Coupled-channel $\Lambda_{c}K^{+}-pD_{s}$ Interaction in Flavor $ \textrm{SU}\left(3\right) $ Limit of Lattice QCD

Abstract

We study $S$-wave interactions in the $I\left(J^{p}\right)=1/2\left(1/2^{-}\right)$ $\Lambda_{c}K^{+}-pD_{s}$ system on the basis of the coupled-channel HAL QCD method. The potentials which are faithful to QCD S-matrix below the $ pD^{*} $ threshold are extracted from Nambu-Bethe-Salpeter wave functions on the lattice in Flavor $ \textrm{SU}\left(3\right) $ Limit. For the simulation, we employ $ 3 $-flavor full QCD gauge configurations on a $\left(1.93 \:\textrm{fm} \right)^{3}$ volume at $m_{\pi}\simeq 872$ MeV. %\textcolor{red}{For the charm quark, the relativistic heavy quark action is employed to treat its dynamics on the lattice}. We present our results of the S-wave coupled-channel potentials for the $\Lambda_{c}K^{+}-pD_{s}$ system in the $1/2\left(1/2^{-}\right)$ state as well as scattering observables obtained from the extracted potential matrix. We observe that the coupling between $\Lambda_{c}K^{+}$ and $pD_{s}$ channels is weak. The phase shifts and scattering length obtained from the extracted potential matrix show that the $\Lambda_{c}K^{+}$ interaction is attractive at low energy and stronger than the $pD_{s}$ interaction though no bound state at $m_{\pi}\geq872$ MeV.