Continuum Limit of Lattice QCD with Staggered Quarks in the Quenched Approximation: A Critical Role for the Chiral Extrapolation

We calculate the light quark spectrum of lattice QCD in the quenched approximation using staggered quarks. We take the light quark mass, infinite volume, continuum limit. With nonlinear chiral extrapolations, we find that the nucleon to $\rho$ mass ratio is $m_N/m_{\rho }=1.254\mathrm{}\pm 0.018\pm 0.028$, where the errors are statistical and systematic (within the quenched approximation), respectively. Since the experimental value is 1.22, our results indicate that the error due to quenching is $\lesssim 5\%$.