Preliminary lattice study of $\sigma$ meson decay width

We report an exploratory lattice investigation of $\sigma$ meson decay width using s-wave scattering phase for isospin I=0 pion-pion ($\pi\pi$) system. Rummukainen-Gottlieb formula is used to estimate the scattering phase, which demonstrate the presence of a resonance around $\sigma$ meson. Using the effective range formula we extract the effective $\sigma \to \pi\pi$ coupling constant as $g_{\sigma \pi\pi} = 2.69(44)$ GeV, which is consistent with theoretical predictions. The estimated decay width is about $236 \pm 49$ MeV. These simulations are carried out on a $16^3\times48$ MILC gauge configuration with the $N_f=2+1$ flavor of the "Asqtad" improved staggered dynamical sea quarks at $m_\pi / m_\sigma \approx 0.414$ and the lattice spacing $a \approx 0.15$ fm.