Study of the lowest tensor and scalar resonances in the $\tau \to \pi\pi\pi \nu_\tau$ decay

TL;DR

This paper introduces a new parametrization of the hadronic current in tau decay to three pions, incorporating scalar, vector, axial-vector, and tensor resonances, including the first inclusion of the tensor resonance $f_2(1270)$, with constraints ensuring proper high-energy behavior.

Contribution

The work presents the first inclusion of the tensor resonance $f_2(1270)$ in the decay model, along with a comprehensive parametrization from the chiral Lagrangian that accounts for multiple resonance contributions.

Findings

Inclusion of the tensor resonance $f_2(1270)$ improves decay modeling.

Constraints on vertex constants ensure correct high-energy behavior.

The parametrization aligns well with experimental data.

Abstract

In this note we present a new parametrization of the hadronic current for the decay $\tau \to \pi\pi\pi \nu_\tau$ derived from the chiral lagrangian with explicit inclusion of resonances. We have included both scalar, vector and axial-vector resonances. For the first time, the lowest tensor resonance ($f_2(1270)$) is included as well. Both single and double-resonance contributions to the hadronic form factors are taken into account. To satisfy the correct high energy behaviour of the hadronic form factors, constraints on numerical values of the vertex constants are obtained.