The preliminary lattice QCD calculation of $\kappa$ meson decay width

TL;DR

This paper reports a pioneering lattice QCD calculation of the $ppa$ meson decay width, using finite size formulas and phase shift analysis to extract resonance parameters from pion-kaon scattering data.

Contribution

It introduces a novel application of a finite size formula extension to compute the $ppa$ decay width directly from lattice QCD simulations.

Findings

Calculated the $ppa$ decay width as 293 b1 101 MeV.

Extracted the effective $ppa d7 pk$ coupling constant as 4.54(76) GeV.

Demonstrated the feasibility of resonance parameter extraction from lattice QCD data.

Abstract

We present a direct lattice QCD calculation of the $\kappa$ meson decay width with the s-wave scattering phase shift for the isospin $I=1/2$ pion-kaon ($\pi K$) system. We employ a special finite size formula, which is the extension of the Rummukainen-Gottlieb formula for the $\pi K$ system in the moving frame, to calculate the scattering phase, which indicates a resonance around $\kappa$ meson mass. Through the effective range formula, we extract the effective $\kappa \to \pi K$ coupling constant $g_{\kappa \pi K} = 4.54(76)$ GeV and decay width $\Gamma = 293 \pm 101$ MeV. Our simulations are done with the MILC gauge configurations with $N_f=2+1$ flavors of the "Asqtad" improved staggered dynamical sea quarks on a $16^3\times48$ lattice at $(m_\pi + m_K) / m_\kappa \approx 0.8$ and lattice spacing $a \approx 0.15$ fm.