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

Citations Over TimeTop 1% of 2017 papers

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, $16(L\ensuremath{\cap}B)+1(\overline{)L}\ensuremath{\cap}B)+2(\overline{)L}\ensuremath{\cap}\overline{)B})$ at dim-6 and $47(\overline{)L}\ensuremath{\cap}B)+5(\overline{)L}\ensuremath{\cap}\overline{)B})$ at dim-7. Here $L/B(\overline{)L}/\overline{)B})$ stands for lepton/baryon number conservation (violation). We verify our counting by the Hilbert series approach for ${n}_{f}$ 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 ${n}_{f}=1$ (3).

Related Papers

• → A model for neutrino anomalies and IceCube data(2019)5 cited
• → Mass properties of active and sterile neutrinos in a phenomenological (3 + 1 + 2) model(2014)14 cited
• → Radiative emission of neutrino pairs in atoms and light sterile neutrinos(2015)7 cited
• → An unorthodox alternative for righthanded neutrinos: lefthanded see-saw(1999)