On the renormalization of the electroweak chiral Lagrangian with a Higgs

TL;DR

This paper develops a comprehensive renormalization framework for the scalar sector of the electroweak chiral Lagrangian with a light Higgs, including one-loop corrections and new counterterms, facilitating future Higgs data analysis.

Contribution

It provides the complete off-shell renormalization procedure for the non-linear electroweak Lagrangian with a Higgs, identifying all necessary counterterms and proposing a new parametrization for field redefinitions.

Findings

Derived the full set of scalar counterterms for consistency.

Identified chiral non-invariant counterterms involving the Higgs.

Formulated renormalization group equations for future Higgs data comparison.

Abstract

We consider the scalar sector of the effective non-linear electroweak Lagrangian with a light "Higgs" particle, up to four derivatives in the chiral expansion. The complete off-shell renormalization procedure is implemented, including one loop corrections stemming from the leading two-derivative terms, for finite Higgs mass. This determines the complete set of independent chiral invariant scalar counterterms required for consistency; these include bosonic operators often disregarded. Furthermore, new counterterms involving the Higgs particle which are apparently chiral non-invariant are identified in the perturbative analysis. A novel general parametrization of the pseudoescalar field redefinitions is proposed, which reduces to the various usual ones for specific values of its parameter; the non-local field redefinitions reabsorbing all chiral non-invariant counterterms are then explicitly determined. The physical results translate into renormalization group equations which may be useful when comparing future Higgs data at different energies.