Operators up to dimension seven in standard model effective field theory extended with sterile neutrinos

Operators up to dimension seven in standard model effective field theory extended with sterile... We revisit the effective field theory of the standard model that is extended with sterile neutrinos, N. We examine the basis of complete and independent effective operators involving N up to mass dimension seven (dim-7). By employing equations of motion, integration by parts, and Fierz and group identities, we construct relations among operators that were considered independent in the previous literature, and we find 7 redundant operators at dim-6, as well as 16 redundant operators and two new operators at dim-7. The correct numbers of operators involving N are, without counting Hermitian conjugates, 16(L∩B)+1(L∩B)+2(L∩B) at dim-6 and 47(L∩B)+5(L∩B) at dim-7. Here L/B(L/B) stands for lepton/baryon number conservation (violation). We verify our counting by the Hilbert series approach for nf generations of the standard model fermions and sterile neutrinos. When operators involving different flavors of fermions are counted separately and their Hermitian conjugates are included, we find there are 29 (1614) and 80 (4206) operators involving sterile neutrinos at dim-6 and dim-7, respectively, for nf=1 (3). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Operators up to dimension seven in standard model effective field theory extended with sterile neutrinos

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Operators up to dimension seven in standard model effective field theory extended with sterile neutrinos

Abstract

We revisit the effective field theory of the standard model that is extended with sterile neutrinos, N. We examine the basis of complete and independent effective operators involving N up to mass dimension seven (dim-7). By employing equations of motion, integration by parts, and Fierz and group identities, we construct relations among operators that were considered independent in the previous literature, and we find 7 redundant operators at dim-6, as well as 16 redundant operators and two new operators at dim-7. The correct numbers of operators involving N are, without counting Hermitian conjugates, 16(L∩B)+1(L∩B)+2(L∩B) at dim-6 and 47(L∩B)+5(L∩B) at dim-7. Here L/B(L/B) stands for lepton/baryon number conservation (violation). We verify our counting by the Hilbert series approach for nf generations of the standard model fermions and sterile neutrinos. When operators involving different flavors of fermions are counted separately and their Hermitian conjugates are included, we find there are 29 (1614) and 80 (4206) operators involving sterile neutrinos at dim-6 and dim-7, respectively, for nf=1 (3).
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.96.015012
Publisher site
See Article on Publisher Site

Abstract

We revisit the effective field theory of the standard model that is extended with sterile neutrinos, N. We examine the basis of complete and independent effective operators involving N up to mass dimension seven (dim-7). By employing equations of motion, integration by parts, and Fierz and group identities, we construct relations among operators that were considered independent in the previous literature, and we find 7 redundant operators at dim-6, as well as 16 redundant operators and two new operators at dim-7. The correct numbers of operators involving N are, without counting Hermitian conjugates, 16(L∩B)+1(L∩B)+2(L∩B) at dim-6 and 47(L∩B)+5(L∩B) at dim-7. Here L/B(L/B) stands for lepton/baryon number conservation (violation). We verify our counting by the Hilbert series approach for nf generations of the standard model fermions and sterile neutrinos. When operators involving different flavors of fermions are counted separately and their Hermitian conjugates are included, we find there are 29 (1614) and 80 (4206) operators involving sterile neutrinos at dim-6 and dim-7, respectively, for nf=1 (3).

Journal

Physical Review DAmerican Physical Society (APS)

Published: Jul 1, 2017

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