Reply to "comment on `Scrutinizing $\pi\pi$ scattering in light of recent lattice phase shifts'"

TL;DR

This paper clarifies differences between two approaches to analyzing $\

Contribution

It provides a detailed clarification of the methodological differences in $\

Findings

Highlights the importance of left-hand cuts and crossing symmetry constraints

Emphasizes the role of these factors in reliably extracting pole information

Responds to previous comments to refine the understanding of $\

Abstract

We reply to the comment [arxiv:2202.08809] by E. van Beveren and G. Rupp on our recent work [arxiv:2202.03124], by further clarifying the difference between the two approaches. We emphasize that the left-hand cuts and constraints of crossing symmetry play an important role in reliably extracting the poles' information below the $\pi\pi$ threshold.