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 ${16}^3\times 48$ MILC gauge configuration with the $N_f=2+1$ flavor of the “Asqtad” improved staggered dynamical sea quarks at $m_{\pi }\mathrm{/}{m}_{\sigma }\approx 0.414$ and the lattice spacing $a \approx 0.15$ fm.