Reply to "Comment on `Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory"'

TL;DR

This paper clarifies the momentum dependence issues in the derivative expansion and discusses conditions for the validity of the HALQCD method in quantum field theory.

Contribution

It emphasizes the importance of momentum dependence in the derivative expansion and analyzes the limitations of the HALQCD method for reliable results.

Findings

Momentum dependence affects the derivative expansion coefficients.

The validity of the HALQCD method depends on specific conditions.

Operator choice independence is crucial for the method's accuracy.

Abstract

We reemphasize the momentum dependence of the coefficients of the derivative expansion as already explained in our paper [1]. We also discuss how the momentum dependence plagues the time-dependent HALQCD method and what is a necessary condition for the method to yield valid results being independent of the choice of the interpolating operators.