Complete NLO operators in the Higgs effective field theory

Abstract

We enumerate the complete and independent sets of operators at the next-to-leading order (NLO) in the Higgs effective field theory (HEFT), based on the Young tensor technique on the Lorentz, gauge, and flavor structures. The operator-amplitude correspondence tells a type of operator forms the on-shell amplitude basis, and for operators involved in Nambu-Goldstone bosons, the amplitude basis is further reduced to the subspace satisfying the Adler zero condition in the soft momentum limit. Different from dynamical fields, the spurion should not enter into the Lorentz sector, instead, it only plays the role of forming the SU(2) invariant together with other dynamical fields. With these new treatments, for the first time, we could obtain the 224 (7704) operators for one (three) generation fermions, 295 (11307) with right-handed neutrinos, and find there were 8 (11) terms of operators missing and many redundant operators can be removed in the effective theory without (with) right-handed neutrinos.