The electroweak chiral Lagrangian reanalyzed

TL;DR

This paper reanalyzes the electroweak chiral Lagrangian using a gauge-invariant approach, clarifying the redundancy of low-energy constants and providing a method to determine these constants through matching full and effective theories.

Contribution

It introduces a gauge-invariant method for analyzing the electroweak chiral Lagrangian and clarifies the redundancy of certain low-energy constants, including their relation to experimental parameters.

Findings

Redundancy of low-energy constants in the no-fermion case.

Removal of certain constants affecting gauge boson self-energies.

Explicit calculation of low-energy constants for the Standard Model with a heavy Higgs.

Abstract

In this paper we reanalyze the electroweak chiral Lagrangian with particular focus on two issues related to gauge invariance. Our analysis is based on a manifestly gauge-invariant approach that we introduced recently. It deals with gauge-invariant Green's functions and provides a method to evaluate the corresponding generating functional without fixing the gauge. First we show, for the case where no fermions are included in the effective Lagrangian, that the set of low-energy constants currently used in the literature is redundant. In particular, by employing the equations of motion for the gauge fields one can choose to remove two low-energy constants which contribute to the self-energies of the gauge bosons. If fermions are included in the effective field theory analysis the situation is more involved. Even in this case, however, these contributions to the self-energies of the gauge bosons can be removed. The relation of this result to the experimentally determined values for the oblique parameters S, T, and U is discussed. In the second part of the paper we consider the matching relation between a full and an effective theory. We show how the low-energy constants of the effective Lagrangian can be determined by matching gauge-invariant Green's functions in both theories. As an application we explicitly evaluate the low-energy constants for the standard model with a heavy Higgs boson. The matching at the one-loop level and at next-to-leading order in the low-energy expansion is performed employing functional methods.