Analytical dispersive parameterization for S-wave $\pi\pi$ and $\pi K$ scattering

TL;DR

This paper introduces a new dispersive parameterization for S-wave $\pi\pi$ and $\pi ext ext K$ scattering amplitudes, validated against lattice data, incorporating chiral perturbation theory insights.

Contribution

The paper presents a novel dispersive parameterization method for S-wave scattering amplitudes that accounts for the Adler zero and is applicable to lattice QCD data.

Findings

Successful application to lattice data at $m_\pi extapprox 240$ MeV.

Extraction of the Adler zero position from chiral perturbation theory.

Enhanced understanding of low-energy $\pi ext ext K$ and $\pi ext extpi$ scattering.

Abstract

In this proceeding, we illustrate the applicability of a new parameterization of the S-wave amplitude on the example of the $\pi\pi \to \pi\pi$ and $\pi K \to \pi K $ lattice data ($m_\pi \sim 240$ MeV) from the HadSpec collaboration. The applied parameterization follows from the dispersive representation for the inverse scattering amplitude. The left-hand cut contribution is parametrized by the series in a suitably constructed conformal variable. The crucial input in the analysis is the Adler zero, whose position we extracted from the chiral perturbation theory at next-to-leading order with the uncertainties propagated from the low-energy constants.