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 $K^{\ast }\bar{K}$ 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.

Comments: 5 pages, 5 figures