\(\tau\) vector and axial-vector spectral functions in the extended linear sigma model

TL;DR

This paper extends the linear sigma model to include electroweak interactions, effectively describing vector and axial-vector meson spectral functions and their resonance contributions within a gauge-invariant framework.

Contribution

It introduces a gauge-invariant extension of the linear sigma model combining chiral and electroweak symmetries for hadron spectral analysis.

Findings

Spectral functions are well described by nd  resonances.

Resonant and non-resonant channels are both essential for accurate spectral lineshapes.

The model successfully integrates electroweak interactions with hadronic phenomenology.

Abstract

The extended linear sigma model describes the vacuum phenomenology of scalar, pseudoscalar, vector and axial-vector mesons at energies \(\simeq 1\text{ GeV}\). We combine the chiral \(U(2)_L\times U(2)_R\) symmetry of this model with a local \(SU(2)_L\times U(1)_Y\) symmetry and obtain a gauge invariant effective description for electroweak interaction of hadrons in the vacuum. Vector and axial-vector spectral functions can be described well by two intermediate resonances \(\rho\) and \(a_1\). They are implemented into this model as chiral partners and yield the predominant contributions to both spectral functions. However, the contributions that arise from the non-resonant decay channels of the weak charged \(W\) bosons are essential for reproducing the lineshapes of the spectral functions.