Operator bases in effective field theories with sterile neutrinos: d ≤ 9
Hao-Lin Li, Zhe Ren, Ming-Lei Xiao, Jiang-Hao Yu, Yu-Hui Zheng
Abstract
A bstract 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 ( ν SMEFT) and low energy effective field theory with light sterile neutrinos ( ν 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 ν 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 ν LEFT for two generations of up-type quarks and three generations of all other fermions.