$\Lambda_c N$ interaction in leading order covariant chiral effective field theory

Abstract

We study the $\Lambda_c N$ interaction in the covariant chiral effective field theory (ChEFT) at leading order. All the relevant low-energy constants are determined by fitting to the lattice QCD simulations from the HAL QCD Collaboration. Extrapolating the results to the physical point, we show that the $\Lambda_c N$ interaction is weakly attractive in the $^1S_0$ channel, but in the $^3S_1$ channel, it is only attractive at extremely low energies and soon turns repulsive for larger laboratory energy. Furthermore, we show that the neglect of the $^3S_1-{}^3D_1$ coupling provided by the leading order covariant ChEFT would result in an attractive interaction in the $^3S_1$ channel at the physical point, which coincides with the previous non-relatistic ChEFT study. As a byproduct, we predict the $^3D_1$ phase shifts and the mixing angel $\varepsilon_1$, which can be checked by future lattice QCD simulations. In addition, we compare the $\Lambda_c N$ interaction with the $\Lambda N$ and $NN$ interactions to study how the baryon-nucleon ($BN$) interactions evolve as a function of the baryon mass with the replacement of a light quark by a strange or charm quark in the baryon ($B$).