$S$-wave kaon-nucleon interactions from lattice QCD at the physical point

Abstract

We investigate S-wave kaon-nucleon ($KN$) interactions with strangeness $S=+1$ in lattice QCD using the time-dependent HAL QCD method. Employing the $(2+1)$-flavor gauge configuration with $m_{\pi }\approx 137\text{MeV}$ and $m_K\approx 502\text{MeV}$, we calculate the $KN$ potentials at the leading order in the derivative expansion. The potentials in both isospin channels ($I=1$ and $I=0$) exhibit repulsion at short distances, while only the $I=0$ potential has a small attractive pocket at intermediate distances. From these potentials, we compute the phase shifts as well as the low-energy scattering parameters. The obtained phase shifts show no signals corresponding to resonances or bound states in both isospin channels, suggesting the absence of the ${\Theta }^{+}(1540)$ pentaquark in the S-wave $KN$ systems. The results for $I=0$ suggest that the scattering amplitudes in this channel are dominated by P-wave components rather than S-wave.

Comments: 34 pages, 20 figures, 4 tables. v3: This version contains an erratum followed by the original manuscript, which is identical to arXiv:2509.00838v2. A numerical error in the KN four-point correlation functions was corrected, and the results affected by this error were updated accordingly. The erratum presents the corrected results and discusses how the conclusions are affected