Study of $a_1(1260)$ in the ${\hat{I}}^{3}p\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}n$ reaction

Abstract

We investigate the discovery potential of the $a_1(1260)$ photoproduction in the ${\hat{I}}^{3}p\to a_1(1260{)}^{+}n$ and ${\hat{I}}^{3}p\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}n$ reactions via the $\ddot{I}€$-exchange mechanism. For the ${\hat{I}}^{3}p\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}n$ 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 $\ddot{I}\ddot{I}€$ then into $\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$. 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 $\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ mass distributions. For the ${\hat{I}}^{3}p\to a_1(1260{)}^{+}n$ reaction, with our model parameters, the total cross section is of the order of 10 $\hat{I}¼$b at photon beam energy $E_{\hat{I}}^3\sim$ 2.5 GeV. It is expected that our model calculations could be tested by future experiments.