# Study of $a_1(1260)$ in the $\gamma p \to \pi^+\pi^+\pi^- n$ reaction

## TL;DR

This paper models the photoproduction of the $a_1(1260)$ meson in gamma-proton reactions, predicting cross sections and invariant mass distributions to guide future experimental searches.

## Contribution

It introduces a theoretical model for $a_1(1260)$ photoproduction, including resonance and non-resonance processes, and compares predictions with experimental data.

## Key findings

- Good agreement with experimental $
ho o
ho o ext{pi}^+ ext{pi}^+ ext{pi}^-$ mass distributions.
- Predicted total cross section around 10 μb at 2.5 GeV photon energy.
- Model can be tested in future experiments.

## Abstract

We investigate the discovery potential of the $a_1(1260)$ photoproduction in the $\gamma p \to a_1(1260)^+ n$ and $\gamma p \to \pi^+\pi^+\pi^- n$ reactions via the $\pi$-exchange mechanism. For the $\gamma p \to \pi^+\pi^+\pi^- n$ reaction, we perform a calculation for the differential and total cross sections by including the contributions from the $a_1(1260)$ intermediate resonance decaying into $\rho \pi$ then into $\pi^+\pi^+\pi^-$. Besides, the non-resonance process is also considered. With a lower mass of $a_1(1260)$, we get a fairly good description of the experimental data for the invariant $\pi^+\pi^+\pi^-$ mass distributions. For the $\gamma p \to a_1(1260)^+ n$ reaction, with our model parameters, the total cross section is of the order of 10 $\mu$b at photon beam energy $E_{\gamma} \sim$ 2.5 GeV. It is expected that our model calculations could be tested by future experiments.