Role of the $\Lambda^+_c(2940)$ in the $\pi^- p \to D^- D^0 p$ reaction close to threshold

TL;DR

This study uses an effective Lagrangian approach to analyze the role of the $\\Lambda^+_c(2940)$ in the $\\pi^- p \\to D^- D^0 p$ reaction near threshold, highlighting how its spin parity affects the total cross section and proposing experimental tests.

Contribution

It introduces a theoretical model considering different spin parity assignments for $\\Lambda^+_c(2940)$ and predicts observable effects on the reaction cross section, aiding in determining its quantum numbers.

Findings

The $J^P = \frac{1}{2}^-$ assignment enhances the total cross section.

The total cross section is sensitive to the cutoff parameter in the form factor.

Differential cross sections can help determine the parity of $\\Lambda^+_c(2940)$.

Abstract

We report on a theoretical study of the $\pi^- p \to D^- D^0 p$ reaction near threshold within an effective Lagrangian approach. The production process is described by $t$ channel $D^{*0}$ meson exchange, $s$-channel nucleon pole, and $u$ channel $\Sigma^{++}_{c}$ exchange. In our work, the final $D^0 p$ results from the ground $\Lambda^+_c(2286)$ state and also dominantly from the excited $\Lambda^+_c(2940)$ state which is assumed as a $D^{*0} p$ molecular state with spin parity $J^P = \frac{1}{2}^+$ or $\frac{1}{2}^-$. We calculate the total cross section of the $\pi^- p \to D^- D^0 p$ reaction. It is shown that the spin parity assignment of $\frac{1}{2}^-$ for $\Lambda^+_c(2940)$ gives a sizable enhancement for the total cross section in comparison with a choice of $J^p = \frac{1}{2}^+$. However, our theoretical result of the total cross section is sensitive to the value of the cutoff parameter involved in the form factor of the exchanged off-shell particles. Moreover, we also calculate the second order differential cross section and find it can be used to determine the parity of the $\Lambda^+_c(2940)$. It is expected that our model calculations can be tested by future experiments at J-PARC in Japan.