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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: mₔ{m₃}=0. 56, mₒ{m₃}=20. 1. We find that to this order, mₒ{m₃} is a known function of mₔ{m₃}. 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.
Kaplan et al. (Mon,) studied this question.