# Properties of non-local wave function equivalent potential with generalized derivative expansion

## TL;DR

This paper investigates the properties and convergence of generalized derivative expansion in non-local wave-function-equivalent potentials within the HAL QCD framework, enhancing the accuracy of lattice QCD calculations.

## Contribution

It introduces a generalized derivative expansion for non-local potentials and demonstrates improved convergence techniques for lattice QCD applications.

## Key findings

- Expansion converges with accurate phase shifts
- Convergence improved by choosing interpolating fields
- Tuning the expansion scale enhances results

## Abstract

We examine the properties of the wave-function-equivalent potentials which HAL QCD collaboration has introduced. We generalize the derivative expansion, and then apply it to energy-independent and non-local potentials in a coupled-channel model. We observe that the expansion converges by comparing the scattering phase shifts computed from these potentials with the exact one. We have also found that the convergence can be improved by either varying the choice of interpolating fields or tuning the expansion scale in the generalized derivative expansion. The results will be utilized in future lattice QCD calculations, allowing for further application of the HAL QCD method.