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

TL;DR

This study predicts the production cross sections of certain charmed baryons and mesons in $K^- p$ scattering, modeling them as molecular states and providing estimates for experimental detection.

Contribution

It introduces a molecular state interpretation for $ ext{Lambda}_c(2910)$ and $ ext{Lambda}_c(2940)$ and calculates their production cross sections in $K^- p$ scattering using an effective Lagrangian approach.

Findings

Cross sections range from ~1.7 nb to ~136 nb at 20 GeV kaon momentum.

Cross section ratios are weakly dependent on model parameters.

Differential cross sections peak at forward angles.

Abstract

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.