The $\pi f_0(500)$ decay of the $a_1(1260)$

TL;DR

This paper calculates the decay width of the $a_1(1260)$ into $ ho o ho o ho o ho$ and $ ho o ho o ho o ho$ and finds it to be around 13-22 MeV, using a dynamical generation approach.

Contribution

It introduces a model where the $a_1(1260)$ and $\sigma$ are dynamically generated from meson interactions, providing a new perspective on their decay mechanisms.

Findings

Decay width estimated at 13-22 MeV.

Highlights discrepancies in experimental measurements.

Supports the dynamical generation hypothesis for these resonances.

Abstract

We evaluate the $a_1(1260) \to \pi \sigma (f_0(500))$ decay width from the perspective that the $a_1(1260)$ resonance is dynamically generated from the pseudoscalar-vector interaction and the $\sigma$ arises from the pseudoscalar-pseudoscalar interaction. A triangle mechanism with $a_1(1260) \to \rho \pi$ followed by $\rho \to \pi \pi$ and a fusion of two pions within the loop to produce the $\sigma$ provides the mechanism for this decay under these assumptions for the nature of the two resonances. We obtain widths of the order of $13-22$ MeV. Present experimental results differ substantially from each other, suggesting that extra efforts should be devoted to the precise extraction of this important partial decay width, which should provide valuable information on the nature of the axial vector and scalar meson resonances and help clarify the role of the $\pi\sigma$ channel in recent lattice QCD calculations of the $a_1$.