$I=\frac{3}{2}$ $\pi K$ $s$-wave scattering length from lattice QCD

TL;DR

This paper computes the $I=3/2$ $ ext{π}K$ s-wave scattering length using lattice QCD with physical quark masses, providing results consistent with experimental data and chiral perturbation theory.

Contribution

It presents the first lattice QCD calculation of the $I=3/2$ $ ext{π}K$ s-wave scattering length with physical quark masses and detailed phase shift analysis.

Findings

Scattering length and effective range parameters agree with chiral perturbation theory.

Results are consistent with experimental measurements.

Numerical methods successfully extract phase shifts from lattice data.

Abstract

The $I=\frac{3}{2}$ $\pi K$ $s$-wave scattering phase shift is computed by lattice quantum chromodynamics with $N_f=3$ flavors of Asqtad-improved staggered fermions. The energy-eigenvalues of $\pi K$ systems at one center of mass frame and six moving frames using moving wall source technique are used to get phase shifts by L\"uscher's formula and its extensions. The calculations are good enough to acquire effective range expansion parameters: scattering length $a$, effective range $r$, and shape parameter $P$, which are in good agreement with our explicit analytical predictions in three-flavor chiral perturbation theory at next-to-leading order. All results are fairly consistent with experimental measurements, phenomenological studies, and lattice estimations. Numerical computations are implemented at a fine ($a\approx0.082$ fm, $L^3 T = 40^3 96$) lattice ensemble with physical quark masses.