The electroweak chiral Lagrangian revisited

TL;DR

This paper revisits the electroweak chiral Lagrangian, demonstrating redundancies in low-energy constants and analyzing their implications for different models and experimental data.

Contribution

It shows that two low-energy constants are redundant using gauge-invariant methods and compares their values in the Standard Model and Technicolor models.

Findings

Two low-energy constants can be removed without loss of generality.

The pattern of constants differs significantly between models.

Current data do not exclude strongly interacting symmetry breaking models.

Abstract

Using a manifestly gauge-invariant approach we show that the set of low-energy constants in the electroweak chiral Lagrangian 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. The relation of this result to the experimentally determined values for the oblique parameters S,T and U is discussed. We then evaluate the matching relation between gauge-invariant Green's functions in the full and the effective theory for the case of the Standard Model with a heavy Higgs boson and compare the results for the independent low-energy constants with those for a simple Technicolor model. Since the pattern of the low-energy constants is very different in these two models it may be misleading to mimic any strongly interacting symmetry breaking sector by a heavy Higgs boson. From our investigation we conclude that current electroweak precision data do not really rule out such strongly interacting models.