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 𝒪(p4), including their full flavor multiplicities. Using a complex dressed spurion that encodes the B−L charge, we classify the ΔL=2 and ΔL=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 𝒪(p4), 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.
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BibTeX
@misc{ge2026leptonnumber,
title = {{Lepton-Number Violation in Higgs Effective Field Theory: Complete Operator Basis and Type-II Seesaw Matching}},
author = {Zizhou Ge and Huayang Song and Xia Wan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.26184},
eprint = {2607.26184},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.26184},
}
RIS
TY - UNPB
TI - Lepton-Number Violation in Higgs Effective Field Theory: Complete Operator Basis and Type-II Seesaw Matching
AU - Zizhou Ge
AU - Huayang Song
AU - Xia Wan
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2607.26184
UR - https://arxiv.org/abs/2607.26184
AB - We construct a complete and nonredundant basis of lepton-number-violating (LNV) operators in the Higgs effective field theory (HEFT) through 𝒪(p^4), including their full flavor multiplicities. Using a complex dressed spurion that encodes the B−L charge, we classify the ΔL=2 and ΔL=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 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.
ER -