$\rho$ Meson Decay in 2+1 Flavor Lattice QCD

We perform a lattice QCD study of the $\rho$ meson decay from the $N_f=2+1$ full QCD configurations generated with a renormalization group improved gauge action and a non-perturbatively $O(a)$-improved Wilson fermion action. The resonance parameters, the effective $\rho \to \pi \pi$ coupling constant and the resonance mass, are estimated from the $P$-wave scattering phase shift for the isospin I=1 two-pion system. The finite size formulas are employed to calculate the phase shift from the energy on the lattice. Our calculations are carried out at two quark masses, $m_{\pi }=410\mathrm{M}\mathrm{e}\mathrm{V}$ ($m_{\pi }\mathrm{/}{m}_{\rho }=0.46$) and $m_{\pi }=300\mathrm{M}\mathrm{e}\mathrm{V}$ ($m_{\pi }\mathrm{/}{m}_{\rho }=0.35$), on a ${32}^3\times 64$ ($La=2.9\mathrm{f}\mathrm{m}$) lattice at the lattice spacing $a=0.091\mathrm{f}\mathrm{m}$. We compare our results at these two quark masses with those given in the previous works using $N_f=2$ full QCD configurations and the experiment.