Model analysis on the effectiveness of the HAL QCD method for hadron-hadron interactions

Abstract

The HAL QCD method has been one of the powerful tools to extract hadron-hadron interactions directly from lattice QCD simulation data. In this paper, we aim at examining the effectiveness of the HAL QCD method by deriving a formula to calculate quantities in the HAL QCD method, such as the so-called R-correlators and HAL QCD local potentials, from the hadron-hadron scattering amplitudes within effective models. In this framework, we can judge whether the HAL QCD local potential, evaluated in the present formula, reproduces the properties of the original hadron-hadron interaction or not via the scattering amplitude, which is a solution of the Lippmann--Schwinger equation with the original hadron-hadron interaction as an input. In an analysis within a simple model of elastic scattering, we show that, when the original interaction is predominantly local, the HAL QCD local potentials quantitatively reproduce phase shifts of the hadron-hadron scatterings and correctly indicate the existence/absence of the bound state with its binding energy $\sim$ MeV. Lattice discretization of spacetime modifies the results only slightly. Furthermore, we consider the $\bar{K} N$ potential in a bare to $\bar{K} N$