Title: $Λ$(1405) in the flavor SU(3) limit using a separable potential in the HAL QCD method Show Chinese title

Title: $Λ$(1405) 在味 SU(3) 极限下使用 HAL QCD 方法中的可分离势

Abstract: Using the HAL QCD method, we investigate S-wave meson-baryon interactions in singlet and two octet channels in the flavor SU(3) limit, where the chiral unitary model predicts that a combination of bound-state poles in these channels corresponds to $\Lambda(1405)$. To avoid the singular behavior of the leading-order potentials of these channels in the derivative expansion, we instead employ a separable potential in the time-dependent HAL QCD method. To calculate all-to-all propagators in the three-point correlation functions including $\Lambda$-baryon source operators with zero momentum, we employ the conventional stochastic estimation combined with the covariant approximation averaging. Separable potentials both in the singlet and octet channels show attraction without singular behavior. Our results of the corresponding phase shifts indicate that the attractive interaction in the singlet channel is stronger than that in the octet. Binding energies are consistent with the estimates from the two-point correlation function within one (two) sigma for the singlet (octet) channel, and this ordering of binding energies is consistent with the mass hierarchy suggested by the chiral unitary model. Show Chinese abstract

Abstract: 使用HAL QCD方法，我们在味SU(3)极限下研究了单态和两个八重态通道中的S波介子-重子相互作用，其中手征单位模型预测这些通道中的束缚态极点的组合对应于$\Lambda(1405)$。为了避免这些通道在导数展开中领先阶势的奇异行为，我们改用时间依赖的HAL QCD方法中的可分离势。为了计算包括零动量的$\Lambda$-重子源算符的三点关联函数中的所有到所有传播子，我们采用了传统随机估计结合协变近似平均。单态和八重态通道中的可分离势都表现出吸引力且没有奇异行为。我们对应的相移结果表明，单态通道中的吸引相互作用比八重态中的更强。结合能与从两点关联函数得出的估计在单态通道中为一个（两个）标准差，在八重态通道中为两个（三个）标准差，这种结合能的顺序与手征单位模型所建议的质量层次一致。