Coupled-channel ${\Lambda }_c{K}^{+}-p{D}_s$ Interaction in Flavor $\text{SU}\left(3\right)$ Limit of Lattice QCD

Abstract

We study $S$-wave interactions in the $I\left(J^p\right)=1/2\left(1/2^{-}\right)$ ${\Lambda }_c{K}^{+}-p{D}_s$ system on the basis of the coupled-channel HAL QCD method. The potentials which are faithful to QCD S-matrix below the $p{D}^{\ast }$ threshold are extracted from Nambu-Bethe-Salpeter wave functions on the lattice in Flavor $\text{SU}\left(3\right)$ Limit. For the simulation, we employ $3$-flavor full QCD gauge configurations on a ${\left(1.93\text{fm}\right)}^3$ 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 ${\Lambda }_c{K}^{+}-p{D}_s$ 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 $p{D}_s$ 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 $p{D}_s$ interaction though no bound state at $m_{\pi }\ge 872$ MeV.

Comments: 20 pages, 7 Figures, 5 tables