$\Lambda_c(2910)$ and $\Lambda_c(2940)$ productions in association with $D_{s0}^{\ast }(2317)^-$ and $D_{s1}(2460)^-$ via $K^- p$ scattering

In the present work, we investigate the productions of $\Lambda_c(2910)$ and $\Lambda_c(2940)$ in association with $D_{s0}^{\ast }(2317)^-$ and $D_{s1}(2460)^-$ via $K^- p$ scattering, where we assign $\Lambda_c(2910)$ and $\Lambda_c(2940)$ as $D^\ast N$ molecular states with $J^P$ quantum numbers to be $1/2^-$ and $3/2^-$, respectively, while treating $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ as $S-$wave $DK$ and $D^\ast K$ molecular states, respectively. Utilizing an effective Lagrangian approach, we evaluated the cross sections for $K^-p \to D^{\ast}_{s0}(2317)^- \Lambda_{c}(2910) / \Lambda_{c}(2940)$ and $K^-p \to D_{s1}(2460)^{-} \Lambda_{c}(2910) / \Lambda_{c}(2940)$. Our estimations at $p_K=20$ GeV yield the following cross sections: \begin{eqnarray} \sigma(K^-p \to D^{\ast}_{s0}(2317)^- \Lambda_{c}(2910)) &=&\left(1.681^{+4.643}_{-1.296}\right)\ \mathrm{nb}, \nonumber \sigma(K^-p \to D^{\ast}_{s0}(2317)^- \Lambda_{c}(2940)) &=& \left(49.07^{+136.30}_{-37.86}\right)\ \mathrm{nb}, \nonumber \sigma(K^-p \to D_{s1}(2460)^{-} \Lambda_{c}(2910)) &=&\left(84.46^{+238.6}_{-65.35}\right)\ \mathrm{nb}, \nonumber \sigma(K^-p \to D_{s1}(2460)^{-} \Lambda_{c}(2940)) &=&\left(13.71^{+38.85}_{-10.61}\right)\ \mathrm{nb}, \nonumber \end{eqnarray} where the central values are estimated with $\Lambda_r=1.1$ GeV, while the uncertainties come from the variation of $\Lambda_r$ from 1.0 to 1.2 GeV. However, the ratios of the cross sections for the considered processes are evaluate to be very weakly dependent on the model parameters. In addition, the differential cross sections for the relevant processes are evaluated, and our estimations indicate that these differential cross sections reach the maximum at the forward angle limit.