Current-mass ratios of the light quarks.

Abstract

We investigate the current-mass ratios of the light quarks by fitting the squares of meson masses to second order in chiral-symmetry breaking, determining corrections to Weinberg's first-order values: $\frac{{m}_{u}}{{m}_{d}}=0.56$, $\frac{{m}_{s}}{{m}_{d}}=20.1$. We find that to this order, $\frac{{m}_{s}}{{m}_{d}}$ is a known function of $\frac{{m}_{u}}{{m}_{d}}$. The values of the quark-mass ratios can be constrained by limiting the size of second-order corrections to the squares of meson masses. We find that for specific values of presently unmeasured phenomenological parameters one can have a massless $u$ quark. In that case 30% of the squares of meson masses arise from operators second order in chiral-symmetry breaking.