Determination of $s$- and $p$-wave $I=1/2$ $K\pi$ scattering amplitudes in $N_{\mathrm{f}}=2+1$ lattice QCD

TL;DR

This study computes $K ext{-}\pi$ scattering amplitudes for $s$- and $p$-waves using lattice QCD with physical quark masses, providing detailed resonance parameters and scattering lengths.

Contribution

First lattice QCD calculation of $s$- and $p$-wave $K ext{-}\pi$ scattering amplitudes with $N_f=2+1$ flavors at near-physical pion mass, including partial wave mixing effects.

Findings

$p$-wave described by Breit-Wigner with $m_{K^*}/m_$ = 3.808(18)

Near-threshold $s$-wave scattering length $m_ a_0 = -0.353(25)

Explicit treatment of partial wave mixing in finite volume

Abstract

The elastic $I=1/2$, $s$- and $p$-wave kaon-pion scattering amplitudes are calculated using a single ensemble of anisotropic lattice QCD gauge field configurations with $N_{\mathrm{f}} = 2+1$ flavors of dynamical Wilson-clover fermions at $m_{\pi} = 230\mathrm{MeV}$. A large spatial extent of $L = 3.7\mathrm{fm}$ enables a good energy resolution while partial wave mixing due to the reduced symmetries of the finite volume is treated explicitly.The $p$-wave amplitude is well described by a Breit-Wigner shape with parameters $m_{K^{*}}/m_{\pi} = 3.808(18)$ and $g^{\mathrm{BW}}_{K^{*}K\pi} = 5.33(20)$ which are insensitive to the inclusion of $d$-wave mixing and variation of the $s$-wave parametrization. An effective range description of the near-threshold $s$-wave amplitude yields $m_{\pi}a_0 = -0.353(25)$.