$\bar{D}$-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 $m_π\simeq 137$ MeV and a lattice spacing of $a\simeq0.084$ 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.

Figures (11)

• Figure 1: LO potential $V_{\text{LO}}(r)$ for the $\bar{D}N$ system in the isospin $I=0$ channel (left), and the $I=1$ channel (right) at Euclidean time slices $t/a=13$ (blue, circle), $t/a=14$ (red, square) and $t/a=15$ (gold, triangle).
• Figure 2: Isospin independent and dependent components $V_0(r)$ and $V_\tau(r)$ at Euclidean time slices $t/a=13$ (blue, circle), $t/a=14$ (red, square) and $t/a=15$ (gold, triangle).
• Figure 3: $V_{\text{LO}}(r)$ for the $\bar{D}N$ system (red, square) and $KN$ system (blue, triangle) in the isospin $I=0$ channel (left), and the $I=1$ channel (right) at Euclidean time slice $t/a=14$. The $KN$ potential is taken from Ref. Murakami:2025owk.
• Figure 4: $r^2 V_{\text{LO}}(r)$ for the $I=0$ (left) and $I=1$ channel (right) at Euclidean time slice $t/a=14$. The blue and pink bands represent the 4G fit and the 3G+TPE fit, respectively.
• Figure 5: $s$-wave phase shifts $\delta_0$ for $I=0$ (left), and $I=1$ (right) channels at Euclidean times $t/a=13$ (blue), $t/a=14$ (red) and $t/a=15$ (gold) from the 4G fit. $\Delta E = E-m_{D}-m_{N}$. The vertical lines at $\Delta E\simeq 140$ MeV show the inelastic threshold of $\bar{D}^\ast N$.