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

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.