The Electroweak Chiral Lagrangian and New Precision Measurements

TL;DR

This work presents a revised, complete electroweak chiral Lagrangian up to dimension four, connecting its operators to oblique parameters $S$, $T$, $U$ and to triple gauge vertices $WW\gamma$ and $WWZ$. It provides a concrete operator basis using the $SU(2)_L\times SU(2)_C$-covariant framework, including a newly identified CP-invariant term corresponding to $g_5^Z$, and discusses how these operators encapsulate high-energy physics above $\Lambda_{\chi}$. A one-loop analysis with a heavy fermion doublet yields quantitative estimates for the oblique parameters and TGV deviations, showing typical effects at the $10^{-3}$ level (with potential $10^{-2}$ in multi-doublet scenarios) and small $g_5^Z$ values around $10^{-4}$, potentially observable at a 500 GeV $e^+e^-$ collider. The results provide a practical bridge between low-energy precision tests and high-energy dynamics, reinforcing the chiral Lagrangian as a comprehensive description of beyond-Standard-Model effects in the electroweak sector. The Appendix completes the CP-violating operator set, underscoring the framework's completeness and its predictive power for future experiments.

Abstract

A revised and complete list of the electroweak chiral lagrangian operators up to dimension-four is provided. The connection of these operators to the $S$, $T$ and $U$ parameters and the parameters describing the triple gauge boson vertices $WWγ$ and $WWZ$ is made, and the size of these parameters from new heavy physics is estimated using a one flavor-doublet model of heavy fermions. The coefficients of the chiral lagrangian operators are also computed in this model.