Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: $I=3/2$ $\pi K$ Scattering Length

TL;DR

This study computes the s-wave scattering length of the pion-kaon system in the I=3/2 channel using lattice QCD with 2+1+1 flavors, providing a precise physical value and estimates for the I=1/2 channel.

Contribution

First lattice QCD calculation of the $ar{K} ext{-}ar{ ext{π}}$ scattering length in the I=3/2 channel with controlled systematic uncertainties.

Findings

$M_{\pi}a_0^{3/2,\text{phys}} = -0.059(2)$

Estimated $M_{\pi}a_0^{1/2,\text{phys}} = 0.163(3)$

Results include statistical and systematic errors from chiral and continuum extrapolations.

Abstract

In this paper we report on results for the s-wave scattering length of the $\pi$-$K$ system in the $I=3/2$ channel from $N_f=2+1+1$ Lattice QCD. The calculation is based on gauge configurations generated by the European Twisted Mass Collaboration with pion masses ranging from about $230$ to $450\,\text{MeV}$ at three values of the lattice spacing. Our main result reads $M_{\pi}\,a_0^{3/2,\text{phys}} = -0.059(2)$. Using chiral perturbation theory we are also able to estimate $M_{\pi}\,a_0^{1/2,\text{phys}} = 0.163(3)$. The error includes statistical and systematic uncertainties, and for the latter in particular errors from the chiral and continuum extrapolations.