Current-Mass Ratios of the Light Quarks

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: $\frac{m_u}{m_d}=0.56\mathrm{}$, $\frac{m_s}{m_d}=20.1\mathrm{}$. 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.