Information on the structure of the a1 from tau decay

TL;DR

This paper compares two methods for analyzing the tau decay into three pions and a neutrino, focusing on the resonance structure attributed to the a1, and finds that a dynamically generated resonance model fits the spectral function well with minimal parameters.

Contribution

It introduces and compares a dynamical resonance generation approach with an explicit resonance model for the a1 in tau decay analysis.

Findings

The molecule scenario describes the spectral function well with only one free parameter.

Adding higher order corrections improves the dynamical model systematically.

Explicit resonance treatment shows peculiar properties that differ from the dynamical approach.

Abstract

The decay $\tau\to \pi\pi\pi\nu$ is analysed using different methods to account for the resonance structure, which is usually ascribed to the a1. One scenario is based on the recently developed techniques to generate axial-vector resonances dynamically, whereas in a second calculation the a1 is introduced as an explicit resonance. We investigate the influence of different assumptions on the result. In the molecule scenario the spectral function is described surprisingly well by adjusting only one free parameter. This result can be systematically improved by adding higher order corrections to the iterated Weinberg-Tomozawa interaction. Treating the a1 as an explicit resonance on the other hand leads to peculiar properties.