Off-shell renormalization in Higgs effective field theories

TL;DR

This paper develops an off-shell one-loop renormalization method for Higgs effective field theories with arbitrary scalar potentials, utilizing auxiliary fields and symmetry constraints to derive algebraic mappings and analyze Higgs self-couplings.

Contribution

It introduces a novel off-shell renormalization approach for Higgs EFTs with arbitrary potentials using auxiliary fields and symmetry constraints.

Findings

Higgs field undergoes a linear Standard Model-like redefinition.

Explicit renormalization of Higgs self-couplings is achieved.

Method applies to the large N limit of the potential.

Abstract

The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential $\sim\left(\Phi^\dagger\Phi-\frac{v^2}2\right)^N$ with $N$ arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields $X_{1,2}$, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the $N\to\infty$ case.