Using the modified matrix element method to constrain Lμ-Lτ interactions

Abstract

In this paper, we explore the discriminatory power of the matrix element method (MEM) in constraining the Lμ-Lτ model at the LHC. The Z′ boson associated with the spontaneously broken U(1)Lμ-Lτ symmetry only interacts with the second and third generation of leptons at tree level, and is thus difficult to produce at the LHC. We argue that the best channels for discovering this Z′ are in Z→4μ and 2μ+ET. Both these channels have a large number of kinematic observables, which strongly motivates the usage of a multivariate technique. The MEM is a multivariate analysis that uses the squared matrix element |M|2 to quantify the likelihood of the testing hypotheses. As the computation of the |M|2 requires knowing the initial and final state momenta and the model parameters, it is not commonly used in new physics searches. Conventionally, new parameters are estimated by maximizing the likelihood of the signal with respect to the background, and we outline scenarios in which this procedure is (in)effective. We illustrate that the new parameters can also be estimated by studying the |M|2 distributions, and, even if our parameter estimation is off, we can gain better sensitivity than cut-and-count methods. Additionally, unlike the conventional MEM, where one integrates over all unknown momenta in processes with ET, we show an example scenario where these momenta can be estimated using the process topology. This procedure, which we refer to as the “modified squared matrix element,” is computationally much faster than the canonical matrix element method and maintains signal-background discrimination. Bringing the MEM and the aforementioned modifications to bear on the Lμ-Lτ model, we find that with 300  fb-1 of integrated luminosity, we are sensitive to the couplings of gZ′≳0.002g1 and MZ′<20  GeV, and gZ′≳0.005g1 and 20  GeV<MZ′<40  GeV, which is about an order of magnitude improvement over the cut-and-count method for the same amount of data.