Rho resonance parameters from lattice QCD

TL;DR

This paper calculates the rho meson resonance parameters from lattice QCD simulations at two pion masses, extrapolates to the physical point using chiral perturbation theory, and finds a lower rho mass possibly due to missing strange quarks.

Contribution

It provides a high-precision lattice QCD determination of rho resonance parameters at different quark masses and introduces an extrapolation method using unitarized chiral perturbation theory.

Findings

Extrapolated rho mass is 720 MeV, lower than the physical value.

Phase shifts are well described by the unitarized chiral model.

The absence of strange quarks may influence the rho mass estimate.

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.