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

We report on a theoretical study of the $π^- p \to a^-_1(1260) p$ and $π^- p \to π^- ρ^0 p$ reactions near threshold within an effective Lagrangian approach. The production process is described by $t$-channel $ρ^0$ meson exchange. For the $π^- p \to π^- ρ^0 p$ reaction, the final $π^- ρ^0$ results from the decay of the $a_1(1260)$ resonance which is assumed as a dynamically generated state from the $K^* \bar K$ and $ρπ$ coupled channel interactions. We calculate the total cross section of the $π^- p \to a^-_1(1260) p$ reaction. It is shown that, with the coupling constant of the $a_1(1260)$ to $ρπ$ channel obtained from the chiral unitary theory and a cut off parameter $Λ_ρ\sim 1.5$ GeV in the form factors, the experimental measurement can be reproduced. Furthermore, the total and differential cross sections of $π^- p \to a^-_1(1260) p \to π^- ρ^0 p$ 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.