Lattice QCD Calculation of the $\rho$ Meson Decay Width

TL;DR

This paper reports a lattice QCD calculation of the $ ho$ meson decay width by analyzing the $P$-wave scattering phase shift of the two-pion system, providing results consistent with experimental data.

Contribution

The study introduces a lattice QCD approach to compute the $ ho$ meson decay width using finite size formulas and moving frames, with results aligning with experimental values.

Findings

Decay width consistent with experimental data

Resonance behavior observed near vector meson mass

Phase shift analysis confirms resonance presence

Abstract

We present a lattice QCD calculation of the $\rho$ meson decay width via the $P$-wave scattering phase shift for the I=1 two-pion system. Our calculation uses full QCD gauge configurations for $N_f=2$ flavors generated using a renormalization group improved gauge action and an improved Wilson fermion action on a $12^3\times24$ lattice at $m_\pi/m_\rho=0.41$ and the lattice spacing $1/a=0.92 {\rm GeV}$. The phase shift calculated with the use of the finite size formula for the two-pion system in the moving frame shows a behavior consistent with the existence of a resonance at a mass close to the vector meson mass obtained in spectroscopy. The decay width estimated from the phase shift is consistent with the experiment, when the quark mass is scaled to the realistic value.