The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle"

TL;DR

This paper develops a comprehensive non-linear effective Lagrangian framework for a light dynamical Higgs in electroweak symmetry breaking, introducing the non-linearity parameter $\xi = (v/f)^2$ to interpolate between linear and strongly-coupled regimes. It constructs a complete CP-even basis of pure-gauge and gauge–Higgs operators up to four derivatives, incorporating $h$-dependent insertions through generic functions ${\cal F}(h)$ and organizing operators by powers of $\xi$ to illuminate their linear siblings. The authors extend the traditional Appelquist–Longhitano chiral basis, include derivative-rich structures, and discuss custodial-symmetry breaking and redundancies when fermion masses are neglected, mapping their basis to existing linear (e.g., SILH) frameworks. The work provides a model-independent toolkit to explore exotic gauge–Higgs couplings and their phenomenological impact, with implications for interpreting LHC data within both non-linear and linear electroweak breaking scenarios.

Abstract

We generalize the basis of CP-even chiral effective operators describing a dynamical Higgs sector, to the case in which the Higgs-like particle is light. Gauge and gauge-Higgs operators are considered up to mass dimension five. This analysis completes the tool needed to explore at leading order the connection between linear realizations of the electroweak symmetry breaking mechanism - whose extreme case is the Standard Model - and non-linear realizations with a light Higgs-like particle present. It may also provide a model-independent guideline to explore which exotic gauge-Higgs couplings may be expected, and their relative strength to Higgsless observable amplitudes. With respect to fermions, the analysis is reduced by nature to the consideration of those flavour-conserving operators that can be written in terms of pure-gauge or gauge-Higgs ones via the equations of motion, but for the standard Yukawa-type couplings.