Mass ratios of the light quarks

Abstract

We derive a consistent set of light quark mass ratios which are compatible with the available constraints of chiral symmetry treated to next-to-leading order. Also required as input is resonance saturation of a set of low-energy amplitudes, in particular for the pion and kaon electromagnetic mass difference. The results (${\mathit{m}}_{\mathit{d}}$+${\mathit{m}}_{\mathit{u}}$)/${\mathit{m}}_{\mathit{s}}$=1/15.5, (${\mathit{m}}_{\mathit{d}}$-${\mathit{m}}_{\mathit{u}}$)/${\mathit{m}}_{\mathit{s}}$=1/29 are modestly different from previous values, and resolve the long-standing puzzle of the η→3π decay rate.