Rho resonance parameters from lattice QCD

Abstract

We perform a high-precision calculation of the phase shifts for $\pi$-$\pi$ scattering in the I = 1, J = 1 channel in the elastic region using elongated lattices with two mass-degenerate quark favors ($N_f=2$). We extract the $\rho$ resonance parameters using a Breit-Wigner fit at two different quark masses, corresponding to $m_{\pi }=226$MeV and $m_{\pi }=315$MeV, and perform an extrapolation to the physical point. The extrapolation is based on a unitarized chiral perturbation theory model that describes well the phase-shifts around the resonance for both quark masses. We find that the extrapolated value, $m_{\rho }=720(1)(15)$MeV, is significantly lower that the physical rho mass and we argue that this shift could be due to the absence of the strange quark in our calculation.

20 pages, 12 figures, version to appear in PRD

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