$\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ productions in $\pi^{-} p$ scattering process

In the present work, we propose to investigate the productions of $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ in the $\pi^{-} p \rightarrow D^{-} D^{0} p$ processes by utilizing an effective Lagrangian approach, where $\Lambda_c(2910)$ and $\Lambda_c(2940)$ are considered as $D^\ast N$ molecular states with $J^P$ quantum numbers to be $1/2^-$ and $3/2^-$, respectively. With the cutoff parameter determined by the upper limit of the cross sections for $\pi^- p \to D^{\ast-} \Lambda_c(2286)$, the ratios of the cross sections for $\pi^- p \to D^{\ast-} \Lambda_c(2286)$, $\pi^- p \to D^{-} \Lambda_c(2286)$, $\pi^- p \to D^{-} \Lambda_c(2910)$, and $\pi^- p \to D^{-} \Lambda_c(2940)$ are estimated to be $1:4.8:1.42:0.26$ at $p_\pi=30$ GeV. Considering that the $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ state can further decay into $D^{0}p$, we estimate the cross sections for $\pi^{-} p \rightarrow D^{-} D^{0} p$ process and the differential cross sections depending on the $D^0 p$ invariant mass spectrum. Our estimations indicate that the total cross sections are $(0.49^{+1.56}_{-0.38})$ nb when $p_{\pi}=15~\mathrm{GeV}$, where the uncertainties result from the variation of the $\Lambda_{r}$. By comparing the contributions of the $s$, $u$, and $t$-channels, we conclude that the $t$-channel plays the predominant role. Moreover, the present estimations suggest that the structure around 2.9 GeV in the $D^0 p$ invariant mass spectrum of the $\pi^{-} p \rightarrow D^{-} D^{0} p$ process should correspond to $\Lambda_c(2910)$ rather than $\Lambda_c(2940)$, which can be tested by further experimental measurements at J-PARC in the future.