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

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.