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

Abstract

In the present work, we investigate the productions of $Λ_c(2910)$ and $Λ_c(2940)$ in association with $D_{s0}^{\ast }(2317)^-$ and $D_{s1}(2460)^-$ via $K^- p$ scattering, where we assign $Λ_c(2910)$ and $Λ_c(2940)$ 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 $K^-p \to D^{\ast}_{s0}(2317)^- Λ_{c}(2910) / Λ_{c}(2940)$ and $K^-p \to D_{s1}(2460)^{-} Λ_{c}(2910) / Λ_{c}(2940)$. Our estimations at $p_K=20$ GeV yield the following cross sections: \begin{eqnarray} σ(K^-p \to D^{\ast}_{s0}(2317)^- Λ_{c}(2910)) &=&\left(1.681^{+4.643}_{-1.296}\right)\ \mathrm{nb}, \nonumber σ(K^-p \to D^{\ast}_{s0}(2317)^- Λ_{c}(2940)) &=& \left(49.07^{+136.30}_{-37.86}\right)\ \mathrm{nb}, \nonumber σ(K^-p \to D_{s1}(2460)^{-} Λ_{c}(2910)) &=&\left(84.46^{+238.6}_{-65.35}\right)\ \mathrm{nb}, \nonumber σ(K^-p \to D_{s1}(2460)^{-} Λ_{c}(2940)) &=&\left(13.71^{+38.85}_{-10.61}\right)\ \mathrm{nb}, \nonumber \end{eqnarray} where the central values are estimated with $Λ_r=1.1$ GeV, while the uncertainties come from the variation of $Λ_r$ 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.