Title: Left-hand cut and the HAL QCD method Show Chinese title

Title: 左切片和HAL QCD方法

Abstract: We investigate how the left-hand cut (LHC) problem is treated in the HAL QCD method. For this purpose, we first consider the effect of the LHC to the scattering problem in non-relativistic quantum mechanics with potentials. We show that the $S$-matrix or the scattering phase shift obtained from the potential including the Yukawa term ($e^{- m_\pi r}/r$) with the infra-red (IR) cutoff $R$ is well-defined even for the complex momentum $k$ as long as $R$ is finite, and they are compared with those obtained by the analytic continuation without the IR cutoff. In the $R\to\infty$ limit, the phase shift approaches the result from the analytic continuation at ${\rm Im}\, k < m_\pi/2$, while they differ at ${\rm Im}\, k > m_\pi/2$, except $k= k_b$, where $k_b$ is the binding momentum. We also observe that $k_b$ can be correctly obtained even at finite but large $R$. Using knowledge obtained in the non-relativistic quantum mechanics, we present how we should treat the LHC in the HAL QCD potential method. Show Chinese abstract

Abstract: 我们研究了HAL QCD方法中如何处理左手切割（LHC）问题。 为此，我们首先考虑LHC对非相对论量子力学中势能散射问题的影响。 我们表明，包含Yukawa项（$e^{- m_\pi r}/r$）和红外（IR）截断$R$的势能得到的$S$矩阵或散射相移在复动量$k$的情况下仍然是定义良好的，只要$R$是有限的，并且它们与通过解析延拓而不使用IR截断得到的结果进行比较。 在 $R\to\infty$ 极限下，相移趋近于从解析延拓得到的结果 ${\rm Im}\, k < m_\pi/2$，而在 ${\rm Im}\, k > m_\pi/2$ 处它们有所不同，除了 $k= k_b$ 处，其中 $k_b$ 是结合动量。 我们还观察到，即使在有限但较大的 $R$ 下，也可以正确获得 $k_b$。 利用非相对论量子力学中获得的知识，我们说明了在 HAL QCD 势方法中应该如何处理 LHC。