Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2012-02-27
Physics
High Energy Physics
High Energy Physics - Lattice
arXiv admin note: substantial text overlap with arXiv:1110.5975, arXiv:1110.1422 and with arXiv:1011.5288 and arXiv:0708.3705
Scientific paper
We present an exploratory lattice QCD calculation of the $\sigma$ meson decay width using the s-wave scattering phase shift for the isospin I=0 pion-pion ($\pi\pi$) system. The finite size formula developed by Rummukainen and Gottlieb is employed to estimate the phase shift, which demonstrates a characteristic consistent with the presence of a resonance around $\sigma$ meson mass. The effective range formula is adopted to describe the phase-shift dependence, and we extract the effective $\sigma \to \pi\pi$ coupling constant $g_{\sigma \pi\pi} = 2.69(44)$ GeV, which is consistent with the theoretical predictions. The decay width estimated from phase shift is about $236 \pm 49$ MeV. Our preliminary lattice simulations are carried out with MILC full QCD gauge configurations in the presence of 2+1 flavors of the "Asqtad" improved staggered dynamical sea quarks on a $16^3\times48$ lattice at $ m_\pi / m_\sigma \approx 0.414$ and lattice spacing $a \approx 0.15$ fm.
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