$\bar{D}$-meson Nucleon Scattering from Lattice QCD at the Physical Point

Abstract

We report the first lattice QCD study of the $s$-wave scattering of the $\bar{D}$-meson and the nucleon at the physical point, utilizing (2+1)-flavor configurations generated by the HAL QCD collaboration with a pion mass of $m_{\pi }\simeq 137$ MeV and a lattice spacing of $a\simeq 0.084$ fm. By applying the HAL QCD method to the four-point correlation function of the $\bar{D}N$ system, we obtain a leading-order potential of the derivative expansion of the interaction kernel, which is then used to extract the $s$-wave phase shifts of low-energy $\bar{D}N$ scattering. Both the isospin $I=0$ and $I=1$ channels have a short-range repulsive core and a shallow attractive pocket in the intermediate to long-range region, though the $I=0$ channel is more attractive than the $I=1$ channel. We also observe that the $\bar{D}N$ potential exhibits more attraction than the $KN$ potential, which is its analog in the strange sector. In terms of the $s$-wave phase shifts, the $I=0$ channel shows a weak attractive behavior in the low-energy region with a positive scattering length of $0.246\pm 0.105{(}_{-0.051}^{+0.084})$ fm, whereas the $I=1$ channel shows repulsion with a negative scattering length of $-0.086\pm 0.050{(}_{-0.001}^{+0.037})$ fm. No bound states are found in both isospin channels, indicating the absence of a pentaquark state in the $s$-wave $\bar{D}N$ system.

Comments: 26 pages, 11 figures, 5 tables