The role of $a_1(1260)$ in $\pi^- p \to a^-_1(1260) p$ and $\pi^- p \to \pi^- \rho^0 p$ reactions near threshold

Abstract

We report on a theoretical study of the $\pi^- p \to a^-_1(1260) p$ and $\pi^- p \to \pi^- \rho^0 p$ reactions near threshold within an effective Lagrangian approach. The production process is described by $t$-channel $\rho^0$ meson exchange. For the $\pi^- p \to \pi^- \rho^0 p$ reaction, the final $\pi^- \rho^0$ results from the decay of the $a_1(1260)$ resonance which is assumed as a dynamically generated state from the $K^* \bar K$ and $\rho \pi$ coupled channel interactions. We calculate the total cross section of the $\pi^- p \to a^-_1(1260) p$ reaction. It is shown that, with the coupling constant of the $a_1(1260)$ to $\rho \pi$ channel obtained from the chiral unitary theory and a cut off parameter $\Lambda_\rho \sim 1.5$ GeV in the form factors, the experimental measurement can be reproduced. Furthermore, the total and differential cross sections of $\pi^- p \to a^-_1(1260) p \to \pi^- \rho^0 p$ reaction are evaluated, and it is expected that our model calculations can be tested by future experiments. These reactions are important for the study of the $a_1(1260)$ resonance and would provide further clue for the nature of $a_1(1260)$ state.