.4 |η | < 0.5 Soft Drop: z = 0.2, β = 0 cut jet ch jet NLL' ⊗ Herwig7 80 < p < 100 GeV/c 2 2 2 10 10 α = 1.5 α = 2 α = 3 10 10 1 1 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.310 0 0.05 0.1 0.15 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.05 0.1 0.15 λ λ λ α ,g α ,g α ,g Figure A.2: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions with MC hadronization corrections in the range 80 l (to the right of a;g a;g the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 24 24 ch jet NP Data ALICE λ ≤ Λ / (p R) Ω=0.2 T 22 22 22 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 20 20 20 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.2 |η | < 0.7 18 NLL' ⊗ F ⊗ PYTHIA8 18 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 16 16 16 40 < p < 60 GeV/c NP 14 14 14 α = 1.5 α = 2 (×0.45) α = 3 (×0.06) 12 12 10 10 8 8 6 6 6 4 4 2 2 10 0 0.2 0.4 10 0 0.1 0.2 0.3 10 0.40 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α 24 24 ch jet NP Data ALICE λ ≤ Λ / (p R) 22 Ω=0.2 22 T pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 20 20 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 18 R = 0.4 |η | < 0.5 18 NLL' ⊗ F ⊗ PYTHIA8 18 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 16 16 40 < p < 60 GeV/c NP 14 14 α = 1.5 α = 2 (×0.45) α = 3 (×0.25) 12 12 10 10 8 8 8 6 6 4 4 4 2 2 10 0 0.2 0.4 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.3 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure A.3: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions using F(k) convolution in the range 40 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet NP Data ALICE λ ≤ Λ / (p R) Ω=0.2 T pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP 25 25 25 Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.2 |η | < 0.7 NLL' ⊗ F ⊗ PYTHIA8 NP jet α = 3 (×0.035) Ω=2.0 20 ch jet 20 20 NLL' ⊗ F ⊗ PYTHIA8 80 < p < 100 GeV/c NP α = 1.5 α = 2 (×0.42) 15 15 10 10 10 5 5 10 0 0.1 0.2 0.310 0 0.1 0.2 10 0 0.05 0.1 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 λ λ λ α α α 22 22 ch jet 22 NP Data ALICE λ ≤ Λ / (p R) Ω=0.2 T pp s = 5.02 TeV 20 NLL' ⊗ F ⊗ PYTHIA8 20 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP 18 18 18 Ω=0.8 R = 0.4 |η | < 0.5 NLL' ⊗ F ⊗ PYTHIA8 NP jet 16 16 16 Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 80 < p < 100 GeV/c NP 14 14 α = 1.5 12 α = 2 (×0.33) 12 α = 3 (×0.15) 10 10 10 8 8 8 6 6 6 4 4 2 2 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.3 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure A.4: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions using F(k) convolution in the range 80 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α 4 4 Data 4 1-α ALICE 10 10 10 λ ≤ z (λ ) α ,g cut α Ω=0.2 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 3 3 3 R = 0.2 |η | < 0.7 Soft Drop: z = 0.2, β = 0 NLL' ⊗ F ⊗ PYTHIA8 10 10 cut 10 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 40 < p < 60 GeV/c NP 2 2 2 α = 1.5 α = 2 α = 3 10 10 10 10 10 1 1 10 0 0.2 0.4 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.3 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0.4 0 0.1 0.2 λ λ λ α ,g α ,g α ,g NP NP α Data 1-α ALICE λ ≤ z (λ ) 4 4 4 α ,g cut α 10 Ω=0.2 10 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 3 R = 0.4 |η | < 0.5 3 NLL' ⊗ F ⊗ PYTHIA8 3 Soft Drop: z = 0.2, β = 0 cut 10 NP 10 jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 40 < p < 60 GeV/c NP 2 2 2 10 α = 1.5 10 α = 2 10 α = 3 10 10 10 1 1 10 0 0.2 0.4 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.3 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g Figure A.5: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions using F(k) convolution in the range 40 l (to the right of the dashed a;g a;g vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α Data 1-α ALICE λ ≤ z (λ ) α ,g cut α Ω=0.2 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 4 4 NP 4 10 10 Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.2 |η | < 0.7 Soft Drop: z = 0.2, β = 0 NLL' ⊗ F ⊗ PYTHIA8 cut NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 3 3 3 80 < p < 100 GeV/c NP 10 10 10 α = 1.5 α = 2 α = 3 2 2 2 10 10 10 10 10 0 0.1 0.2 0.310 0 0.1 0.2 10 0 0.05 0.1 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 λ λ λ α ,g α ,g α ,g NP NP α Data 1-α ALICE λ ≤ z (λ ) α ,g cut α Ω=0.2 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 4 4 4 NP 10 10 10 Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.4 |η | < 0.5 NLL' ⊗ F ⊗ PYTHIA8 Soft Drop: z = 0.2, β = 0 cut NP jet 3 3 3 Ω=2.0 ch jet 10 10 10 NLL' ⊗ F ⊗ PYTHIA8 80 < p < 100 GeV/c NP α = 1.5 α = 2 α = 3 2 2 2 10 10 10 10 10 10 1 1 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.310 0 0.05 0.1 0.15 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.05 0.1 0.15 λ λ λ α ,g α ,g α ,g Figure A.6: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions using F(k) convolution in the range 80 l (to the right of the dashed a;g a;g vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration B The ALICE Collaboration 143 98 76 35 31 55 143 S. Acharya , D. Adamová , A. Adler , G. Aglieri Rinella , M. Agnello , N. Agrawal , Z. Ahammed , 16 78 39 52 95 110 16;41 S. Ahmad , S.U. Ahn , I. Ahuja , Z. Akbar , A. Akindinov , M. Al-Turany , S.N. Alam , 91 61 7 73 16 14 26 D. Aleksandrov , B. Alessandro , H.M. Alfanda , R. Alfaro Molina , B. Ali , Y. Ali , A. Alici , 127 35 21 70 21 115 7 N. Alizadehvandchali , A. Alkin , J. Alme , T. Alt , L. Altenkamper , I. Altsybeev , M.N. Anaam , 49 93 146 35 107 58 55 C. Andrei , D. Andreou , A. Andronic , M. Angeletti , V. Anguelov , F. Antinori , P. Antonioli , 16 82 117 70 26 61 20 C. Anuj , N. Apadula , L. Aphecetche , H. Appelshäuser , S. Arcelli , R. Arnaldi , I.C. Arsene , 148;107 35 110 80 16 57 42 M. Arslandok , A. Augustinus , R. Averbeck , S. Aziz , M.D. Azmi , A. Badalà , Y.W. Baek , 131;110 70 51 104 31 140 2 44 X. Bai , R. Bailhache , Y. Bailung , R. Bala , A. Balbino , A. Baldisseri , B. Balis , M. Ball , 4 27 108 87 147 97 137 D. Banerjee , R. Barbera , L. Barioglio , M. Barlou , G.G. Barnaföldi , L.S. Barnby , V. Barret , 130 35 70 28 137 83 117 77 C. Bartels , K. Barth , E. Bartsch , F. Baruffaldi , N. Bastid , S. Basu , G. Batigne , B. Batyunya , 50 114 92 148 139 146 D. Bauri , J.L. Bazo Alba , I.G. Bearden , C. Beattie , I. Belikov , A.D.C. Bell Hechavarria , 26 127 115 96 71 25 49 F. Bellini , R. Bellwied , S. Belokurova , V. Belyaev , G. Bencedi , S. Beole , A. Bercuci , 101 107 107 69 35 143 104 Y. Berdnikov , A. Berdnikova , L. Bergmann , M.G. Besoiu , L. Betev , P.P. Bhaduri , A. Bhasin , 104 4 43 23 25 53 38 I.R. Bhat , M.A. Bhat , B. Bhattacharjee , P. Bhattacharya , L. Bianchi , N. Bianchi , J. Bielcík ˇ , 98 120 108 147 4 121 91 110 J. Bielcík ˇ ová , J. Biernat , A. Bilandzic , G. Biro , S. Biswas , J.T. Blair , D. Blau , M.B. Blidaru , 70 29;59 99 96 23 63 147 96 C. Blume , G. Boca , F. Bock , A. Bogdanov , S. Boi , J. Bok , L. Boldizsár , A. Bolozdynya , 39 35 142;59 140 84 148 25 70 M. Bombara , P.M. Bond , G. Bonomi , H. Borel , A. Borissov , H. Bossi , E. Botta , L. Bratrud , 110 123 38 109;34 130 111 P. Braun-Munzinger , M. Bregant , M. Broz , G.E. Bruno , M.D. Buckland , D. Budnikov , 70 31 117 116 74;134 14 120 H. Buesching , S. Bufalino , O. Bugnon , P. Buhler , Z. Buthelezi , J.B. Butt , S.A. Bysiak , 28;7 148 110 114 122 46 24 M. Cai , H. Caines , A. Caliva , E. Calvo Villar , J.M.M. Camacho , R.S. Camacho , P. Camerini , 123 35;26 140 140 23 31 F.D.M. Canedo , F. Carnesecchi , R. Caron , J. Castillo Castellanos , E.A.R. Casula , F. Catalano , 77 50 143 35 130 143 C. Ceballos Sanchez , P. Chakraborty , S. Chandra , S. Chapeland , M. Chartier , S. Chattopadhyay , 112 23 46 7 138 138 S. Chattopadhyay , A. Chauvin , T.G. Chavez , T. Cheng , C. Cheshkov , B. Cheynis , V. Chibante 35 124 63 35 93 92 83 Barroso , D.D. Chinellato , S. Cho , P. Chochula , P. Christakoglou , C.H. Christensen , P. Christiansen , 136 56 26 55 110 II; 55 I; 126 T. Chujo , C. Cicalo , L. Cifarelli , F. Cindolo , M.R. Ciupek , G. Clai , J. Cleymans , 54 113 109;54;34;147 82 35 III; 61 F. Colamaria , J.S. Colburn , D. Colella , A. Collu , M. Colocci , M. Concas , G. Conesa 81 80 24 38 140 99 32 Balbastre , Z. Conesa del Valle , G. Contin , J.G. Contreras , M.L. Coquet , T.M. Cormier , P. Cortese , 125 35 29;59 137 82 71 7 M.R. Cosentino , F. Costa , S. Costanza , P. Crochet , R. Cruz-Torres , E. Cuautle , P. Cui , 99 58 107 69 112 89 4 4 50 L. Cunqueiro , A. Dainese , M.C. Danisch , A. Danu , I. Das , P. Das , P. Das , S. Das , S. Dash , 89 30 54 25 40 23 30 S. De , A. De Caro , G. de Cataldo , L. De Cilladi , J. de Cuveland , A. De Falco , D. De Gruttola , N. De 61 24 30 51 123 144 30 Marco , C. De Martin , S. De Pasquale , S. Deb , H.F. Degenhardt , K.R. Deja , L. Dello Stritto , 25 7 19 34 35 8 126 138;7 S. Delsanto , W. Deng , P. Dhankher , D. Di Bari , A. Di Mauro , R.A. Diaz , T. Dietel , Y. Ding , 35 19 21 65 63 69 70 20 R. Divià , D.U. Dixit , Ø. Djuvsland , U. Dmitrieva , J. Do , A. Dobrin , B. Dönigus , O. Dordic , 143 110;93 103 89 137 13 146 A.K. Dubey , A. Dubla , S. Dudi , M. Dukhishyam , P. Dupieux , N. Dzalaiova , T.M. Eder , 99 21 70 54 117 26 102 R.J. Ehlers , V.N. Eikeland , F. Eisenhut , D. Elia , B. Erazmus , F. Ercolessi , F. Erhardt , 115 21 80 35 113 94 108 A. Erokhin , M.R. Ersdal , B. Espagnon , G. Eulisse , D. Evans , S. Evdokimov , L. Fabbietti , 28 81 7 53 99 31 61 115 M. Faggin , J. Faivre , F. Fan , A. Fantoni , M. Fasel , P. Fecchio , A. Feliciello , G. Feoﬁlov , 46 140 25 107 120 111 A. Fernández Téllez , A. Ferrero , A. Ferretti , V.J.G. Feuillard , J. Figiel , S. Filchagin , 65 56;21 35;109 127 121 74 110 D. Finogeev , F.M. Fionda , G. Fiorenza , F. Flor , A.N. Flores , S. Foertsch , P. Foka , 91 62 147 35 30 81 65 92 S. Fokin , E. Fragiacomo , E. Frajna , U. Fuchs , N. Funicello , C. Furget , A. Furs , J.J. Gaardhøje , 25 114 139 122 87 110 46 M. Gagliardi , A.M. Gago , A. Gal , C.D. Galvan , P. Ganoti , C. Garabatos , J.R.A. Garcia , 10 117 35 90 146 110 121 E. Garcia-Solis , K. Garg , C. Gargiulo , A. Garibli , K. Garner , P. Gasik , E.F. Gauger , 129 72 117 143 4 26 53 A. Gautam , M.B. Gay Ducati , M. Germain , P. Ghosh , S.K. Ghosh , M. Giacalone , P. Gianotti , 110;61 28 140 107 85 145 P. Giubellino , P. Giubilato , A.M.C. Glaenzer , P. Glässel , D.J.Q. Goh , V. Gonzalez , 73 40 2 120 36 73 L.H. González-Trueba , S. Gorbunov , M. Gorgon , L. Görlich , S. Gotovac , V. Grabski , 144 82 64 35 96 I; 1 77;1 L.K. Graczykowski , L. Greiner , A. Grelli , C. Grigoras , V. Grigoriev , A. Grigoryan , S. Grigoryan , 21 35;61 35 110 124 81 O.S. Groettvik , F. Grosa , J.F. Grosse-Oetringhaus , R. Grosso , G.G. Guardiano , R. Guernane , 117 92 135 7 104 104 46 147 M. Guilbaud , K. Gulbrandsen , T. Gunji , W. Guo , A. Gupta , R. Gupta , S.P. Guzman , L. Gyulai , 110 80 70 85 147 7 121 M.K. Habib , C. Hadjidakis , G. Halimoglu , H. Hamagaki , G. Hamar , M. Hamid , R. Hannigan , 144;89 110 148 10 35 99 M.R. Haque , A. Harlenderova , J.W. Harris , A. Harton , J.A. Hasenbichler , H. Hassan , 55 44 148 135 108 110 37 D. Hatzifotiadou , P. Hauer , L.B. Havener , S. Hayashi , S.T. Heckel , E. Hellbär , H. Helstrup , 38 46 9 146 37 35 T. Herman , E.G. Hernandez , G. Herrera Corral , F. Herrmann , K.F. Hetland , H. Hillemanns , 130 139 64 93 146 149 38 C. Hills , B. Hippolyte , B. Hofman , B. Hohlweger , J. Honermann , G.H. Hong , D. Horak , 110 2 15 7 35 133 70 100 S. Hornung , A. Horzyk , R. Hosokawa , Y. Hou , P. Hristov , C. Hughes , P. Huhn , T.J. Humanic , 112 146 127 40 35;130 111 14 136 H. Hushnud , L.A. Husova , A. Hutson , D. Hutter , J.P. Iddon , R. Ilkaev , H. Ilyas , M. Inaba , 34 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 35 91 38;98 112 110 101 94 G.M. Innocenti , M. Ippolitov , A. Isakov , M.S. Islam , M. Ivanov , V. Ivanov , V. Izucheev , 2 82 35 82 119 119 64 M. Jablonski , B. Jacak , N. Jacazio , P.M. Jacobs , S. Jadlovska , J. Jadlovsky , S. Jaelani , 124;123 144 104 144 76 102 113 C. Jahnke , M.J. Jakubowska , A. Jalotra , M.A. Janik , T. Janson , M. Jercic , O. Jevons , 71 99;146 113 35;110 70 70 35 A.A.P. Jimenez , F. Jonas , P.G. Jones , J.M. Jowett , J. Jung , M. Jung , A. Junique , 113 118 66 35 96 7 79 102 A. Jusko , J. Kaewjai , P. Kalinak , A. Kalweit , V. Kaplin , S. Kar , A. Karasu Uysal , D. Karatovic , 65 65 144 65 91 76 O. Karavichev , T. Karavicheva , P. Karczmarczyk , E. Karpechev , A. Kazantsev , U. Kebschull , 48 64 35 44 93 7 16 R. Keidel , D.L.D. Keijdener , M. Keil , B. Ketzer , Z. Khabanova , A.M. Khan , S. Khan , 101 94 16 120 37 17;63 17 128 A. Khanzadeev , Y. Kharlov , A. Khatun , A. Khuntia , B. Kileng , B. Kim , C. Kim , D.J. Kim , 75 149 42 107 149 75 107 18 149 70 E.J. Kim , J. Kim , J.S. Kim , J. Kim , J. Kim , J. Kim , M. Kim , S. Kim , T. Kim , S. Kirsch , 40 95 144 2 6 35 82 146 I. Kisel , S. Kiselev , A. Kisiel , J.P. Kitowski , J.L. Klay , J. Klein , S. Klein , C. Klein-Bösing , 70 108 35 127 118 107 110 M. Kleiner , T. Klemenz , A. Kluge , A.G. Knospe , C. Kobdaj , M.K. Köhler , T. Kollegger , 77 96 94 70 108 35;2 A. Kondratyev , N. Kondratyeva , E. Kondratyuk , J. Konig , S.A. Konigstorfer , P.J. Konopka , 144 2 119 98 88 115 120 G. Kornakov , S.D. Koryciak , L. Koska , A. Kotliarov , O. Kovalenko , V. Kovalenko , M. Kowalski , 66 39 110 113;66 98 38 107 I. Králik , A. Kravcáková , L. Kreis , M. Krivda , F. Krizek , K. Krizkova Gajdosova , M. Kroesen , 70 101 40 35 139 93 136 M. Krüger , E. Kryshen , M. Krzewicki , V. Kucera , C. Kuhn , P.G. Kuijer , T. Kumaoka , 143 103 103 35;89 88 65 65 D. Kumar , L. Kumar , N. Kumar , S. Kundu , P. Kurashvili , A. Kurepin , A.B. Kurepin , 111 98 113 63 63 149 40 A. Kuryakin , S. Kushpil , J. Kvapil , M.J. Kweon , J.Y. Kwon , Y. Kwon , S.L. La Pointe , P. La 27 82 118 35 132 35 35;53 35 Rocca , Y.S. Lai , A. Lakrathok , M. Lamanna , R. Langoy , K. Lapidus , P. Larionov , E. Laudi , 35;108 38 115 142;24;59 40 97 L. Lautner , R. Lavicka , T. Lazareva , R. Lea , J. Lehrbach , R.C. Lemmon , I. León 122 19 35;108 147 11 7 132 113 17 Monzón , E.D. Lesser , M. Lettrich , P. Lévai , X. Li , X.L. Li , J. Lien , R. Lietava , B. Lim , 17 40 49 110 19 7 130 21 S.H. Lim , V. Lindenstruth , A. Lindner , C. Lippmann , A. Liu , D.H. Liu , J. Liu , I.M. Lofnes , 96 99 36 107 137 8 146 V. Loginov , C. Loizides , P. Loncar , J.A. Lopez , X. Lopez , E. López Torres , J.R. Luhder , 28 62 41 65 35 44 139 M. Lunardon , G. Luparello , Y.G. Ma , A. Maevskaya , M. Mager , T. Mahmoud , A. Maire , 101 104 20 IV; 77 95 51 110 M. Malaev , N.M. Malik , Q.W. Malik , L. Malinina , D. Mal’Kevich , N. Mallick , P. Malzacher , 33;57 91 137 54 7 68 24 G. Mandaglio , V. Manko , F. Manso , V. Manzari , Y. Mao , J. Mareš , G.V. Margagliotti , 55 110 121 70 107 35 127 A. Margotti , A. Marín , C. Markert , M. Marquard , N.A. Martin , P. Martinengo , J.L. Martinez , 46 117 110 25 56 80 M.I. Martínez , G. Martínez García , S. Masciocchi , M. Masera , A. Masoni , L. Massacrier , 141;54 108 83 123 120 120 A. Mastroserio , A.M. Mathis , O. Matonoha , P.F.T. Matuoka , A. Matyja , C. Mayer , 35 25 35 I; 60 134 70 22 A.L. Mazuecos , F. Mazzaschi , M. Mazzilli , M.A. Mazzoni , J.E. Mdhluli , A.F. Mechler , F. Meddi , 65 73 116;30 127 13 126;74 Y. Melikyan , A. Menchaca-Rocha , E. Meninno , A.S. Menon , M. Meres , S. Mhlanga , 136 61;25 138 108 77;95 147 Y. Miake , L. Micheletti , L.C. Migliorin , D.L. Mihaylov , K. Mikhaylov , A.N. Mishra , 110 4 64 89 V; 16 45 D. Misk ´ owiec , A. Modak , A.P. Mohanty , B. Mohanty , M. Mohisin Khan , M.A. Molander , 92 108 146 46 65 35 Z. Moravcova , C. Mordasini , D.A. Moreira De Godoy , L.A.P. Moreno , I. Morozov , A. Morsch , 35 53 36 146 143 82 23 T. Mrnjavac , V. Muccifora , E. Mudnic , D. Mühlheim , S. Muhuri , J.D. Mulligan , A. Mulliri , 123 70 135 126 35 66 144 M.G. Munhoz , R.H. Munzer , H. Murakami , S. Murray , L. Musa , J. Musinsky , J.W. Myrcha , 134;50 88 50 55 54 14 83 107 B. Naik , R. Nair , B.K. Nandi , R. Nania , E. Nappi , M.U. Naru , A.F. Nassirpour , A. Nath , 133 20 71 37 40 115 92 C. Nattrass , A. Neagu , L. Nellen , S.V. Nesbo , G. Neskovic , D. Nesterov , B.S. Nielsen , 91 91 101 55 12 77 130 S. Nikolaev , S. Nikulin , V. Nikulin , F. Noferini , S. Noh , P. Nomokonov , J. Norman , 136 144 91 21 85 83 96 N. Novitzky , P. Nowakowski , A. Nyanin , J. Nystrand , M. Ogino , A. Ohlson , V.A. Okorokov , 144 133 148 128 61 J. Oleniacz , A.C. Oliveira Da Silva , M.H. Oliver , A. Onnerstad , C. Oppedisano , A. Ortiz 71 47 83 120 85 107 50 Velasquez , T. Osako , A. Oskarsson , J. Otwinowski , K. Oyama , Y. Pachmayer , S. Padhan , 142;59 71 54 145 140 143 63 128 D. Pagano , G. Paic ´ , A. Palasciano , J. Pan , S. Panebianco , P. Pareek , J. Park , J.E. Parkkila , 127 104;35 23 7 64 7 72 S.P. Pathak , R.N. Patra , B. Paul , H. Pei , T. Peitzmann , X. Peng , L.G. Pereira , H. Pereira Da 140 91 8 140 5 38 49 117;72 Costa , D. Peresunko , G.M. Perez , S. Perrin , Y. Pestov , V. Petrácek ˇ , M. Petrovici , R.P. Pezzi , 62 13 117 55;35 127 27 53 82 S. Piano , M. Pikna , P. Pillot , O. Pinazza , L. Pinsky , C. Pinto , S. Pisano , M. Płoskon ´ , 102 70 99 94 31 102 49 M. Planinic , F. Pliquett , M.G. Poghosyan , B. Polichtchouk , S. Politano , N. Poljak , A. Pop , 137 82 77 4 55 61 S. Porteboeuf-Houssais , J. Porter , V. Pozdniakov , S.K. Prasad , R. Preghenella , F. Prino , 145 65 35 93 25 127 113 C.A. Pruneau , I. Pshenichnov , M. Puccio , S. Qiu , L. Quaglia , R.E. Quishpe , S. Ragoni , 140 32 139 46 34 81 A. Rakotozaﬁndrabe , L. Ramello , F. Rami , S.A.R. Ramirez , A.G.T. Ramos , T.A. Rancien , 105 105 45 51 93 99;133 40 R. Raniwala , S. Raniwala , S.S. Räsänen , R. Rath , I. Ravasenga , K.F. Read , A.R. Redelbach , VI; 88 21 70 35 37 70 39 K. Redlich , A. Rehman , P. Reichelt , F. Reidt , H.A. Reme-ness , R. Renfordt , Z. Rescakova , 107 101 101 83 20 35 27 69 K. Reygers , A. Riabov , V. Riabov , T. Richert , M. Richter , W. Riegler , F. Riggi , C. Ristea , 46 20 94 77 70 35 M. Rodríguez Cahuantzi , K. Røed , R. Rogalev , E. Rogochaya , T.S. Rogoschinski , D. Rohr , 21 46 144 53 33;57 71 58 D. Röhrich , P.F. Rojas , P.S. Rokita , F. Ronchetti , A. Rosano , E.D. Rosas , A. Rossi , 29;59 51 112 50 26 83 24 77 A. Rotondi , A. Roy , P. Roy , S. Roy , N. Rubini , O.V. Rueda , R. Rui , B. Rumyantsev , 2 90 91 101 120 128 144 P.G. Russek , A. Rustamov , E. Ryabinkin , Y. Ryabov , A. Rybicki , H. Rytkonen , W. Rzesa , 35 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 45 117 94 21 38 143 89 50 O.A.M. Saarimaki , R. Sadek , S. Sadovsky , J. Saetre , K. Šafaˇ rík , S.K. Saha , S. Saha , B. Sahoo , 50 51 67 51 67 143 136 104 P. Sahoo , R. Sahoo , S. Sahoo , D. Sahu , P.K. Sahu , J. Saini , S. Sakai , S. Sambyal , I; 101;96 145 143 43 108 148 99;121 V. Samsonov , D. Sarkar , N. Sarkar , P. Sarma , V.M. Sarti , M.H.P. Sas , J. Schambach , 70 49 107 107 110 106 35 H.S. Scheid , C. Schiaua , R. Schicker , A. Schmah , C. Schmidt , H.R. Schmidt , M.O. Schmidt , 106 99;70 133 139 35 139 110 M. Schmidt , N.V. Schmidt , A.R. Schmier , R. Schotter , J. Schukraft , Y. Schutz , K. Schwarz , 110 26 61 15 135 135 110;96 K. Schweda , G. Scioli , E. Scomparin , J.E. Seger , Y. Sekiguchi , D. Sekihata , I. Selyuzhenkov , 139 63 65 108 69 74 65 S. Senyukov , J.J. Seo , D. Serebryakov , L. Šerkšnyte ˙ , A. Sevcenco , T.J. Shaba , A. Shabanov , 117 35 112 94 103 120 104 A. Shabetai , R. Shahoyan , W. Shaikh , A. Shangaraev , A. Sharma , H. Sharma , M. Sharma , 103 104 104 127 47 86 95 N. Sharma , S. Sharma , U. Sharma , O. Sheibani , K. Shigaki , M. Shimomura , S. Shirinkin , 41 91 56 88 123 83 35 Q. Shou , Y. Sibiriak , S. Siddhanta , T. Siemiarczuk , T.F. Silva , D. Silvermyr , G. Simonetti , 108 89 104 51 143 143 112 13 32 B. Singh , R. Singh , R. Singh , R. Singh , V.K. Singh , V. Singhal , T. Sinha , B. Sitar , M. Sitta , 20 107 45 148 64 114 127 T.B. Skaali , G. Skorodumovs , M. Slupecki , N. Smirnov , R.J.M. Snellings , C. Soncco , J. Song , 118 28 133 120 107 69 133 A. Songmoolnak , F. Soramel , S. Sorensen , I. Sputowska , J. Stachel , I. Stan , P.J. Steffanic , 107 117 20 37 93 123 S.F. Stiefelmaier , D. Stocco , I. Storehaug , M.M. Storetvedt , C.P. Stylianidis , A.A.P. Suaide , 47 80 65 35 95 98 104 T. Sugitate , C. Suire , M. Sukhanov , M. Suljic , R. Sultanov , M. Šumbera , V. Sumberia , 52 67 13 13 14 108 137 S. Sumowidagdo , S. Swain , A. Szabo , I. Szarka , U. Tabassam , S.F. Taghavi , G. Taillepied , 124 21 137;7 131 117 49 35 J. Takahashi , G.J. Tambave , S. Tang , Z. Tang , M. Tarhini , M.G. Tarzila , A. Tauro , G. Tejeda 46 35 25 127 3 143 121 Muñoz , A. Telesca , L. Terlizzi , C. Terrevoli , G. Tersimonov , S. Thakur , D. Thomas , 138 65 127 119 70 65 53 R. Tieulent , A. Tikhonov , A.R. Timmins , M. Tkacik , A. Toia , N. Topilskaya , M. Toppi , 19 80 38 33;57 55;71 50 35;28 F. Torales-Acosta , T. Tork , S.R. Torres , A. Triﬁró , S. Tripathy , T. Tripathy , S. Trogolo , 34 3 128 144 38 111 58 G. Trombetta , V. Trubnikov , W.H. Trzaska , T.P. Trzcinski , B.A. Trzeciak , A. Tumkin , R. Turrisi , 20 21 138 59;142 23 39 59;29 61 T.S. Tveter , K. Ullaland , A. Uras , M. Urioni , G.L. Usai , M. Vala , N. Valle , S. Vallero , 64 64 93 93 35 N. van der Kolk , L.V.R. van Doremalen , M. van Leeuwen , R.J.G. van Weelden , P. Vande Vyvre , 147 147 147 46 87 91 D. Varga , Z. Varga , M. Varga-Kofarago , A. Vargas , M. Vasileiou , A. Vasiliev , O. Vázquez 53;108 115 25 46 64 147 64 Doce , V. Vechernin , E. Vercellin , S. Vergara Limón , L. Vermunt , R. Vértesi , M. Verweij , 36 134 113 54 91 30 92 L. Vickovic , Z. Vilakazi , O. Villalobos Baillie , G. Vino , A. Vinogradov , T. Virgili , V. Vislavicius , 77 35 107 95 145 34 35 A. Vodopyanov , B. Volkel , M.A. Völkl , K. Voloshin , S.A. Voloshin , G. Volpe , B. von Haller , 108 119 65 39 21 41 41 116 I. Vorobyev , D. Voscek , N. Vozniuk , J. Vrláková , B. Wagner , C. Wang , D. Wang , M. Weber , 35 35 146 70 20 88 110 A. Wegrzynek , S.C. Wenzel , J.P. Wessels , J. Wiechula , J. Wikne , G. Wilk , J. Wilkinson , 146 107 140 133 121 41 131 7 G.A. Willems , B. Windelband , M. Winn , W.E. Witt , J.R. Wright , W. Wu , Y. Wu , R. Xu , 143 79 47 47 21 47 7 64 A.K. Yadav , S. Yalcin , Y. Yamaguchi , K. Yamakawa , S. Yang , S. Yano , Z. Yin , H. Yokoyama , 17 63 21 107 24 14 35 64 I.-K. Yoo , J.H. Yoon , S. Yuan , A. Yuncu , V. Zaccolo , A. Zaman , C. Zampolli , H.J.C. Zanoli , 35 115 68 111 101 7 41 N. Zardoshti , A. Zarochentsev , P. Závada , N. Zaviyalov , M. Zhalov , B. Zhang , S. Zhang , 7 131 115 11 95 7 92 7;110 X. Zhang , Y. Zhang , V. Zherebchevskii , Y. Zhi , N. Zhigareva , D. Zhou , Y. Zhou , J. Zhu , 7 26 3 142;59 Y. Zhu , A. Zichichi , G. Zinovjev , N. Zurlo Afﬁliation notes Deceased II Also at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India VI Also at: Institute of Theoretical Physics, University of Wroclaw, Poland Collaboration Institutes A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia AGH University of Science and Technology, Cracow, Poland Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India Budker Institute for Nuclear Physics, Novosibirsk, Russia California Polytechnic State University, San Luis Obispo, California, United States 36 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration Central China Normal University, Wuhan, China Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico Chicago State University, Chicago, Illinois, United States China Institute of Atomic Energy, Beijing, China Chungbuk National University, Cheongju, Republic of Korea Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovakia COMSATS University Islamabad, Islamabad, Pakistan Creighton University, Omaha, Nebraska, United States Department of Physics, Aligarh Muslim University, Aligarh, India Department of Physics, Pusan National University, Pusan, Republic of Korea Department of Physics, Sejong University, Seoul, Republic of Korea Department of Physics, University of California, Berkeley, California, United States Department of Physics, University of Oslo, Oslo, Norway Department of Physics and Technology, University of Bergen, Bergen, Norway Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia, Pavia, Italy Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy European Organization for Nuclear Research (CERN), Geneva, Switzerland Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic Faculty of Science, P.J. Šafárik University, Košice, Slovakia Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany Fudan University, Shanghai, China Gangneung-Wonju National University, Gangneung, Republic of Korea Gauhati University, Department of Physics, Guwahati, India Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany Helsinki Institute of Physics (HIP), Helsinki, Finland High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico Hiroshima University, Hiroshima, Japan Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation (ZTT), Worms, Germany Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania Indian Institute of Technology Bombay (IIT), Mumbai, India Indian Institute of Technology Indore, Indore, India Indonesian Institute of Sciences, Jakarta, Indonesia INFN, Laboratori Nazionali di Frascati, Frascati, Italy INFN, Sezione di Bari, Bari, Italy INFN, Sezione di Bologna, Bologna, Italy INFN, Sezione di Cagliari, Cagliari, Italy INFN, Sezione di Catania, Catania, Italy INFN, Sezione di Padova, Padova, Italy 37 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration INFN, Sezione di Pavia, Pavia, Italy INFN, Sezione di Roma, Rome, Italy INFN, Sezione di Torino, Turin, Italy INFN, Sezione di Trieste, Trieste, Italy Inha University, Incheon, Republic of Korea Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands Institute for Nuclear Research, Academy of Sciences, Moscow, Russia Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic Institute of Space Science (ISS), Bucharest, Romania Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico iThemba LABS, National Research Foundation, Somerset West, South Africa Jeonbuk National University, Jeonju, Republic of Korea Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany Joint Institute for Nuclear Research (JINR), Dubna, Russia Korea Institute of Science and Technology Information, Daejeon, Republic of Korea KTO Karatay University, Konya, Turkey Laboratoire de Physique des 2 Inﬁnis, Irène Joliot-Curie, Orsay, France Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France Lawrence Berkeley National Laboratory, Berkeley, California, United States Lund University Department of Physics, Division of Particle Physics, Lund, Sweden Moscow Institute for Physics and Technology, Moscow, Russia Nagasaki Institute of Applied Science, Nagasaki, Japan Nara Women’s University (NWU), Nara, Japan National and Kapodistrian University of Athens, School of Science, Department of Physics , Athens, Greece National Centre for Nuclear Research, Warsaw, Poland National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India National Nuclear Research Center, Baku, Azerbaijan National Research Centre Kurchatov Institute, Moscow, Russia Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark Nikhef, National institute for subatomic physics, Amsterdam, Netherlands NRC Kurchatov Institute IHEP, Protvino, Russia NRC «Kurchatov»Institute - ITEP, Moscow, Russia NRNU Moscow Engineering Physics Institute, Moscow, Russia Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom Nuclear Physics Institute of the Czech Academy of Sciences, Rež u Prahy, Czech Republic Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States Ohio State University, Columbus, Ohio, United States Petersburg Nuclear Physics Institute, Gatchina, Russia Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia Physics Department, Panjab University, Chandigarh, India Physics Department, University of Jammu, Jammu, India Physics Department, University of Rajasthan, Jaipur, India Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany Physik Department, Technische Universität München, Munich, Germany Politecnico di Bari and Sezione INFN, Bari, Italy Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany Russian Federal Nuclear Center (VNIIEF), Sarov, Russia 38 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom Sección Física, Departamento de Ciencias, Pontiﬁcia Universidad Católica del Perú, Lima, Peru St. Petersburg State University, St. Petersburg, Russia Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France Suranaree University of Technology, Nakhon Ratchasima, Thailand Technical University of Košice, Košice, Slovakia The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland The University of Texas at Austin, Austin, Texas, United States Universidad Autónoma de Sinaloa, Culiacán, Mexico Universidade de São Paulo (USP), São Paulo, Brazil Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil Universidade Federal do ABC, Santo Andre, Brazil University of Cape Town, Cape Town, South Africa University of Houston, Houston, Texas, United States University of Jyväskylä, Jyväskylä, Finland University of Kansas, Lawrence, Kansas, United States University of Liverpool, Liverpool, United Kingdom University of Science and Technology of China, Hefei, China University of South-Eastern Norway, Tonsberg, Norway University of Tennessee, Knoxville, Tennessee, United States University of the Witwatersrand, Johannesburg, South Africa University of Tokyo, Tokyo, Japan University of Tsukuba, Tsukuba, Japan Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Inﬁnis de Lyon , Lyon, France Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Saclay, France Università degli Studi di Foggia, Foggia, Italy Università di Brescia, Brescia, Italy Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India Warsaw University of Technology, Warsaw, Poland Wayne State University, Detroit, Michigan, United States Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany Wigner Research Centre for Physics, Budapest, Hungary Yale University, New Haven, Connecticut, United States Yonsei University, Seoul, Republic of Korea http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png High Energy Physics - 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eISSN: ARCH-3333
DOI: 10.1007/JHEP05(2022)061
Publisher site: See Article on Publisher Site

Abstract

The jet angularities are a class of jet substructure observables which characterize the angular and momentum distribution of particles within jets. These observables are sensitive to momentum scales ranging from perturbative hard scatterings to nonperturbative fragmentation into ﬁnal-state hadrons. We report measurements of several groomed and ungroomed jet angularities in pp collisions at s = 5:02 TeV with the ALICE detector. Jets are reconstructed using charged particle tracks at midrapidity (jhj < 0:9). The anti-k algorithm is used with jet resolution parameters R = 0:2 and ch jet R = 0:4 for several transverse momentum p intervals in the 20100 GeV/c range. Using the jet grooming algorithm Soft Drop, the sensitivity to softer, wide-angle processes, as well as the underly- ing event, can be reduced in a way which is well-controlled in theoretical calculations. We report the ungroomed jet angularities, l , and groomed jet angularities, l , to investigate the interplay be- a a ,g tween perturbative and nonperturbative effects at low jet momenta. Various angular exponent param- eters a = 1, 1.5, 2, and 3 are used to systematically vary the sensitivity of the observable to collinear and soft radiation. Results are compared to analytical predictions at next-to-leading-logarithmic ac- curacy, which provide a generally good description of the data in the perturbative regime but exhibit discrepancies in the nonperturbative regime. Moreover, these measurements serve as a baseline for future ones in heavy-ion collisions by providing new insight into the interplay between perturbative and nonperturbative effects in the angular and momentum substructure of jets. They supply crucial guidance on the selection of jet resolution parameter, jet transverse momentum, and angular scaling variable for jet quenching studies. © 2021 CERN for the beneﬁt of the ALICE Collaboration. Reproduction of this article or parts of it is allowed as speciﬁed in the CC-BY-4.0 license. See Appendix B for the list of collaboration members arXiv:2107.11303v2 [nucl-ex] 1 Dec 2022 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 1 Introduction In high-energy particle collisions, jet observables are sensitive to a variety of processes in quantum chro- modynamics (QCD), from the initial hard (high Q ) parton scattering to a scale evolution culminating in hadronization near L . Jets reconstructed with a radius (resolution) parameter near R = 1 and with QCD jet sufﬁciently large transverse momentum p provide a proxy for the dynamics of the initial hard parton jet scattering, whereas those reconstructed with smaller R or at lower p become sensitive to nonperturba- tive effects. In this article, jet substructure observables are deﬁned by clustering particles into a jet and then constructing an observable from its constituents to characterize its internal radiation pattern. Jet substructure techniques have provided one of the key tools to study rare event topologies in pp col- lisions, for example by tagging boosted objects that decay into jets [1]. Moreover, measurements of jet substructure enable stringent tests of perturbative QCD (pQCD) and facilitate studies of nonpertur- bative effects which are not yet under satisfactory theoretical control [2]. Jet substructure observables offer both ﬂexibility and rigor: they can be constructed to be theoretically calculable from ﬁrst-principles pQCD while simultaneously maintaining sensitivity to jet radiation in speciﬁc regions of phase-space. Jet grooming algorithms, such as Soft Drop [3–5], can additionally be used to remove soft, wide-angle radiation via well-controlled approaches, reducing nonperturbative effects. This deﬁnes two families of jet substructure observables: one that can be constructed from all jet constituents and one based on a subset of jet constituents which remain after grooming procedures. One such set of observables are the generalized jet angularities [6, 7]. Expanding upon the jet girth g (also known as the jet radial moment), the generalized jet angularities form a class of jet substructure observables deﬁned by k k a l z q ; (1) a i i where the sum runs over the jet constituents i, and k and a are continuous free parameters. The ﬁrst jet factor z p =p describes the momentum fraction carried by the constituent, and the second factor i T;i q DR =R denotes the separation in rapidity (y) and azimuthal angle (j ) of the constituent from the jet i i 2 2 axis, where DR Dy +Dj and R is the jet resolution parameter. The jet angularities are infrared- i i and collinear- (IRC-)safe for k = 1 and a > 0 [8, 9]. We consider the ungroomed jet angularities, denoted as l , as well as the groomed jet angularities in which the sum runs only over the constituents of the groomed jet, denoted as l . These include the jet girth [10], l , and the jet thrust [11], l , a;g 1 2 jet 2 2 which is related to the jet mass m by l = (m =p ) +O(l ); l , however, is more robust against jet 2 jet 2 nonperturbative effects than m since it does not depend explicitly on the hadron masses. jet The IRC-safe jet angularities offer the possibility to systematically vary the observable deﬁnition in a way that is theoretically calculable and therefore provide a rich opportunity to study both perturbative and nonperturbative QCD [12–15]. This article considers jet angularities constructed from charged-particle jets. While charged-particle jets are IRC-unsafe [16], comparisons to these theoretical predictions can nonetheless be carried out by following a nonperturbative correction procedure, as outlined in Sec. 5.1. Jet angularities were recently calculated in pp collisions both in the ungroomed [9] and groomed [17] cases, as well as for jets produced in association with a Z boson [18]. These calculations use all-order resummation of large logarithms up to next-to-leading-logarithmic (NLL ) accuracy [19]. Measurements of l and l will serve to test these analytical predictions, in particular the role of resummation effects a a;g and power corrections. Moreover, by measuring multiple values of a , one can test the predicted scaling of nonperturbative shape functions that are used to model hadronization, which depend only on a single The notation l is employed to represent the jet angularities instead of the commonly-used notation l in order to avoid conﬂict with the letter b , which is also used to denote the angular parameter of the Soft Drop grooming algorithm. 2 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration nonperturbative parameter for all values of a [20, 21]. Several measurements of jet angularities have been performed in hadronic collisions. The ungroomed jet angularity l has been measured in pp collisions by the ATLAS, CMS, and ALICE Collaborations [22– 24] in addition to pp collisions by the CDF Collaboraiton [25]. The ungroomed jet angularity l has also been measured in pp collisions by the CMS Collaboration [24]. The closely related ungroomed and groomed jet mass have been extensively measured in pp collisions by the ATLAS and CMS Collabora- tions [23, 24, 26–35], and the ungroomed mass was also studied in pp collisions by the CDF Collabo- ration [25] and in p–Pb collisions by the ALICE Collaboration [36]. Many of these measurements have focused on using jet substructure for tagging objects at high p , rather than for fundamental studies of QCD, and with the exception of the jet mass there have not yet been comparisons of jet angularities to an- alytical calculations, nor have any such comparisons been made for charged-particle jets. In this article, we perform the ﬁrst measurements of groomed jet angularities in pp collisions, and a systematic scan of jet the IRC-safe ungroomed jet angularities. These measurements focus on low to moderate p , and small to moderate R. Moreover, the measurements are performed in pp collisions at a center-of-mass energy s = 5:02 TeV, the same center-of-mass energy at which ALICE recorded data in heavy-ion collisions during LHC Run 2, and where no jet angularity measurements have been made. These measurements serve as a baseline for future measurements of the jet angularities in heavy-ion col- lisions, in which a deconﬁned state of strongly-interacting matter is produced [37–40]. Measurements of jets and jet substructure in heavy-ion collisions may provide key insight into the physical properties of this deconﬁned state [41–43]. The jet angularities are sensitive both to medium-induced broadening as well as jet collimation [44–46]; by systematically varying the weight of collinear radiation, one may be able to efﬁciently discriminate between jet quenching models. In Pb–Pb collisions, l has been mea- sured for R = 0:2 by the ALICE Collaboration [22], and the ungroomed and groomed jet mass have been measured for R = 0:4 by the ATLAS, CMS, and ALICE Collaborations [30, 34, 36]. The interpreta- tion of previous measurements is unclear, with strong modiﬁcation being observed in Pb–Pb collisions compared to pp collisions for the case when a = 1 and R = 0:2, but little to no modiﬁcation seen for the R = 0:4 jet mass. Future measurements over a range of R and a offer a compelling opportunity to disentangle the roles of medium-induced broadening, jet collimation, and medium response in jet evo- lution. By measuring small to moderate R jets in pp collisions, which are theoretically challenging and involve signiﬁcant resummation effects [47], the ability of pQCD to describe the small-radius jets that are measured in heavy-ion collisions can be tested. This article reports measurements of ungroomed and groomed jet angularities for a = 1, 1.5, 2, and 3 in pp collisions at s = 5:02 TeV. In addition to the standard jet girth (a = 1) and jet mass (related to a = 2) parameters, a = 1:5 and a = 3 are included to test the universality of a nonperturbative shape function by varying effects of soft, wide-angle radiation, as discussed below in Sec. 5.1.2, and to serve as a reference for future jet quenching measurements in heavy-ion collisions. Grooming is performed according to the Soft Drop grooming procedure with z = 0:2 and b = 0 [48]. Charged particle jets were cut reconstructed at midrapidity using the anti-k algorithm with jet resolution (radius) parameters R = 0:2 ch jet and R = 0:4 in four equally-sized p intervals from 20 to 100 GeV=c. The results are compared to NLL pQCD predictions, as well as to the PYTHIA8 [49] and Herwig7 [50, 51] Monte Carlo generators. 2 Experimental setup and data sets A description of the ALICE detector and its performance can be found in Refs. [52, 53]. The pp data used in this analysis were collected in 2017 during LHC Run 2 at s = 5:02 TeV [54]. A minimum bias (MB) trigger was used; this requires a coincidence of hits in the V0 scintillator detectors, which provide full azimuthal coverage and cover the pseudorapidity ranges of 2:8 < h < 5:1 and 3:7 < h < 1:7 [55]. The event selection also requires the location of the primary vertex to be within 10 cm from the nom- 3 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration inal interaction point (IP) along the beam direction and within 1 cm of the IP in the transverse plane. Beam-induced background events were removed using two neutron Zero Degree Calorimeters located at 112:5 m along the beam axis from the center of the detector. Events with multiple reconstructed vertices were rejected, and track quality selection criteria ensured that tracks used in the analysis were from only one vertex. Events were acquired at instantaneous luminosities between approximately 10 31 2 1 and 10 cm s , corresponding to a low level of pileup with approximately 0:004 < m < 0:03 events per bunch crossing. The pp data sample contains 870 million events and corresponds to an integrated luminosity of 18.0(4) nb [56]. This analysis uses charged particle tracks reconstructed from clusters in both the Time Projection Cham- ber (TPC) [57] and the Inner Tracking System (ITS) [58]. Two types of tracks are deﬁned: global tracks and complementary tracks. Global tracks are required to include at least one hit in the silicon pixel de- tector (SPD), comprising the ﬁrst two layers of the ITS, and to satisfy a number of quality criteria [59], including having at least 70 out of a maximum of 159 TPC space points and at least 80% of the geo- metrically ﬁndable space points in the TPC. Complementary tracks do not contain any hits in the SPD, but otherwise satisfy the tracking criteria, and are reﬁt with a constraint to the primary vertex of the event. Including this second class of tracks ensures approximately uniform azimuthal acceptance, while preserving similar transverse momentum p resolution to tracks with SPD hits, as determined from the ﬁt quality. Tracks with p > 0:15 GeV=c are accepted over pseudorapidity jhj < 0:9 and azimuthal T;track angle 0 < j < 2p . All tracks are assigned a mass equal to the p mass. The instrumental performance of the ALICE detector and its response to particles is estimated with a GEANT3 [60] model. The tracking efﬁciency in pp collisions, as estimated by propagating pp events from PYTHIA8 Monash 2013 [49] through the ALICE GEANT3 detector simulation, is approximately 67% at p = 0:15 GeV=c, rises to approximately 84% at p = 1 GeV=c, and remains above T;track T;track 75% at higher p . The momentum resolution s(p )=p is estimated from the covariance matrix of T T T the track ﬁt [53] and is approximately 1% at p = 1 GeV=c. This increases with p , reaching T;track T;track approximately 4% at p = 50 GeV=c. T;track 3 Analysis method 3.1 Jet reconstruction Jets are reconstructed from charged tracks with p > 150 MeV=c using the FastJet package [61]. The anti-k algorithm is used with the E recombination scheme for resolution parameters R = 0:2 and ch jet 0:4 [62]. All reconstructed charged-particle jets in the transverse momentum range 5 < p < 200 GeV=c are analyzed in order to maximize statistics in the unfolding procedure (described below). Each jet axis is required to be within the ﬁducial volume of the TPC, h < 0:9 R. Jets containing a track jet with p > 100 GeV=c are removed from the collected data sample, due to limited momentum resolu- tion. In order to make consistent comparisons between the data and the theoretical calculations, the background due to the underlying event is not subtracted from the data, and instead the underlying event (along with other nonperturbative effects) is included in model corrections, as described in Sec. 5.1. The jet reconstruction performance is studied by comparing jets reconstructed from PYTHIA8-generated events at “truth level” (before the particles undergo interactions with the detector) to those at “detector level” (after the ALICE GEANT3 detector simulation). Two collections of jets are constructed: pp truth level (PYTHIA truth) and pp detector level (PYTHIA with detector simulation). The detector- level jets are then geometrically matched with truth-level jets within DR < 0:6 R while additionally requiring that each match be unique. Table 1 shows approximate values of the mean jet energy scale D E . ch jet ch jet ch jet ch jet ch jet shift, D = p p =p , the jet energy resolution, JER = s p p , and the JES T;det T;truth T;truth T;det T;truth ch jet ch jet jet reconstruction efﬁciency, e , for both R = 0:2 and R = 0:4, where p is the detector-level p , reco T;det 4 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration Table 1: Approximate values characterizing the jet reconstruction performance for R = 0:2 and 0:4 in pp collisions. D is the mean jet energy scale shift, JER is the jet energy resolution, and e is the reconstruction efﬁciency. JES reco R = 0:2 R = 0:4 ch jet p 20 GeV=c 100 GeV=c 20 GeV=c 100 GeV=c D –12% –24% –13% –21% JES JER 22% 21% 21% 21% e 94% 100% 97% 100 reco ch jet ch jet and p is the truth-level p . The jet energy scale shift is a long-tailed asymmetric distribution T;truth T ch jet ch jet due to tracking inefﬁciency [63] with a peak at p = p , and D should be understood only as a JES T;det T;truth rough characterization of this distribution. The ungroomed jet angularities are reconstructed using all of the charged-particle jet constituents ac- cording to Eq. (1). For the groomed jet angularities, Soft Drop grooming [3] is performed, in which the constituents of each jet are reclustered with the Cambridge–Aachen algorithm [64] with resolution parameter R, forming an angularly-ordered tree data structure. Each node corresponds to a constituent 2 2 p Dy +Dj T;subleading DR track, and each edge is a branch splitting deﬁned by z and q . The p +p R R T;leading T;subleading jet tree is then traversed starting from the largest-angle splitting, and the Soft Drop condition, z > z q , cut is recursively evaluated. Here, z is the subleading branch p fraction deﬁned above, and z and b are T cut tunable, free parameters of the grooming algorithm. For this analysis, b = 0 is used to maximize the perturbative calculability [17], while z = 0:2 is chosen (as opposed to the more common z = 0:1) cut cut since higher-accuracy branch tagging can be achieved in future heavy-ion collision analyses [48]. If the Soft Drop condition is not satisﬁed, then the softer subleading branch is discarded and the next splitting in the harder branch is examined in the same way. If, however, the condition is satisﬁed, then the groom- ing procedure is concluded, with all remaining constituents deﬁning the groomed jet. The groomed jet angularity is then deﬁned according to Eq. (1) using the groomed jet constituents, but still with the un- ch jet groomed p and ungroomed jet axis to deﬁne q , since the groomed jet observable is a property of the ch jet ch jet original (ungroomed) jet object. Note that while the ungroomed p is IRC-safe, the groomed p T,g is Sudakov safe [65]. If the jet does not contain a splitting that passes the Soft Drop condition, then the groomed jet contains zero constituents (“untagged”) and does not have a deﬁned groomed jet angularity. 3.2 Corrections ch jet The reconstructed p and l differ from their true values due to tracking inefﬁciency, particle– material interactions, and track p resolution. To account for these effects, PYTHIA8 Monash 2013 [49, 66] and the ALICE GEANT3 detector simulation are used to construct a 4D response matrix that ch jet ch jet ch jet ch jet describes the detector response mapping of p and l to p and l , where p and p a;truth a;det T;truth T;det T;det T;truth are as above, and l and l are the analogous detector- and truth-level l . The truth-level jet was a;det a;truth a constructed from the charged primary particles of the PYTHIA event, deﬁned as all particles with a mean proper lifetime larger than 1 cm/c, and excluding the decay products of these particles [67]. ch jet A 2D unfolding in p and l is then performed using the iterative Bayesian unfolding algorithm [68, 69] implemented in the RooUnfold package [70] to recover the true jet spectrum at the charged- hadron level. This technique utilizes a “prior" distribution (equivalent to the per-bin MC prediction) as a starting point, before iteratively updating the distribution using Bayes’ theorem in conjunction with the calculated response matrix and measured data (see Refs. [68, 69] for details). Since the jet yield in each ch jet ch jet ch jet reported p interval varies widely, with higher-p jets being less probable than lower-p jets, T T T ch jet and since the shape and mean value of the jet angularity distributions also changes with p , a separate ch jet 2D unfolding for each reported p bin is performed in order to optimize the observable binning at both 5 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration truth and detector levels, thus ensuring sufﬁcient jet yield is included in the procedure for all distributions while simultaneously maximizing the number of bins for regions of phase space where higher yield is available. The bin migration in all cases is dominated by a strong diagonal mapping in the response ch jet matrix coupled with a slight smearing along the p and l axes. The smearing in l is roughly a;truth a T;truth ch jet symmetric about the diagonal, whereas the smearing in p tends to be skewed towards lower values ch jet of p due to tracking efﬁciency effects. T;truth In the groomed case, the number of untagged jets in the unfolding procedure is included as an additional bin adjacent to the lower edge of the l distributions. This is done so that the unfolding procedure will correct for detector effects on the groomed jet tagging fraction as well as account for bin migration effects for jets which are groomed away at detector-level but not truth-level, or vice versa. To validate the performance of the unfolding procedure, a set of refolding and closure tests is performed, in which either the response matrix is multiplied by the unfolded data and compared to the original detector-level spectrum, or in which the shape of the input MC spectrum is modiﬁed to account for the fact that the actual distribution may be different than the MC input spectrum. The number of iterations, which sets the strength of regularization, is chosen to be the minimal value such that all unfolding tests succeed. This results in the number of iterations being equal to 3 for all distributions. In all cases, closure is achieved compatible with statistical uncertainties. The distributions after unfolding are corrected for the kinematic efﬁciency, deﬁned as the efﬁciency of ch jet ch jet reconstructing a truth-level jet at a particular p and l value given a reconstructed jet p and a;truth T;truth T;det l range. Kinematic inefﬁciency results from effects including smearing from the Soft Drop threshold a;det ch jet and p -smearing of the jet out of the selected p range. Any “missed” jets, those jets which exist at T;det truth level but not at detector level, are handled by this kinematic efﬁciency correction. In this analysis, minimal detector-level cuts are applied, and the kinematic efﬁciency is therefore greater than 99% in all ch jet cases. Since a wide p range is taken, the effect of “fake” jets, those jets which exist at detector level T;truth but not truth level, is taken to be negligible. 4 Systematic uncertainties The systematic uncertainties in the unfolded results arise from uncertainties in the tracking efﬁciency and unfolding procedure, as well as the model-dependence of the response matrix, and the track mass assumption. Table 2 summarizes the systematic uncertainty contributions. Each of these sources of uncertainty dominate in certain regions of the measured observables, with the exception of the track mass assumption which is small in all cases. The total systematic uncertainty is taken as the sum in quadrature of the individual uncertainties described below. The tracking efﬁciency uncertainty is estimated to be 4% by varying track selection parameters and the ITS–TPC matching requirement. In order to assign a systematic uncertainty to the nominal result, a response matrix is constructed using the same techniques as for the ﬁnal result except that an additional 4% of tracks are randomly rejected before the jet ﬁnding. This response matrix is then used to unfold the distribution in place of the nominal response matrix, and the result is compared to the default result, with the differences in each bin taken as a symmetric uncertainty. This uncertainty constitutes a smaller effect in the groomed jet angularities, where single-particle jets, being the most sensitive to the tracking efﬁciency, are groomed away by the Soft Drop condition. The uncertainty on the track momentum resolution is a sub-leading effect to the tracking efﬁciency and is taken to be negligible. Several variations of the unfolding procedure are performed in order to estimate the systematic uncer- tainty arising from the unfolding regularization procedure: 1. The number of iterations was varied by2 and the average difference with respect to the nominal 6 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration result is taken as the systematic uncertainty. ch jet ch jet 0:5 2. The prior distribution is scaled by a power law in p and a linear scaling in l , (p ) T T [1(l 0:5)]. The average difference between the result unfolded with this prior and the original is taken as the systematic uncertainty. 3. The binning in l was varied to be slightly ﬁner and coarser than the nominal binning, by com- bining (splitting) some adjacent bins with low (high) jet yield, or by shifting the bin boundaries to be between the nominal boundaries. ch jet 4. The lower and upper bounds in the p range were increased to 10 and decreased to 120 GeV=c, T;det respectively. These values are chosen as reasonable values to estimate sensitivity to truncation effects. The total unfolding systematic uncertainty is then the standard deviation of the variations, å s =N, i=1 i where N = 4 and s is the systematic uncertainty due to a single variation, since they each comprise independent measurements of the same underlying systematic uncertainty in the regularization. A systematic uncertainty associated with the model-dependent reliance on the Monte Carlo generator which is used to unfold the spectra is included. We construct a fast simulation to parameterize the tracking efﬁciency and track p resolution, and build response matrices using PYTHIA8 Monash 2013 and Herwig7 (default tune) as generators. Even though a full detector simulation using PYTHIA8 has also been generated, a fast simulation is used for this purpose so that there is complete parity between the two generators in the calculation of this systematic uncertainty. This fast simulation provides agreement within10% of the full detector simulation for R = 0:2 jets, with some larger deviations seen in the tails of the jet angularity distributions for R = 0:4 jets. These two response matrices are then used to unfold the measured data, and the differences between the two unfolded results in each interval are taken as a ch jet symmetric uncertainty. This uncertainty is most signiﬁcant at lower p . In order to assess the uncertainty due to the track mass assumption, K meson and proton masses are randomly assigned to 13% and 5.5% of tracks, respectively, in both the data and the response matrix. These numbers are chosen from the (approximate) inclusive number of each respective particle measured ch jet at midrapidity in pp events by ALICE [71]. Neither the measurement inside the jets nor the p - dependence are considered, so these numbers are taken to constitute a reasonable maximum uncertainty. The bin-by-bin difference of the unfolded result to the nominal result is taken as a symmetric uncertainty. 5 Results and discussion ch jet We report the l and l distributions for a = 1, 1.5, 2, and 3 in four equally-sized intervals of p a a;g between 20 and 100 GeV/c. The distributions are reported as differential cross sections: 1 ds 1 dN 1 ds 1 dN jets gr jets (ungroomed), or (groomed), (2) s dl N dl s dl N dl a jets a inc a;g inc jets a;g ch jet where N is the number of jets within a given p range and s is the corresponding cross section. jets For the groomed case, some jets are removed by the grooming procedure, and therefore two different quantities are deﬁned: N , the number of jets which have at least one splitting satisfying the Soft gr jets Drop condition, and N , the total number of inclusive jets, with both N and N being within inc jets gr jets inc jets ch jet the given p range. s is the cross section corresponding to the latter inclusive quantity. For the un- inc groomed case, N = N and s = s , so the redundant labels are dropped. It is useful to normalize inc jets jets inc the groomed differential cross section by the number of inclusive jets since the groomed jet angularities 7 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet Table 2: Summary of systematic uncertainties for a representative sample of a , R, and p . A moderately high ch jet 60 < p < 80 GeV=c with R = 0:4 is chosen to show the variation with a , and two additional rows show the ch jet trends with smaller p and R. Relative uncertainty ch jet a R p (GeV=c) Trk. eff. Unfolding Generator Mass hypothesis Total 1 0.4 60–80 1–15% 2–7% 1–5% 0–2% 7–16% 2 0.4 60–80 1–10% 1–8% 1–5% 1–3% 4–12% 3 0.4 60–80 1–10% 2–4% 1–4% 0–4% 4–11% 2 0.4 20–40 1–16% 1–4% 1–43% 0–5% 2–44% 2 0.2 60–80 2–12% 2–7% 1–9% 0–2% 3–12% a;g 1 0.4 60–80 1–7% 2–8% 1–6% 0–4% 2–13% 2 0.4 60–80 1–8% 2–9% 1–5% 0–4% 3–12% 3 0.4 60–80 1–6% 2–7% 1–11% 0–7% 4–16% 2 0.4 20–40 1–8% 2–5% 1–40% 0–3% 2–42% 2 0.2 60–80 1–7% 1–8% 1–12% 0–3% 1–15% are a property of the inclusively-measured jet population and are thus typically normalized as such in theoretical calculations [17]. The ungroomed jet angularity distributions are shown in Fig. 1 and Fig. 2 for R = 0:4 and R = 0:2, respec- tively. By the deﬁnitions given in Eq. 2, these distributions are all normalized to unity. As a increases, the distributions skew towards small l , since q is smaller than unity. For larger R, the distributions are a i narrower than for smaller R, as expected due to the collinear nature of jet fragmentation. For small R ch jet and low p there is a visible peak at l = 0, which is due to single particle jets. These distributions are compared to PYTHIA8 Monash 2013 [49, 66] and Herwig7 (default tune) [50, 51] from truth-level projections of the respective response matrices, with jet reconstruction assigning tracks the p meson mass as in the measured data. These comparisons show deviations up to approximately +50%(30%). The largest deviations are for small values of l , where nonperturbative physics becomes signiﬁcant (see Sec. 5.1 for discussion). The groomed jet angularity distributions for z = 0:2 and b = 0 are shown in Fig. 3 for R = 0:4 and cut Fig. 4 for R = 0:2. Note that these distributions are shown on a logarithmic scale due to the distributions being more strongly peaked and falling faster with l as compared to the ungroomed distributions. The groomed jet angularities have signiﬁcantly smaller values than the ungroomed jet angularities, due to the removal of soft wide-angle radiation. The fraction of “untagged” jets, those that do not contain a splitting which passes the Soft Drop condition, ranges from 10 to 12%. Unlike the ungroomed jet angularities, which are normalized to unity, the groomed jet angularities are normalized to the Soft Drop tagging fraction. Since the tagging rate is fairly large, the measured distributions are therefore normalized close to unity. PYTHIA and Herwig describe the groomed jet angularities slightly better than the ungroomed jet angularities, with most deviations seen in the ungroomed distributions improving by 10–20% in the groomed case. Comparing to the two MC generators, the data are in slightly better agreement with Herwig7 than with PYTHIA8, especially for R = 0:4. The data cover a wide range of a and multiple R down to low p , and therefore are subject to vary- ing inﬂuence from nonperturbative effects. Accordingly, these data can be used to study nonpertubative effects. The level and location of the disagreements with PYTHIA and Herwig provide further con- straints on nonperturbative effects in MC event generators. Moreover, the comparison of the groomed 8 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 14 14 α = 1 α = 1 ALICE Syst. uncertainty α = 1.5 α = 1.5 pp s = 5.02 TeV PYTHIA8 Monash 2013 12 12 α = 2 α = 2 charged jets anti-k Herwig7 10 α = 3 (×0.5) 10 α = 3 (×0.5) R = 0.4 |η | < 0.5 jet ch jet ch jet 8 8 20 < p < 40 GeV/c 40 < p < 60 GeV/c T T 6 6 4 4 2 2 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α α = 1 α = 1 9 9 α = 1.5 (×0.7) α = 1.5 (×0.7) 8 8 α = 2 (×0.5) α = 2 (×0.5) 7 7 α = 3 (×0.3) α = 3 (×0.3) 6 6 ch jet ch jet 60 < p < 80 GeV/c 80 < p < 100 GeV/c 5 5 T T 4 4 3 3 2 2 1 1 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α 1.5 1.5 1 1 0.5 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α Figure 1: Comparison of ungroomed jet angularities l in pp collisions for R = 0:4 to MC predictions using ch jet PYTHIA8 and Herwig7, as described in the text. Four equally-sized p intervals are shown, with edges ranging between 20 and 100 GeV=c. The distributions are normalized to unity. dσ 1 dσ Data 1 Data Data Data Herwig7 PYTHIA8 PYTHIA8 Herwig7 σ σ dλ dλ α α dσ dσ Data 1 Data Data 1 Data Herwig7 Herwig7 PYTHIA8 σ PYTHIA8 σ dλ dλ α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 14 14 α = 1 α = 1 ALICE Syst. uncertainty α = 1.5 α = 1.5 pp s = 5.02 TeV PYTHIA8 Monash 2013 12 12 α = 2 α = 2 charged jets anti-k Herwig7 10 α = 3 (×0.5) 10 α = 3 (×0.5) R = 0.2 |η | < 0.7 jet ch jet ch jet 8 8 20 < p < 40 GeV/c 40 < p < 60 GeV/c T T 6 6 4 4 2 2 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α α = 1 α = 1 9 9 α = 1.5 (×0.7) α = 1.5 (×0.7) 8 8 α = 2 (×0.5) α = 2 (×0.5) 7 7 α = 3 (×0.3) α = 3 (×0.3) 6 6 ch jet ch jet 60 < p < 80 GeV/c 80 < p < 100 GeV/c 5 5 T T 4 4 3 3 2 2 1 1 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α 1.5 1.5 1 1 0.5 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α α Figure 2: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 to MC predictions using ch jet PYTHIA8 and Herwig7, as described in the text. Four equally-sized p intervals are shown, with edges ranging between 20 and 100 GeV=c. The distributions are normalized to unity. dσ 1 dσ Data 1 Data Data Data Herwig7 PYTHIA8 PYTHIA8 Herwig7 σ σ dλ dλ α α dσ dσ Data 1 Data Data 1 Data Herwig7 Herwig7 PYTHIA8 σ PYTHIA8 σ dλ dλ α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 7 7 10 10 α = 1 α = 1 ALICE 6 6 Syst. uncertainty 10 10 α = 1.5 (×0.5) α = 1.5 (×0.5) pp s = 5.02 TeV PYTHIA8 Monash 2013 5 5 10 10 α = 2 (×0.2) α = 2 (×0.2) charged jets anti-k Herwig7 4 4 10 10 α = 3 (×0.03) α = 3 (×0.03) R = 0.4 |η | < 0.5 3 jet 3 10 10 Soft Drop z = 0.2 β = 0 cut 2 2 10 10 ch jet ch jet 20 < p < 40 GeV/c 40 < p < 60 GeV/c 10 10 T T 1 1 - 1 - 1 10 10 - 2 - 2 10 10 - 3 - 3 10 10 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g α = 1 α = 1 10 10 α = 1.5 (×0.25) α = 1.5 (×0.25) α = 2 (×0.1) α = 2 (×0.1) α = 3 (×0.02) α = 3 (×0.02) 1 1 - 1 - 1 10 10 ch jet ch jet - 2 - 2 60 < p < 80 GeV/c 80 < p < 100 GeV/c 10 10 T T 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 1.5 1.5 1 1 0.5 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g Figure 3: Comparison of groomed jet angularities l in pp collisions for R = 0:4 to MC predictions using a;g ch jet PYTHIA8 and Herwig7, as described in the text. Four equally-sized p intervals are shown between 20 and 100 GeV=c. The distributions are normalized to the groomed jet tagging fraction. dσ dσ 1 1 Data Data Data Data σ σ Herwig7 PYTHIA8 PYTHIA8 Herwig7 dλ dλ inc inc α ,g α ,g dσ 1 dσ Data Data Data Data σ σ Herwig7 Herwig7 PYTHIA8 PYTHIA8 dλ dλ inc inc α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 7 7 10 α = 1 10 α = 1 ALICE Syst. uncertainty 6 6 α = 1.5 (×0.5) α = 1.5 (×0.5) 10 10 pp s = 5.02 TeV PYTHIA8 Monash 2013 5 5 α = 2 (×0.2) α = 2 (×0.2) 10 charged jets anti-k 10 Herwig7 4 4 α = 3 (×0.03) α = 3 (×0.03) R = 0.2 |η | < 0.7 10 10 jet 3 3 10 10 Soft Drop z = 0.2 β = 0 cut 2 2 10 ch jet 10 ch jet 20 < p < 40 GeV/c 40 < p < 60 GeV/c T T 10 10 1 1 - 1 - 1 10 10 - 2 - 2 10 10 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 2 2 10 10 α = 1 α = 1 α = 1.5 (×0.25) α = 1.5 (×0.25) 10 10 α = 2 (×0.1) α = 2 (×0.1) α = 3 (×0.02) α = 3 (×0.02) 1 1 - 1 - 1 10 10 - 2 - 2 10 10 ch jet ch jet - 3 - 3 60 < p < 80 GeV/c 80 < p < 100 GeV/c 10 10 T T 0 0.2 0.4 0.6 0 0.2 0.4 1.5 1.5 1 1 0.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g 1.5 1.5 1 1 0.5 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 λ λ α ,g α ,g Figure 4: Comparison of groomed jet angularities l in pp collisions for R = 0:2 to MC predictions using a;g ch jet PYTHIA8 and Herwig7, as described in the text. Four equally-sized p intervals are shown between 20 and 100 GeV=c. The distributions are normalized to the groomed jet tagging fraction. dσ dσ 1 1 Data Data Data Data σ σ Herwig7 PYTHIA8 PYTHIA8 Herwig7 dλ dλ inc inc α ,g α ,g dσ 1 dσ Data Data Data Data σ σ Herwig7 Herwig7 PYTHIA8 PYTHIA8 dλ dλ inc inc α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration and the ungroomed jet angularities with MC event generators allows direct sensitivity to radiation that was groomed away, which is highly nonperturbative. 5.1 Comparison to analytical calculations The measured ungroomed and groomed jet angularities are compared with analytical calculations [9, 17] which use all-order resummations of large logarithms to next-to-leading logarithmic (NLL ) ac- curacy [19]. In particular, the calculations resum logarithms of l , R, and z . In the case of the a cut n k l logarithms, the cumulant of the cross section includes the complete set of terms of form a ln l a a for k = 2n, 2n 1, and 2n 2. The calculations are valid up to power corrections in l , R, and z , a cut and do not include non-global logarithms [72]. These calculations are based on the framework of Soft Collinear Effective Theory (SCET) [73], in which the jet cross section is factorized into a “hard func- tion" corresponding to the initial scattering, and a “jet function" corresponding to the fragmentation of a hard-scattered parton into a jet. For the calculation of the jet angularities, the jet function is then further factorized into collinear and soft functions. Systematic uncertainties on the analytical predictions are estimated by systematically varying ﬁfteen combinations of scales that emerge in the calculation. For the ungroomed jet angularities, the collinear-soft momentum scale for the factorization formalism becomes nonperturbative for [9] l . ; (3) ch jet p R where L is the energy scale at which a becomes nonperturbative, which is taken to be approximately 1 GeV=c. For the groomed jet angularities with b = 0, this soft factorization scale becomes nonpertur- bative for [17] 1a l . z : (4) a;g cut ch jet p R Accordingly, the analytical predictions are expected to describe the data only at sufﬁciently large l , ch jet which depends on p , R, and z . On the other hand, for l = O(1), power corrections in l become cut a a important, and are not included in the NLL calculations. Note that for l > z , the groomed and a;g cut ungroomed predictions are identical at the parton level. For values of l that are sufﬁciently large to be described by SCET, corrections for nonperturbative effects must still be applied in order to compare these parton-level calculations to our charged-hadron- level measurements. These nonperturbative effects include hadronization, the underlying event, and the selection of charged particle jets. Note that track-based observables are IRC-unsafe. In general, nonperturbative track functions can be used to directly compare track-based measurements to analytical calculations [16, 74, 75]; however, such an approach has not yet been developed for jet angularities. Two techniques are used, described in the following subsections, to apply the nonperturbative corrections. 5.1.1 MC-based hadronization correction The ﬁrst technique relies solely on MC generators to transform the parton-level calculations into the ﬁnal predictions at the charged-hadron level. Two response matrices are constructed, one using PYTHIA 8.244 and the other using Herwig7, which map the jet angularity distributions from jets reconstructed at the ﬁnal-state parton level (after the parton shower) to those from jets reconstructed at the charged-hadron level. This is done by requiring a unique geometrical match between the parton and charged-hadron-level jets of DR < R=2. The PYTHIA8 simulation uses the default Monash 2013 tune, which is tuned to both e e and pp data [66], with the only change being that the minimum shower p (TimeShower:pTmin) is set to 0.2 GeV=c, one half of its default value, in order to better match the NLL predictions at parton level. Herwig7 is also run with the default tune [76]. The response matrix generated with both MC parton jet parton jet ch jet simulations is 4D, mapping p and l to p and l . a;truth b T;truth 13 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet Since the NLL predictions are generated as normalized distributions, each p interval is ﬁrst scaled by jet a value corresponding to the inclusive p cross section, calculated at Next-to-Leading Order (NLO) with NLL resummation of logarithms in the jet radius [77]. The 4D response matrix discussed above is then jet multiplied by these scaled 2D NLL predictions (in both p , ranging from 10 to 200 GeV=c, and l ) to obtain the theoretical predictions at charged-hadron level. To propagate the systematic uncertainty on the original NLL calculations, this “folding" procedure is performed individually for each of ﬁfteen scale variations, from which a total systematic uncertainty is constructed from the minimum and maximum variation in each interval. Note that this procedure introduces a model-dependence to the comparison, and in fact signiﬁcantly reduces the magnitude of the systematic uncertainties compared to the parton level; the repetition of this procedure with both PYTHIA8 and Herwig7 is meant to estimate the size of this model dependence. Although the perturbative accuracy of the MC generators is not clear, by restricting these comparisons ch jet to p > 60 GeV=c, there is adequate matching between the analytical calculations and the MC gen- erators’ ﬁnal-state parton-level predictions to employ the nonperturbative corrections via this mapping procedure. After the folding step, an additional bin-by-bin correction is applied for multi-parton inter- actions in the underlying event using the respective event generator. More speciﬁcally, a ratio is created between the 2D jet angularity distributions generated with multi-parton interactions on versus off at the charged-hadron level, which is then multiplied bin-by-bin by the folded distributions. In all cases, the corrections performed with PYTHIA and those with Herwig are similar in magnitude, indicating that this correction procedure is reasonable. Figure 5 shows comparisons of the measured ungroomed jet angularities to the folded theoretical predic- ch jet tions for 60 < p < 80 GeV=c, for both R = 0:2 (top) and R = 0:4 (bottom) and for a = 1:5 (left), 2 (middle), and 3 (right). Figure 6 shows the corresponding comparisons for the groomed jet angularities. ch jet The comparisons for 80 < p < 100 GeV=c are shown in Appendix A. Predictions for the a = 1 dis- tributions are not currently available due to enhanced sensitivity to soft-recoil, which requires a different factorization [22]. A dashed vertical line is drawn as a rough estimate for the division of perturbative- and nonperturbative- ch jet dominated regions, via Eq. 3 or Eq. 4 with L = 1 GeV=c and the mean p for each interval. Note that the transition from values of l which are dominated by perturbative versus nonperturbative physics is actually smooth, and this vertical line is merely intended as a visual guide. The nonperturbative- NP dominated region of the jet angularities is denoted as l . Since the integral for all of the distributions in Fig. 1 through Fig. 4 is ﬁxed at unity by construction, it is important to note that disagreement in the nonperturbative-dominated region induces disagreement in the perturbative-dominated region. Discrepancy in the nonperturbative region is expected due to the divergence of a and the corresponding signiﬁcance of higher-order terms in the perturbative expansion — and will necessarily induce disagreement in the perturbative-dominated region. Accordingly, for these NP theoretical comparisons, the distributions are normalized such that the integral above l is unity. 5.1.2 Shape function based correction An alternate correction technique is also used, which employs a nonperturbative shape function F(k) [14, 20, 21] to correct for the effects caused by hadronization and the underlying event. The shape function is deﬁned as 4k 2k F(k) = exp ; (5) W W where k is a momentum scale parameter of the shape function, and W is described by a single parameter W = O(1 GeV=c) obeying the scaling relation W = W=(a 1); (6) 14 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet NP ALICE 18 18 18 λ ≤ Λ / (p R) Data pp s = 5.02 TeV Syst. uncertainty 16 16 charged jets anti-k NLL' ⊗ PYTHIA8 R = 0.2 |η | < 0.7 14 14 jet ch jet NLL' ⊗ Herwig7 60 < p < 80 GeV/c 12 12 12 α = 1.5 α = 2 (×0.3) α = 3 (×0.12) 10 10 8 8 8 6 6 4 4 2 2 2 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 10 0.30 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.1 0.2 λ λ λ α α α 24 24 24 ch jet NP ALICE λ ≤ Λ / (p R) Data 22 22 pp s = 5.02 TeV Syst. uncertainty 20 20 20 charged jets anti-k NLL' ⊗ PYTHIA8 R = 0.4 |η | < 0.5 18 18 18 jet ch jet NLL' ⊗ Herwig7 16 60 < p < 80 GeV/c 16 16 14 14 α = 1.5 α = 2 (×0.65) α = 3 (×0.27) 12 12 10 10 8 8 8 6 6 6 4 4 2 2 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure 5: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions with MC hadronization corrections in the range 60 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α 1-α ALICE λ ≤ z (λ ) Data α ,g cut α pp s = 5.02 TeV Syst. uncertainty charged jets anti-k NLL' ⊗ PYTHIA8 3 3 3 10 10 R = 0.2 |η | < 0.7 Soft Drop: z = 0.2, β = 0 cut jet ch jet NLL' ⊗ Herwig7 60 < p < 80 GeV/c 2 2 2 10 10 α = 1.5 α = 2 α = 3 10 10 1 1 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g NP NP α 1-α ALICE λ ≤ z (λ ) Data α ,g cut α pp s = 5.02 TeV Syst. uncertainty 3 charged jets anti-k 3 NLL' ⊗ PYTHIA8 3 10 T 10 10 R = 0.4 |η | < 0.5 Soft Drop: z = 0.2, β = 0 cut jet ch jet NLL' ⊗ Herwig7 60 < p < 80 GeV/c 2 2 2 10 10 α = 1.5 α = 2 α = 3 10 10 1 1 1 10 0 0.2 0.4 10 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g Figure 6: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions with MC hadronization corrections in the range 60 l (to the right of a;g a;g the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration and expected to hold universally for hadronization corrections (but not necessarily for underlying event corrections). To correct the parton-level calculations to the hadron level, this shape function is convolved with the perturbative (parton level) jet angularity distribution via numerical integration over argument k ds ds pert shift = F(k) l l (k) dk; (7) jet jet dp dl dp dl a a T T shift where the shift term l (k) is either [17, 21]: k k shift 1a l (k) = (ungroomed), or z (groomed, with b = 0). (8) a cut jet jet p R p R T T shift The limits of the integral are thus given by the values of k for which the argument l l (k) is between 0 and 1. Since the nonperturbative parameter W is not calculable within perturbation theory, four values (0.2, 0.4, 0.8, and 2 GeV=c) are chosen to observe the different shifting effects. These distributions are then corrected once more using a similar PYTHIA8 folding procedure as described above to account for the effects of only reconstructing charged-particle jets. This correction is dominated by a shift and jet smearing along the p axis. The comparisons to the ungroomed predictions are shown in Fig. 7, and the groomed predictions are shown in Fig. 8. The shape function approach, speciﬁcally the scaling given in Eq. 6, is not fully justiﬁed in the groomed case [78, 79]; nevertheless, reasonable agreement is observed. Since this shape convolution does not require matching to MC at the parton level, the comparisons are extended to the ch jet 40 < p < 60 GeV=c interval, but below this the perturbative accuracy of the parton-level predictions ch jet ch jet is insufﬁcient for rigorous comparisons. The comparisons for 40 < p < 60 GeV=c and 80 < p < T T 100 GeV=c are shown in Appendix A. 5.2 Discussion The l distributions are generally consistent with the calculations within uncertainties when l is suf- a a jet ﬁciently large to be in the pQCD regime. This holds approximately independent of a , R, and p , and whether or not the jets are groomed. In some distributions, however, particularly for R = 0:4, modest disagreement is observed at large l . This disagreement cannot be unambiguously associated with a particular value of l due to the self-normalization of the observable, but rather demonstrates an overall inconsistency in the shape of the distribution. This disagreement could be caused by the unaccounted power corrections in l , or other effects — and suggests a need for further theoretical investigation. Nev- ertheless, the overall agreement with the perturbative calculations is striking, given the low-to-moderate jet p and R considered. NP For a = 1:5, the majority of the distributions can be described perturbatively, as l is conﬁned towards NP the left-hand side of the distributions. As a increases to a = 3, the inﬂuence of the l region grows, and the ungroomed distributions become strongly nonperturbative. Similarly, as R increases from R = 0:2 to ch jet R = 0:4, or as p increases, the size of the perturbative region increases. In the nonperturbative region NP l < l , the l distributions diverge from the calculations. This is expected, since the perturbative a a NP approximations break down for l < l , and neither the MC or shape function corrections are neces- sarily expected to fully correct for missing physics at higher orders or for nonperturbative coupling. In some distributions, the shape-function-based correction is sometimes able to describe the data partially into the nonperturbative regime for suitable values of W. While the overall level of agreement is comparable in both the ungroomed and groomed cases, grooming widens the pQCD regime, as indicated by the location of the dashed blue line in Figures [5-8]. On the other hand, grooming shifts the distributions themselves to signiﬁcantly smaller values of l . Neverthe- less, this highlights the potential beneﬁt of grooming in heavy-ion collisions in order to retain a larger degree of perturbative control in addition to controlling effects of the underlying event. 17 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet NP Data ALICE 20 20 20 λ ≤ Λ / (p R) Ω=0.2 T pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP 18 18 18 Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 16 16 R = 0.2 |η | < 0.7 NLL' ⊗ F ⊗ PYTHIA8 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 14 14 60 < p < 80 GeV/c NP 12 12 α = 1.5 α = 2 (×0.3) α = 3 (×0.12) 10 10 10 8 8 8 6 6 4 4 2 2 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 10 0.30 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.1 0.2 λ λ λ α α α ch jet NP Data ALICE λ ≤ Λ / (p R) 30 30 30 α Ω=0.2 T pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP 25 25 Ω=0.8 R = 0.4 |η | < 0.5 NLL' ⊗ F ⊗ PYTHIA8 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 60 < p < 80 GeV/c NP 20 20 20 α = 1.5 α = 2 (×0.65) α = 3 (×0.27) 15 15 15 10 10 5 5 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure 7: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions using F(k) convolution in the range 60 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α 4 4 Data 4 1-α ALICE 10 10 λ ≤ z (λ ) α ,g cut α Ω=0.2 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 3 R = 0.2 |η | < 0.7 3 3 Soft Drop: z = 0.2, β = 0 NLL' ⊗ F ⊗ PYTHIA8 cut 10 NP 10 jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 60 < p < 80 GeV/c NP 2 α = 1.5 2 α = 2 2 α = 3 10 10 10 10 10 1 1 1 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g NP NP α Data 1-α ALICE λ ≤ z (λ ) α ,g cut α Ω=0.2 4 4 4 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 10 10 10 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.4 |η | < 0.5 NLL' ⊗ F ⊗ PYTHIA8 Soft Drop: z = 0.2, β = 0 cut NP 3 3 3 jet 10 10 Ω=2.0 10 ch jet NLL' ⊗ F ⊗ PYTHIA8 60 < p < 80 GeV/c NP 2 α = 1.5 2 α = 2 2 α = 3 10 10 10 10 10 1 1 10 0 0.2 0.4 10 0 0.1 0.2 0.310 0 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g Figure 8: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions using F(k) convolution in the range 60 l (to the right of the dashed a;g a;g vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration The performance of the two nonperturbative correction methods — based entirely on MC generators, or on shape functions — are comparable in the perturbative regime. Comparing different values of W for the ungroomed case, where Eq. 6 is justiﬁed, there is in many cases only a small difference between the calculations with W = 0:2, 0.4, and 0.8 GeV=c. However, for a = 1:5 and a = 2, larger values of W (W = 2 GeV=c) appear to have more tension with the data in the perturbative regime than smaller values. For a = 3, the perturbative region is too small to make any clear statement. One must bear in NP mind, however, that l is only a rough characterization of the regime of validity of the perturbative calculation. Consequently, it is unknown whether this disagreement is due to the value of W or due to the breakdown of the perturbative calculation. For smaller values of W (e.g. W = 0:2 or 0:4 GeV=c), the predicted scaling of Eq. 6 is consistent with the data. Note that the value of W which describes the data is O(1) as expected for hadronization corrections. These smaller values contrast with a previous jet result of W = 3:5 GeV=c for the ungroomed mass of R = 0:4 jets at 200 < p < 300 GeV=c [80], suggesting that the underlying event contribution to W, which is not expected to obey the scaling of jet Eq. 6, may be modiﬁed by jets measured at different p or by the choice to reconstruct jets using only charged-particle tracks. No signiﬁcant R-dependence is observed in the scaling behavior in this analysis, suggesting that any scaling-breaking underlying event contributions, when also combined with hadronization corrections, are small for R = 0:2 and 0.4. 6 Conclusion The generalized jet angularities are reported both with and without Soft Drop grooming, l and l , a;g a respectively, for charged-particle jets in pp collisions at s = 5:02 TeV with the ALICE detector. This measurement of both the ungroomed and, for the ﬁrst time, the groomed jet angularities provides con- straints on models and captures the interplay between perturbative and nonperturbative effects in QCD. Systematic variations of the contributions from collinear and soft radiation of the shower, captured within a given R, are provided by measuring the jet angularities for a selection of a parameters. These results consequently provide rigorous tests of pQCD calculations. The theoretical predictions at NLL in SCET show an overall agreement with the data for jets with values of l in the perturbative regime delimited by a collinear-soft momentum scale in the factorization framework of about 1 GeV=c. The calculations, after accounting for nonperturbative effects by two different methods, are compatible within about 20% or better with the data in the perturbative region for all explored values of R and a . However, larger deviations of up to about 50% are observed in the tails of some distributions, suggesting a need for further theoretical study. By making comparisons solely in the perburbatively-dominated regime, consistency is seen with a predicted universal scaling of the nonperturbative shape function parameter W with value W < 1. A clear breakdown of the agreement is observed for small l , where the perturbative calculation is expected to fail. Such nonperturbative effects include soft splittings and hadronization, and these effects dominate over signiﬁcant regions of the phase space of moderate and low-energy jets. This is corroborated by the comparison of the measured groomed jet angularities to the equivalent theoretical calculations, which demonstrate a wider range of agreement with the perturbative calculations. These comparisons provide critical guidance for measurements in high-energy heavy-ion collisions where the internal structure of jets may undergo modiﬁcations via scatterings of jet fragments with the hot and dense QCD medium. Our measurements demonstrate that any comparison to pQCD must also con- sider the regimes of l and l that are controlled by perturbative processes as opposed to those that a a;g are dominated by nonperturbative processes. This provides guidance for the selections of a , R, and ch jet p , and indicates the importance of capturing the complete spectrum of processes (perturbative and non-perturbative) in theory calculations attempting to explain jet quenching. These measurements further highlight that disagreement between theoretical predictions and data in the 20 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration nonperturbative regime will necessarily induce disagreement in the perturbative regime, when in fact the perturbative accuracy of predictions should only be scrutinized within the perturbative regime. In practice, these measurements give a clear indication that careful inspection is needed when interpreting measurements of jet substructure based on models of jet quenching in heavy-ion collisions for observ- ables including the jet angularity and the jet mass. Future measurements will beneﬁt from the provided guidance demonstrating not only the agreement of jet angularities with pQCD calculations in the per- ch jet turbative regime but also on selecting on jet angularity differentially with a , R, and p in order to maximize theoretical control and interpretation of the perturbative and nonpertubative regimes of jet substructure observables. Acknowledgements We gratefully acknowledge Kyle Lee and Felix Ringer for providing theoretical predictions, and for valuable discussions regarding the comparison of these predictions to our measurements. The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable con- tributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics In- stitute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and National- stiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Cientíﬁco e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientiﬁque (CNRS), France; Bundesmin- isterium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Ofﬁce, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientiﬁc and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tec- nología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Coun- cil of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontiﬁcia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technol- 21 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ogy Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientiﬁc Research, Institute of Atomic Physics and Ministry of Research and Innova- tion and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Rus- sian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technol- ogy (SUT), National Science and Technology Development Agency (NSDTA) and Ofﬁce of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Ofﬁce of Nuclear Physics (DOE NP), United States of America. 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T T 25 25 ch jet NP ALICE λ ≤ Λ / (p R) Data pp s = 5.02 TeV Syst. uncertainty charged jets anti-k NLL' ⊗ PYTHIA8 20 20 R = 0.2 |η | < 0.7 jet α = 3 (×0.035) NLL' ⊗ Herwig7 ch jet 80 < p < 100 GeV/c 15 15 15 α = 1.5 α = 2 (×0.42) 10 10 5 5 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 0.1 10 10 10 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 λ λ λ α α α ch jet NP ALICE λ ≤ Λ / (p R) 20 Data 20 20 α pp s = 5.02 TeV Syst. uncertainty 18 18 charged jets anti-k NLL' ⊗ PYTHIA8 16 R = 0.4 |η | < 0.5 16 16 jet NLL' ⊗ Herwig7 ch jet 80 < p < 100 GeV/c 14 14 14 12 12 12 α = 1.5 α = 2 (×0.33) α = 3 (×0.15) 10 10 8 8 6 6 4 4 2 2 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 10 10 10 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure A.1: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions with MC hadronization corrections in the range 80 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α 1-α ALICE λ ≤ z (λ ) Data α ,g cut α pp s = 5.02 TeV 4 4 4 10 10 10 Syst. uncertainty charged jets anti-k NLL' ⊗ PYTHIA8 R = 0.2 |η | < 0.7 Soft Drop: z = 0.2, β = 0 cut jet ch jet NLL' ⊗ Herwig7 80 < p < 100 GeV/c 3 3 3 10 10 10 α = 1.5 α = 2 α = 3 2 2 2 10 10 10 10 10 0 0.1 0.2 0.310 0 0.1 0.2 10 0 0.05 0.1 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 λ λ λ α ,g α ,g α ,g NP NP α 1-α ALICE λ ≤ z (λ ) Data α ,g cut α pp s = 5.02 TeV Syst. uncertainty 3 charged jets anti-k 3 NLL' ⊗ PYTHIA8 3 T 10 10 R = 0.4 |η | < 0.5 Soft Drop: z = 0.2, β = 0 cut jet ch jet NLL' ⊗ Herwig7 80 < p < 100 GeV/c 2 2 2 10 10 α = 1.5 α = 2 α = 3 10 10 1 1 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.310 0 0.05 0.1 0.15 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.05 0.1 0.15 λ λ λ α ,g α ,g α ,g Figure A.2: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions with MC hadronization corrections in the range 80 l (to the right of a;g a;g the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 24 24 ch jet NP Data ALICE λ ≤ Λ / (p R) Ω=0.2 T 22 22 22 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 20 20 20 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.2 |η | < 0.7 18 NLL' ⊗ F ⊗ PYTHIA8 18 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 16 16 16 40 < p < 60 GeV/c NP 14 14 14 α = 1.5 α = 2 (×0.45) α = 3 (×0.06) 12 12 10 10 8 8 6 6 6 4 4 2 2 10 0 0.2 0.4 10 0 0.1 0.2 0.3 10 0.40 0.1 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α 24 24 ch jet NP Data ALICE λ ≤ Λ / (p R) 22 Ω=0.2 22 T pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 20 20 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 18 R = 0.4 |η | < 0.5 18 NLL' ⊗ F ⊗ PYTHIA8 18 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 16 16 40 < p < 60 GeV/c NP 14 14 α = 1.5 α = 2 (×0.45) α = 3 (×0.25) 12 12 10 10 8 8 8 6 6 4 4 4 2 2 10 0 0.2 0.4 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.3 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure A.3: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions using F(k) convolution in the range 40 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration ch jet NP Data ALICE λ ≤ Λ / (p R) Ω=0.2 T pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP 25 25 25 Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.2 |η | < 0.7 NLL' ⊗ F ⊗ PYTHIA8 NP jet α = 3 (×0.035) Ω=2.0 20 ch jet 20 20 NLL' ⊗ F ⊗ PYTHIA8 80 < p < 100 GeV/c NP α = 1.5 α = 2 (×0.42) 15 15 10 10 10 5 5 10 0 0.1 0.2 0.310 0 0.1 0.2 10 0 0.05 0.1 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 λ λ λ α α α 22 22 ch jet 22 NP Data ALICE λ ≤ Λ / (p R) Ω=0.2 T pp s = 5.02 TeV 20 NLL' ⊗ F ⊗ PYTHIA8 20 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP 18 18 18 Ω=0.8 R = 0.4 |η | < 0.5 NLL' ⊗ F ⊗ PYTHIA8 NP jet 16 16 16 Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 80 < p < 100 GeV/c NP 14 14 α = 1.5 12 α = 2 (×0.33) 12 α = 3 (×0.15) 10 10 10 8 8 8 6 6 6 4 4 2 2 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.3 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α α α Figure A.4: Comparison of ungroomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) ch jet to analytical NLL predictions using F(k) convolution in the range 80 l (to the right of the dashed vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α α ∫ ∫ Theory Theory dλ dλ dλ dλ α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α 1 1 Data Data dσ dσ dσ dσ ⁄ dλ ⁄ dλ α α ∫ ∫ dλ dλ dλ dλ Theory Theory α α α α NP NP λ λ α α p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α 4 4 Data 4 1-α ALICE 10 10 10 λ ≤ z (λ ) α ,g cut α Ω=0.2 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 3 3 3 R = 0.2 |η | < 0.7 Soft Drop: z = 0.2, β = 0 NLL' ⊗ F ⊗ PYTHIA8 10 10 cut 10 NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 40 < p < 60 GeV/c NP 2 2 2 α = 1.5 α = 2 α = 3 10 10 10 10 10 1 1 10 0 0.2 0.4 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.3 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0.4 0 0.1 0.2 λ λ λ α ,g α ,g α ,g NP NP α Data 1-α ALICE λ ≤ z (λ ) 4 4 4 α ,g cut α 10 Ω=0.2 10 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 NP Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 3 R = 0.4 |η | < 0.5 3 NLL' ⊗ F ⊗ PYTHIA8 3 Soft Drop: z = 0.2, β = 0 cut 10 NP 10 jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 40 < p < 60 GeV/c NP 2 2 2 10 α = 1.5 10 α = 2 10 α = 3 10 10 10 1 1 10 0 0.2 0.4 10 0 0.1 0.2 0.3 10 0.4 0 0.1 0.2 0.3 1 1 1 - 1 - 1 - 1 10 10 10 0 0.2 0.4 0 0.1 0.2 0.3 0 0.1 0.2 λ λ λ α ,g α ,g α ,g Figure A.5: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions using F(k) convolution in the range 40 l (to the right of the dashed a;g a;g vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration NP NP α Data 1-α ALICE λ ≤ z (λ ) α ,g cut α Ω=0.2 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 4 4 NP 4 10 10 Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.2 |η | < 0.7 Soft Drop: z = 0.2, β = 0 NLL' ⊗ F ⊗ PYTHIA8 cut NP jet Ω=2.0 ch jet NLL' ⊗ F ⊗ PYTHIA8 3 3 3 80 < p < 100 GeV/c NP 10 10 10 α = 1.5 α = 2 α = 3 2 2 2 10 10 10 10 10 0 0.1 0.2 0.310 0 0.1 0.2 10 0 0.05 0.1 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0 0.1 0.2 0 0.05 λ λ λ α ,g α ,g α ,g NP NP α Data 1-α ALICE λ ≤ z (λ ) α ,g cut α Ω=0.2 pp s = 5.02 TeV NLL' ⊗ F ⊗ PYTHIA8 4 4 4 NP 10 10 10 Syst. uncertainty Ω=0.4 charged jets anti-k NLL' ⊗ F ⊗ PYTHIA8 T NP Ω=0.8 R = 0.4 |η | < 0.5 NLL' ⊗ F ⊗ PYTHIA8 Soft Drop: z = 0.2, β = 0 cut NP jet 3 3 3 Ω=2.0 ch jet 10 10 10 NLL' ⊗ F ⊗ PYTHIA8 80 < p < 100 GeV/c NP α = 1.5 α = 2 α = 3 2 2 2 10 10 10 10 10 10 1 1 10 0 0.1 0.2 0.3 0.4 10 0 0.1 0.2 0.310 0 0.05 0.1 0.15 0.2 1 1 1 - 1 - 1 - 1 10 10 10 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0 0.05 0.1 0.15 λ λ λ α ,g α ,g α ,g Figure A.6: Comparison of groomed jet angularities l in pp collisions for R = 0:2 (top) and R = 0:4 (bottom) a;g ch jet to analytical NLL predictions using F(k) convolution in the range 80 l (to the right of the dashed a;g a;g vertical line) is unity. Divided bins are placed into the left (NP) region. 1 1 dσ dσ dσ dσ Data Data ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ Theory dλ dλ Theory dλ dλ α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g 1 1 Data dσ dσ Data dσ dσ ⁄ dλ ⁄ dλ α ,g α ,g ∫ ∫ dλ dλ dλ dλ Theory Theory α ,g α ,g α ,g α ,g NP NP λ λ α ,g α ,g p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration B The ALICE Collaboration 143 98 76 35 31 55 143 S. Acharya , D. Adamová , A. Adler , G. Aglieri Rinella , M. Agnello , N. Agrawal , Z. Ahammed , 16 78 39 52 95 110 16;41 S. Ahmad , S.U. Ahn , I. Ahuja , Z. Akbar , A. Akindinov , M. Al-Turany , S.N. Alam , 91 61 7 73 16 14 26 D. Aleksandrov , B. Alessandro , H.M. Alfanda , R. Alfaro Molina , B. Ali , Y. Ali , A. Alici , 127 35 21 70 21 115 7 N. Alizadehvandchali , A. Alkin , J. Alme , T. Alt , L. Altenkamper , I. Altsybeev , M.N. Anaam , 49 93 146 35 107 58 55 C. Andrei , D. Andreou , A. Andronic , M. Angeletti , V. Anguelov , F. Antinori , P. Antonioli , 16 82 117 70 26 61 20 C. Anuj , N. Apadula , L. Aphecetche , H. Appelshäuser , S. Arcelli , R. Arnaldi , I.C. Arsene , 148;107 35 110 80 16 57 42 M. Arslandok , A. Augustinus , R. Averbeck , S. Aziz , M.D. Azmi , A. Badalà , Y.W. Baek , 131;110 70 51 104 31 140 2 44 X. Bai , R. Bailhache , Y. Bailung , R. Bala , A. Balbino , A. Baldisseri , B. Balis , M. Ball , 4 27 108 87 147 97 137 D. Banerjee , R. Barbera , L. Barioglio , M. Barlou , G.G. Barnaföldi , L.S. Barnby , V. Barret , 130 35 70 28 137 83 117 77 C. Bartels , K. Barth , E. Bartsch , F. Baruffaldi , N. Bastid , S. Basu , G. Batigne , B. Batyunya , 50 114 92 148 139 146 D. Bauri , J.L. Bazo Alba , I.G. Bearden , C. Beattie , I. Belikov , A.D.C. Bell Hechavarria , 26 127 115 96 71 25 49 F. Bellini , R. Bellwied , S. Belokurova , V. Belyaev , G. Bencedi , S. Beole , A. Bercuci , 101 107 107 69 35 143 104 Y. Berdnikov , A. Berdnikova , L. Bergmann , M.G. Besoiu , L. Betev , P.P. Bhaduri , A. Bhasin , 104 4 43 23 25 53 38 I.R. Bhat , M.A. Bhat , B. Bhattacharjee , P. Bhattacharya , L. Bianchi , N. Bianchi , J. Bielcík ˇ , 98 120 108 147 4 121 91 110 J. Bielcík ˇ ová , J. Biernat , A. Bilandzic , G. Biro , S. Biswas , J.T. Blair , D. Blau , M.B. Blidaru , 70 29;59 99 96 23 63 147 96 C. Blume , G. Boca , F. Bock , A. Bogdanov , S. Boi , J. Bok , L. Boldizsár , A. Bolozdynya , 39 35 142;59 140 84 148 25 70 M. Bombara , P.M. Bond , G. Bonomi , H. Borel , A. Borissov , H. Bossi , E. Botta , L. Bratrud , 110 123 38 109;34 130 111 P. Braun-Munzinger , M. Bregant , M. Broz , G.E. Bruno , M.D. Buckland , D. Budnikov , 70 31 117 116 74;134 14 120 H. Buesching , S. Bufalino , O. Bugnon , P. Buhler , Z. Buthelezi , J.B. Butt , S.A. Bysiak , 28;7 148 110 114 122 46 24 M. Cai , H. Caines , A. Caliva , E. Calvo Villar , J.M.M. Camacho , R.S. Camacho , P. Camerini , 123 35;26 140 140 23 31 F.D.M. Canedo , F. Carnesecchi , R. Caron , J. Castillo Castellanos , E.A.R. Casula , F. Catalano , 77 50 143 35 130 143 C. Ceballos Sanchez , P. Chakraborty , S. Chandra , S. Chapeland , M. Chartier , S. Chattopadhyay , 112 23 46 7 138 138 S. Chattopadhyay , A. Chauvin , T.G. Chavez , T. Cheng , C. Cheshkov , B. Cheynis , V. Chibante 35 124 63 35 93 92 83 Barroso , D.D. Chinellato , S. Cho , P. Chochula , P. Christakoglou , C.H. Christensen , P. Christiansen , 136 56 26 55 110 II; 55 I; 126 T. Chujo , C. Cicalo , L. Cifarelli , F. Cindolo , M.R. Ciupek , G. Clai , J. Cleymans , 54 113 109;54;34;147 82 35 III; 61 F. Colamaria , J.S. Colburn , D. Colella , A. Collu , M. Colocci , M. Concas , G. Conesa 81 80 24 38 140 99 32 Balbastre , Z. Conesa del Valle , G. Contin , J.G. Contreras , M.L. Coquet , T.M. Cormier , P. Cortese , 125 35 29;59 137 82 71 7 M.R. Cosentino , F. Costa , S. Costanza , P. Crochet , R. Cruz-Torres , E. Cuautle , P. Cui , 99 58 107 69 112 89 4 4 50 L. Cunqueiro , A. Dainese , M.C. Danisch , A. Danu , I. Das , P. Das , P. Das , S. Das , S. Dash , 89 30 54 25 40 23 30 S. De , A. De Caro , G. de Cataldo , L. De Cilladi , J. de Cuveland , A. De Falco , D. De Gruttola , N. De 61 24 30 51 123 144 30 Marco , C. De Martin , S. De Pasquale , S. Deb , H.F. Degenhardt , K.R. Deja , L. Dello Stritto , 25 7 19 34 35 8 126 138;7 S. Delsanto , W. Deng , P. Dhankher , D. Di Bari , A. Di Mauro , R.A. Diaz , T. Dietel , Y. Ding , 35 19 21 65 63 69 70 20 R. Divià , D.U. Dixit , Ø. Djuvsland , U. Dmitrieva , J. Do , A. Dobrin , B. Dönigus , O. Dordic , 143 110;93 103 89 137 13 146 A.K. Dubey , A. Dubla , S. Dudi , M. Dukhishyam , P. Dupieux , N. Dzalaiova , T.M. Eder , 99 21 70 54 117 26 102 R.J. Ehlers , V.N. Eikeland , F. Eisenhut , D. Elia , B. Erazmus , F. Ercolessi , F. Erhardt , 115 21 80 35 113 94 108 A. Erokhin , M.R. Ersdal , B. Espagnon , G. Eulisse , D. Evans , S. Evdokimov , L. Fabbietti , 28 81 7 53 99 31 61 115 M. Faggin , J. Faivre , F. Fan , A. Fantoni , M. Fasel , P. Fecchio , A. Feliciello , G. Feoﬁlov , 46 140 25 107 120 111 A. Fernández Téllez , A. Ferrero , A. Ferretti , V.J.G. Feuillard , J. Figiel , S. Filchagin , 65 56;21 35;109 127 121 74 110 D. Finogeev , F.M. Fionda , G. Fiorenza , F. Flor , A.N. Flores , S. Foertsch , P. Foka , 91 62 147 35 30 81 65 92 S. Fokin , E. Fragiacomo , E. Frajna , U. Fuchs , N. Funicello , C. Furget , A. Furs , J.J. Gaardhøje , 25 114 139 122 87 110 46 M. Gagliardi , A.M. Gago , A. Gal , C.D. Galvan , P. Ganoti , C. Garabatos , J.R.A. Garcia , 10 117 35 90 146 110 121 E. Garcia-Solis , K. Garg , C. Gargiulo , A. Garibli , K. Garner , P. Gasik , E.F. Gauger , 129 72 117 143 4 26 53 A. Gautam , M.B. Gay Ducati , M. Germain , P. Ghosh , S.K. Ghosh , M. Giacalone , P. Gianotti , 110;61 28 140 107 85 145 P. Giubellino , P. Giubilato , A.M.C. Glaenzer , P. Glässel , D.J.Q. Goh , V. Gonzalez , 73 40 2 120 36 73 L.H. González-Trueba , S. Gorbunov , M. Gorgon , L. Görlich , S. Gotovac , V. Grabski , 144 82 64 35 96 I; 1 77;1 L.K. Graczykowski , L. Greiner , A. Grelli , C. Grigoras , V. Grigoriev , A. Grigoryan , S. Grigoryan , 21 35;61 35 110 124 81 O.S. Groettvik , F. Grosa , J.F. Grosse-Oetringhaus , R. Grosso , G.G. Guardiano , R. Guernane , 117 92 135 7 104 104 46 147 M. Guilbaud , K. Gulbrandsen , T. Gunji , W. Guo , A. Gupta , R. Gupta , S.P. Guzman , L. Gyulai , 110 80 70 85 147 7 121 M.K. Habib , C. Hadjidakis , G. Halimoglu , H. Hamagaki , G. Hamar , M. Hamid , R. Hannigan , 144;89 110 148 10 35 99 M.R. Haque , A. Harlenderova , J.W. Harris , A. Harton , J.A. Hasenbichler , H. Hassan , 55 44 148 135 108 110 37 D. Hatzifotiadou , P. Hauer , L.B. Havener , S. Hayashi , S.T. Heckel , E. Hellbär , H. Helstrup , 38 46 9 146 37 35 T. Herman , E.G. Hernandez , G. Herrera Corral , F. Herrmann , K.F. Hetland , H. Hillemanns , 130 139 64 93 146 149 38 C. Hills , B. Hippolyte , B. Hofman , B. Hohlweger , J. Honermann , G.H. Hong , D. Horak , 110 2 15 7 35 133 70 100 S. Hornung , A. Horzyk , R. Hosokawa , Y. Hou , P. Hristov , C. Hughes , P. Huhn , T.J. Humanic , 112 146 127 40 35;130 111 14 136 H. Hushnud , L.A. Husova , A. Hutson , D. Hutter , J.P. Iddon , R. Ilkaev , H. Ilyas , M. Inaba , 34 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration 35 91 38;98 112 110 101 94 G.M. Innocenti , M. Ippolitov , A. Isakov , M.S. Islam , M. Ivanov , V. Ivanov , V. Izucheev , 2 82 35 82 119 119 64 M. Jablonski , B. Jacak , N. Jacazio , P.M. Jacobs , S. Jadlovska , J. Jadlovsky , S. Jaelani , 124;123 144 104 144 76 102 113 C. Jahnke , M.J. Jakubowska , A. Jalotra , M.A. Janik , T. Janson , M. Jercic , O. Jevons , 71 99;146 113 35;110 70 70 35 A.A.P. Jimenez , F. Jonas , P.G. Jones , J.M. Jowett , J. Jung , M. Jung , A. Junique , 113 118 66 35 96 7 79 102 A. Jusko , J. Kaewjai , P. Kalinak , A. Kalweit , V. Kaplin , S. Kar , A. Karasu Uysal , D. Karatovic , 65 65 144 65 91 76 O. Karavichev , T. Karavicheva , P. Karczmarczyk , E. Karpechev , A. Kazantsev , U. Kebschull , 48 64 35 44 93 7 16 R. Keidel , D.L.D. Keijdener , M. Keil , B. Ketzer , Z. Khabanova , A.M. Khan , S. Khan , 101 94 16 120 37 17;63 17 128 A. Khanzadeev , Y. Kharlov , A. Khatun , A. Khuntia , B. Kileng , B. Kim , C. Kim , D.J. Kim , 75 149 42 107 149 75 107 18 149 70 E.J. Kim , J. Kim , J.S. Kim , J. Kim , J. Kim , J. Kim , M. Kim , S. Kim , T. Kim , S. Kirsch , 40 95 144 2 6 35 82 146 I. Kisel , S. Kiselev , A. Kisiel , J.P. Kitowski , J.L. Klay , J. Klein , S. Klein , C. Klein-Bösing , 70 108 35 127 118 107 110 M. Kleiner , T. Klemenz , A. Kluge , A.G. Knospe , C. Kobdaj , M.K. Köhler , T. Kollegger , 77 96 94 70 108 35;2 A. Kondratyev , N. Kondratyeva , E. Kondratyuk , J. Konig , S.A. Konigstorfer , P.J. Konopka , 144 2 119 98 88 115 120 G. Kornakov , S.D. Koryciak , L. Koska , A. Kotliarov , O. Kovalenko , V. Kovalenko , M. Kowalski , 66 39 110 113;66 98 38 107 I. Králik , A. Kravcáková , L. Kreis , M. Krivda , F. Krizek , K. Krizkova Gajdosova , M. Kroesen , 70 101 40 35 139 93 136 M. Krüger , E. Kryshen , M. Krzewicki , V. Kucera , C. Kuhn , P.G. Kuijer , T. Kumaoka , 143 103 103 35;89 88 65 65 D. Kumar , L. Kumar , N. Kumar , S. Kundu , P. Kurashvili , A. Kurepin , A.B. Kurepin , 111 98 113 63 63 149 40 A. Kuryakin , S. Kushpil , J. Kvapil , M.J. Kweon , J.Y. Kwon , Y. Kwon , S.L. La Pointe , P. La 27 82 118 35 132 35 35;53 35 Rocca , Y.S. Lai , A. Lakrathok , M. Lamanna , R. Langoy , K. Lapidus , P. Larionov , E. Laudi , 35;108 38 115 142;24;59 40 97 L. Lautner , R. Lavicka , T. Lazareva , R. Lea , J. Lehrbach , R.C. Lemmon , I. León 122 19 35;108 147 11 7 132 113 17 Monzón , E.D. Lesser , M. Lettrich , P. Lévai , X. Li , X.L. Li , J. Lien , R. Lietava , B. Lim , 17 40 49 110 19 7 130 21 S.H. Lim , V. Lindenstruth , A. Lindner , C. Lippmann , A. Liu , D.H. Liu , J. Liu , I.M. Lofnes , 96 99 36 107 137 8 146 V. Loginov , C. Loizides , P. Loncar , J.A. Lopez , X. Lopez , E. López Torres , J.R. Luhder , 28 62 41 65 35 44 139 M. Lunardon , G. Luparello , Y.G. Ma , A. Maevskaya , M. Mager , T. Mahmoud , A. Maire , 101 104 20 IV; 77 95 51 110 M. Malaev , N.M. Malik , Q.W. Malik , L. Malinina , D. Mal’Kevich , N. Mallick , P. Malzacher , 33;57 91 137 54 7 68 24 G. Mandaglio , V. Manko , F. Manso , V. Manzari , Y. Mao , J. Mareš , G.V. Margagliotti , 55 110 121 70 107 35 127 A. Margotti , A. Marín , C. Markert , M. Marquard , N.A. Martin , P. Martinengo , J.L. Martinez , 46 117 110 25 56 80 M.I. Martínez , G. Martínez García , S. Masciocchi , M. Masera , A. Masoni , L. Massacrier , 141;54 108 83 123 120 120 A. Mastroserio , A.M. Mathis , O. Matonoha , P.F.T. Matuoka , A. Matyja , C. Mayer , 35 25 35 I; 60 134 70 22 A.L. Mazuecos , F. Mazzaschi , M. Mazzilli , M.A. Mazzoni , J.E. Mdhluli , A.F. Mechler , F. Meddi , 65 73 116;30 127 13 126;74 Y. Melikyan , A. Menchaca-Rocha , E. Meninno , A.S. Menon , M. Meres , S. Mhlanga , 136 61;25 138 108 77;95 147 Y. Miake , L. Micheletti , L.C. Migliorin , D.L. Mihaylov , K. Mikhaylov , A.N. Mishra , 110 4 64 89 V; 16 45 D. Misk ´ owiec , A. Modak , A.P. Mohanty , B. Mohanty , M. Mohisin Khan , M.A. Molander , 92 108 146 46 65 35 Z. Moravcova , C. Mordasini , D.A. Moreira De Godoy , L.A.P. Moreno , I. Morozov , A. Morsch , 35 53 36 146 143 82 23 T. Mrnjavac , V. Muccifora , E. Mudnic , D. Mühlheim , S. Muhuri , J.D. Mulligan , A. Mulliri , 123 70 135 126 35 66 144 M.G. Munhoz , R.H. Munzer , H. Murakami , S. Murray , L. Musa , J. Musinsky , J.W. Myrcha , 134;50 88 50 55 54 14 83 107 B. Naik , R. Nair , B.K. Nandi , R. Nania , E. Nappi , M.U. Naru , A.F. Nassirpour , A. Nath , 133 20 71 37 40 115 92 C. Nattrass , A. Neagu , L. Nellen , S.V. Nesbo , G. Neskovic , D. Nesterov , B.S. Nielsen , 91 91 101 55 12 77 130 S. Nikolaev , S. Nikulin , V. Nikulin , F. Noferini , S. Noh , P. Nomokonov , J. Norman , 136 144 91 21 85 83 96 N. Novitzky , P. Nowakowski , A. Nyanin , J. Nystrand , M. Ogino , A. Ohlson , V.A. Okorokov , 144 133 148 128 61 J. Oleniacz , A.C. Oliveira Da Silva , M.H. Oliver , A. Onnerstad , C. Oppedisano , A. Ortiz 71 47 83 120 85 107 50 Velasquez , T. Osako , A. Oskarsson , J. Otwinowski , K. Oyama , Y. Pachmayer , S. Padhan , 142;59 71 54 145 140 143 63 128 D. Pagano , G. Paic ´ , A. Palasciano , J. Pan , S. Panebianco , P. Pareek , J. Park , J.E. Parkkila , 127 104;35 23 7 64 7 72 S.P. Pathak , R.N. Patra , B. Paul , H. Pei , T. Peitzmann , X. Peng , L.G. Pereira , H. Pereira Da 140 91 8 140 5 38 49 117;72 Costa , D. Peresunko , G.M. Perez , S. Perrin , Y. Pestov , V. Petrácek ˇ , M. Petrovici , R.P. Pezzi , 62 13 117 55;35 127 27 53 82 S. Piano , M. Pikna , P. Pillot , O. Pinazza , L. Pinsky , C. Pinto , S. Pisano , M. Płoskon ´ , 102 70 99 94 31 102 49 M. Planinic , F. Pliquett , M.G. Poghosyan , B. Polichtchouk , S. Politano , N. Poljak , A. 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Yadav , S. Yalcin , Y. Yamaguchi , K. Yamakawa , S. Yang , S. Yano , Z. Yin , H. Yokoyama , 17 63 21 107 24 14 35 64 I.-K. Yoo , J.H. Yoon , S. Yuan , A. Yuncu , V. Zaccolo , A. Zaman , C. Zampolli , H.J.C. Zanoli , 35 115 68 111 101 7 41 N. Zardoshti , A. Zarochentsev , P. Závada , N. Zaviyalov , M. Zhalov , B. Zhang , S. Zhang , 7 131 115 11 95 7 92 7;110 X. Zhang , Y. Zhang , V. Zherebchevskii , Y. Zhi , N. Zhigareva , D. Zhou , Y. Zhou , J. Zhu , 7 26 3 142;59 Y. Zhu , A. Zichichi , G. Zinovjev , N. Zurlo Afﬁliation notes Deceased II Also at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India VI Also at: Institute of Theoretical Physics, University of Wroclaw, Poland Collaboration Institutes A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia AGH University of Science and Technology, Cracow, Poland Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India Budker Institute for Nuclear Physics, Novosibirsk, Russia California Polytechnic State University, San Luis Obispo, California, United States 36 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration Central China Normal University, Wuhan, China Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico Chicago State University, Chicago, Illinois, United States China Institute of Atomic Energy, Beijing, China Chungbuk National University, Cheongju, Republic of Korea Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovakia COMSATS University Islamabad, Islamabad, Pakistan Creighton University, Omaha, Nebraska, United States Department of Physics, Aligarh Muslim University, Aligarh, India Department of Physics, Pusan National University, Pusan, Republic of Korea Department of Physics, Sejong University, Seoul, Republic of Korea Department of Physics, University of California, Berkeley, California, United States Department of Physics, University of Oslo, Oslo, Norway Department of Physics and Technology, University of Bergen, Bergen, Norway Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia, Pavia, Italy Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy European Organization for Nuclear Research (CERN), Geneva, Switzerland Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic Faculty of Science, P.J. Šafárik University, Košice, Slovakia Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany Fudan University, Shanghai, China Gangneung-Wonju National University, Gangneung, Republic of Korea Gauhati University, Department of Physics, Guwahati, India Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany Helsinki Institute of Physics (HIP), Helsinki, Finland High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico Hiroshima University, Hiroshima, Japan Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation (ZTT), Worms, Germany Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania Indian Institute of Technology Bombay (IIT), Mumbai, India Indian Institute of Technology Indore, Indore, India Indonesian Institute of Sciences, Jakarta, Indonesia INFN, Laboratori Nazionali di Frascati, Frascati, Italy INFN, Sezione di Bari, Bari, Italy INFN, Sezione di Bologna, Bologna, Italy INFN, Sezione di Cagliari, Cagliari, Italy INFN, Sezione di Catania, Catania, Italy INFN, Sezione di Padova, Padova, Italy 37 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration INFN, Sezione di Pavia, Pavia, Italy INFN, Sezione di Roma, Rome, Italy INFN, Sezione di Torino, Turin, Italy INFN, Sezione di Trieste, Trieste, Italy Inha University, Incheon, Republic of Korea Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands Institute for Nuclear Research, Academy of Sciences, Moscow, Russia Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic Institute of Space Science (ISS), Bucharest, Romania Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico iThemba LABS, National Research Foundation, Somerset West, South Africa Jeonbuk National University, Jeonju, Republic of Korea Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany Joint Institute for Nuclear Research (JINR), Dubna, Russia Korea Institute of Science and Technology Information, Daejeon, Republic of Korea KTO Karatay University, Konya, Turkey Laboratoire de Physique des 2 Inﬁnis, Irène Joliot-Curie, Orsay, France Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France Lawrence Berkeley National Laboratory, Berkeley, California, United States Lund University Department of Physics, Division of Particle Physics, Lund, Sweden Moscow Institute for Physics and Technology, Moscow, Russia Nagasaki Institute of Applied Science, Nagasaki, Japan Nara Women’s University (NWU), Nara, Japan National and Kapodistrian University of Athens, School of Science, Department of Physics , Athens, Greece National Centre for Nuclear Research, Warsaw, Poland National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India National Nuclear Research Center, Baku, Azerbaijan National Research Centre Kurchatov Institute, Moscow, Russia Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark Nikhef, National institute for subatomic physics, Amsterdam, Netherlands NRC Kurchatov Institute IHEP, Protvino, Russia NRC «Kurchatov»Institute - ITEP, Moscow, Russia NRNU Moscow Engineering Physics Institute, Moscow, Russia Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom Nuclear Physics Institute of the Czech Academy of Sciences, Rež u Prahy, Czech Republic Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States Ohio State University, Columbus, Ohio, United States Petersburg Nuclear Physics Institute, Gatchina, Russia Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia Physics Department, Panjab University, Chandigarh, India Physics Department, University of Jammu, Jammu, India Physics Department, University of Rajasthan, Jaipur, India Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany Physik Department, Technische Universität München, Munich, Germany Politecnico di Bari and Sezione INFN, Bari, Italy Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany Russian Federal Nuclear Center (VNIIEF), Sarov, Russia 38 p Measurements of the jet angularities in pp collisions at s = 5:02 TeV ALICE Collaboration Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom Sección Física, Departamento de Ciencias, Pontiﬁcia Universidad Católica del Perú, Lima, Peru St. Petersburg State University, St. Petersburg, Russia Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France Suranaree University of Technology, Nakhon Ratchasima, Thailand Technical University of Košice, Košice, Slovakia The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland The University of Texas at Austin, Austin, Texas, United States Universidad Autónoma de Sinaloa, Culiacán, Mexico Universidade de São Paulo (USP), São Paulo, Brazil Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil Universidade Federal do ABC, Santo Andre, Brazil University of Cape Town, Cape Town, South Africa University of Houston, Houston, Texas, United States University of Jyväskylä, Jyväskylä, Finland University of Kansas, Lawrence, Kansas, United States University of Liverpool, Liverpool, United Kingdom University of Science and Technology of China, Hefei, China University of South-Eastern Norway, Tonsberg, Norway University of Tennessee, Knoxville, Tennessee, United States University of the Witwatersrand, Johannesburg, South Africa University of Tokyo, Tokyo, Japan University of Tsukuba, Tsukuba, Japan Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Inﬁnis de Lyon , Lyon, France Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Saclay, France Università degli Studi di Foggia, Foggia, Italy Università di Brescia, Brescia, Italy Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India Warsaw University of Technology, Warsaw, Poland Wayne State University, Detroit, Michigan, United States Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany Wigner Research Centre for Physics, Budapest, Hungary Yale University, New Haven, Connecticut, United States Yonsei University, Seoul, Republic of Korea

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High Energy Physics - Experiment – arXiv (Cornell University)

Published: Jul 23, 2021

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Measurements of the groomed and ungroomed jet angularities in pp collisions at $\sqrt{s} = 5.02$ TeV

Measurements of the groomed and ungroomed jet angularities in pp collisions at $\sqrt{s} = 5.02$ TeV

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Measurements of the groomed and ungroomed jet angularities in pp collisions at $\sqrt{s} = 5.02$ TeV

Measurements of the groomed and ungroomed jet angularities in pp collisions at $\sqrt{s} = 5.02$ TeV

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