We present a lattice QCD calculation of the parameters of the $\rho$ meson decay. The study is carried out on spatially asymmetric boxes using nHYP-smeared clover fermions with two mass-degenerate quark flavors. Our calculations are carried out at a pion mass $m_{\pi }=304(2)\mathrm{MeV}$ on the set of lattices $V={24}^2\times \eta 24\times 48$ with $\eta =1.0$, 1.25, and 2.0 with lattice spacing $a=0.1255(7)\mathrm{fm}$. The resonance mass $m_{\rho }=827(3)(5)\mathrm{MeV}$ and coupling constant $g_{\rho \pi \pi }=6.67(42)$ are calculated using the $P$-wave scattering phase shifts. We construct a $2\times 2$ correlation matrix to extract the energy of the scattering states and compute the phase shifts using the finite volume formula. By varying the degree of asymmetry, we are able to compute a set of phase shifts that are evenly distributed throughout the spectral region where the $\rho$ decays.

• Received 9 November 2012

DOI:https://doi.org/10.1103/PhysRevD.87.014503