Lattice QCD study on $K^\ast(892)$ meson decay width

TL;DR

This study uses lattice QCD to analyze the decay width of the $K^ ext{*}(892)$ meson through pion-kaon scattering phase shifts, providing results consistent with experimental data.

Contribution

It presents an exploratory lattice QCD approach to determine the $K^ ext{*}(892)$ decay width using modified phase shift analysis and effective range formulas.

Findings

Decay width of $64.9 \, ext{MeV}$ with uncertainty

Effective coupling constant $g_{K^* o ext{pi} K} = 6.38(78)$

Resonance behavior observed at $K^*(892)$ mass

Abstract

We deliver an exploratory lattice QCD examination of the $K^\ast(892)$ meson decay width with the help of the p-wave scattering phase $\delta_1$ of pion-kaon ($\pi K$) system in the isospin $I=1/2$ channel, which are extracted by the modified Rummukainen-Gottlieb formula for two-particle system with arbitrary mass, and it clearly reveals the entity of a resonance at a mass around $K^\ast(892)$ meson mass. The effective range formula is applied to describe the energy dependence of the scattering phase and we obtain the effective $K^\ast \to \pi K$ coupling constant as $g_{K^\ast \pi K} = 6.38(78)$, and subsequently achieve the decay width to be $64.9 \pm 8.0$ MeV, which is in reasonable accordance with the current experiment. Our lattice investigations are conducted on a $20^3\times48$ MILC full QCD gauge configuration at $(m_\pi + m_K) / m_{K^\ast} \approx 0.739$ and the lattice spacing $a \approx 0.15$ fm.