Study of an anomalous tau lepton decay using a chiral Lagrangian with vector mesons

TL;DR

This paper analyzes the anomalous tau lepton decay into hadrons using a chiral Lagrangian approach that includes vector mesons, highlighting the effects of isospin breaking and intrinsic parity violation on form factors and resonance structures.

Contribution

The study introduces a detailed calculation of vector and axial vector form factors in tau decay using a chiral Lagrangian with vector mesons, accounting for isospin breaking and parity violations.

Findings

Resonance structure of rho observed in invariant mass distribution

Vector current contribution is intrinsic parity violating

Axial current contribution is G parity violating and suppressed

Abstract

The hadronic tau decay $\tau^- \to \nu_\tau \eta \pi^- \pi^0$ occurs through V-A weak current. In this decay mode, the vector current contribution is intrinsic parity violating and the axial current contribution is G parity violating. The latter contribution is suppressed due to tiny isospin breaking. We have computed both vector and axial vector form factors using a chiral Lagrangian with vector mesons including the effect of isospin breaking and intrinsic parity violation. A numerical result of the invariant mass distribution is shown and the structure of $\rho$ resonance can be seen in the distribution with respect to $M_{\pi^- \pi^0}$.