Lepton-Number Violation in Higgs Effective Field Theory: Complete Operator Basis and Type-II Seesaw Matching

Abstract

We construct a complete and nonredundant basis of lepton-number-violating (LNV) operators in the Higgs effective field theory (HEFT) through $\mathcal{O}(p^4)$, including their full flavor multiplicities. Using a complex dressed spurion that encodes the $B-L$ charge, we classify the $\Delta L=2$ and $\Delta L=4$ sectors, including baryon-number-violating operators, and independently validate the counting using Hilbert-series methods. As a concrete application, we present the first complete tree-level matching of the type-II seesaw model onto HEFT through $\mathcal{O}(p^4)$, covering the bosonic, lepton-number-conserving, and LNV sectors. Using the nonlinear field representation and primary-HEFT power counting, we retain the full dependence of the matching coefficients on the independent scalar masses, the neutral-scalar mixing, and the doublet and triplet vacuum expectation values. We compare our results with the corresponding real-triplet matching and a broken-phase effective field theory. We further discuss implications for LNV processes, Higgs physics, and electroweak observables.

arXiv comment53 pages