Phenomenological model for the $\gamma\gamma \to \pi^+\pi^-\pi^0$ reaction

TL;DR

This paper develops a phenomenological model for the gamma-gamma to three-pion reaction, incorporating various resonances and channels, and successfully describes existing experimental data while predicting distributions for future measurements.

Contribution

The paper introduces a comprehensive phenomenological model including multiple resonances and channels for the gamma-gamma to three-pion reaction, with a focus on gauge invariance and high-energy behavior.

Findings

Good agreement with ARGUS and L3 data on total cross sections.

Predictions for invariant mass distributions in the 0.8 to 2.0 GeV energy range.

Model captures essential reaction mechanisms and resonance contributions.

Abstract

We present a phenomenological model for the $\gamma\gamma \to \pi^+\pi^-\pi^0$ reaction by including the production mechanism of the $a_2(1320)$ resonance, as well as the contributions from the $\sigma/f_0(500)\, \pi^0$ and $f_2(1270)\, \pi^0 $ production channels. Furthermore, the $\gamma\gamma\to\rho^{\pm} \pi^{\mp}\to\pi^{+}\pi^-\pi^0$ channel, which is essential for a description in the low-energy region, is investigated carefully by introducing the complete set of gauge invariant and Lorentz-covariant tensors for the $\gamma\gamma\to\rho^\pm \pi^\mp$ subprocess. The full amplitude is constructed to yield a correct high-energy Regge behavior. Within our model, we achieve a very reasonable description of ARGUS and L3 data of the total cross section, as well as of the $\pi^\pm\pi^0$ and $\pi^+\pi^-$ invariant mass distributions. We also predict the invariant mass distributions in the $\gamma\gamma$ center-of-mass energy range from $0.8$ GeV to $2.0$ GeV, which will be studied by the forthcoming data of the BESIII collaboration.