Lattice study on kaon pion scattering length in the $I=3/2$ channel

TL;DR

This study calculates the $K ext{-}\pi$ scattering length in the $I=3/2$ channel using lattice QCD with improved Wilson quarks, analyzing systematic errors and comparing results with theoretical and experimental data.

Contribution

First lattice QCD calculation of $K ext{-}\pi$ scattering length in the $I=3/2$ channel with systematic error analysis and comparison to other approaches.

Findings

Results agree with Roy equation and Chiral Perturbation Theory predictions.

Finite volume and lattice spacing effects are quantitatively analyzed.

Extrapolated scattering length matches experimental data within errors.

Abstract

Using the tadpole improved Wilson quark action on small, coarse and anisotropic lattices, $K\pi$ scattering length in the $I=3/2$ channel is calculated within quenched approximation. The results are extrapolated towards the chiral and physical kaon mass region. Finite volume and finite lattice spacing errors are also analyzed and a result in the infinite volume and continuum limit is obtained. Our result is compared with the results obtained using Roy equations, Chiral Perturbation Theory, dispersion relations and the experimental data.