2016/12/14 by Yi Liao, Xiao-Dong Ma · 188 citations
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Dimension (graph theory) #Fermion #Hermitian matrix #Mathematical physics #Mathematics #Neutrino #Neutrino Physics Research #Neutrino oscillation #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Standard Model (mathematical formulation) #Sterile neutrino #hep-ph
paper · pdf · doi:10.1103/physrevd.96.015012
published in Physical review. D/Physical review. D. 96(1) (American Physical Society) · 14 pages, 0 figures, 4 tables
arxiv created 2016/12/14 · openalex created_date 2017/02/24 · openalex publication_date 2017/07/13 · arxiv updated 2017/07/19 · openalex updated_date 2026/08/05
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\ensuremath∩B)+1()L\ensuremath∩B)+2()L\ensuremath∩)B) at dim-6 and 47()L\ensuremath∩B)+5()L\ensuremath∩)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).