Operator Bases in Effective Field Theories with Sterile Neutrinos: $d \leq 9$

TL;DR

This paper systematically constructs complete bases of effective operators involving sterile neutrinos up to dimension 9 in both SMEFT and LEFT frameworks, enabling comprehensive parametrization of neutrino-related effects.

Contribution

It provides the first complete and independent operator bases at dimensions 5 to 9 for theories with sterile neutrinos, including detailed enumeration for different generations.

Findings

Identified 2 to 1358 operators in νSMEFT depending on dimension and generations.

Found 24 to 789,426 operators in νLEFT across dimensions and generations.

Established systematic parametrization of Lorentz-invariant effects involving sterile neutrinos.

Abstract

We obtain the complete and independent bases of effective operators at mass dimension 5, 6, 7, 8, 9 in both standard model effective field theory with light sterile right-handed neutrinos ($\nu$SMEFT) and low energy effective field theory with light sterile neutrinos ($\nu$LEFT). These theories provide systematical parametrizations on all possible Lorentz-invariant physical effects involving in the Majorana/Dirac neutrinos, with/without the lepton number violations. In the $\nu$SMEFT, we find that there are 2 (18), 29 (1614), 80 (4206), 323 (20400), 1358 (243944) independent operators with sterile neutrinos included at the dimension 5, 6, 7, 8, 9 for one (three) generation of fermions, while 24, 5223, 3966, 25425, 789426 independent operators in the $\nu$LEFT.