$Λ_{c}(2910)$ and $Λ_{c}(2940)$ productions in $π^{-} p$ scattering process

Abstract

In the present work, we propose to investigate the productions of $Λ_{c}(2910)$ and $Λ_{c}(2940)$ in the $π^{-} p \rightarrow D^{-} D^{0} p$ processes by utilizing an effective Lagrangian approach, where $Λ_c(2910)$ and $Λ_c(2940)$ 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 $π^- p \to D^{\ast-} Λ_c(2286)$, the ratios of the cross sections for $π^- p \to D^{\ast-} Λ_c(2286)$, $π^- p \to D^{-} Λ_c(2286)$, $π^- p \to D^{-} Λ_c(2910)$, and $π^- p \to D^{-} Λ_c(2940)$ are estimated to be $1:4.8:1.42:0.26$ at $p_π=30$ GeV. Considering that the $Λ_{c}(2910)$ and $Λ_{c}(2940)$ state can further decay into $D^{0}p$, we estimate the cross sections for $π^{-} p \rightarrow D^{-} D^{0} p$ 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 $p_π=15~\mathrm{GeV}$, where the uncertainties result from the variation of the $Λ_{r}$. 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 $π^{-} p \rightarrow D^{-} D^{0} p$ process should correspond to $Λ_c(2910)$ rather than $Λ_c(2940)$, which can be tested by further experimental measurements at J-PARC in the future.