The three-pion decays of the $a_1(1260)$

TL;DR

This paper models the three-pion decay of the $a_1(1260)$ resonance assuming it is dynamically generated from $ ho ext{--} ext{K}K^*$ interactions, including final state interactions, and predicts decay widths and mass distributions.

Contribution

It introduces a dynamical generation model for $a_1(1260)$ decays that incorporates coupled channel interactions and final state effects, differing from previous approaches.

Findings

Calculated decay width differs significantly from other models.

Predicted invariant mass distributions can be tested experimentally.

Highlights the importance of the $ ho ext{--} ext{K}K^*$ component in the $a_1(1260)$ wave function.

Abstract

We investigate the decay of $a^+_1(1260) \to \pi^+ \pi^+ \pi^-$ with the assumption that the $a_1(1260)$ is dynamically generated from the coupled channel $\rho \pi$ and $\bar{K}K^*$ interactions. In addition to the tree level diagrams that proceed via $a^+_1(1260) \to \rho^0 \pi^+ \to \pi^+\pi^+ \pi^-$, we take into account also the final state interactions of $\pi\pi \to \pi \pi$ and $K \bar{K} \to \pi \pi$. We calculate the invariant $\pi^+ \pi^-$ mass distribution and also the total decay width of $a^+_1(1260) \to \pi^+ \pi^+ \pi^-$ as a function of the mass of $a_1(1260)$. The calculated total decay width of $a_1(1260)$ is significantly different from other model calculations and tied to the dynamical nature of the $a_1(1260)$ resonance. The future experimental observations could test of model calculations and would provide vary valuable information on the relevance of the $\rho \pi$ component in the $a_1(1260)$ wave function.