Abstract
We revisit the effective field theory of the standard model that is extended with sterile neutrinos, . We examine the basis of complete and independent effective operators involving 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 are, without counting Hermitian conjugates, at dim-6 and at dim-7. Here stands for lepton/baryon number conservation (violation). We verify our counting by the Hilbert series approach for 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 (3).
- Received 24 February 2017
DOI:https://doi.org/10.1103/PhysRevD.96.015012
© 2017 American Physical Society