In this paper, employing an all-to-all quark propagator technique, we investigate the kaon-nucleon interactions in lattice QCD. We calculate the S-wave kaon-nucleon potentials at the leading order in the derivative expansion in the time-dependent HAL QCD method, using (2+1)-flavor gauge configurations at the lattice spacing $a \approx 0.09$ fm on $32^3 \times 64$ lattices and the pion mass $m_{\pi} \approx 570$ MeV. We take the one-end trick for all-to-all propagators, which allows us to put the zero momentum hadron operators at both source and sink and to smear quark operators at the source. We find the stronger repulsive interaction in the $I=1$ channel than in the $I=0$. The phase shifts obtained by solving the Schrodinger equations with the potentials qualitatively reproduce the energy dependence of the experimental phase shifts, and have the similar behavior to the previous results from lattice QCD without all-to-all propagators. Our study demonstrates that the all-to-all quark propagator technique with the one-end trick is useful to study interactions for meson-baryon systems in the HAL QCD method, so that we will apply it to meson-baryon systems which contain quark-antiquark creation/annihilation processes in our future studies.

中文翻译：

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HAL QCD 方法中全对全传播子的 S 波 kaon-核子势

在本文中，我们采用全对全夸克传播器技术，研究了格子 QCD 中的 kaon-核子相互作用。我们在瞬态 HAL QCD 方法中使用 (2+1)-flavor 规范配置在晶格间距 $a \approx 0.09 $ fm on $32 中计算导数扩展中领先阶的 S 波 kaon-核子势^3 \times 64$ 格子和 pion 质量 $m_{\pi} \大约 570$ MeV。我们对全对全传播器采用了单端技巧，这使我们能够将零动量强子算子放在源和汇处，并在源处涂抹夸克算子。我们发现 $I=1$ 通道中的排斥相互作用比 $I=0$ 中更强。通过用势解薛定谔方程获得的相移定性地再现了实验相移的能量依赖性，并且具有与先前来自格子 QCD 的结果类似的行为，而没有全对全传播器。我们的研究表明，具有单端技巧的全对全夸克传播器技术对于研究 HAL QCD 方法中介子-重子系统的相互作用非常有用，因此我们将其应用于包含夸克-重子系统的介子-重子系统。我们未来研究中的反夸克产生/湮灭过程。