Light Quark Mass Spectrum in Quantum Chromodynamics

Quantum chromodynamics has placed the problem of hadronic symmetry breaking on a rational basis. The current-quark mass ratios can be shown to be renormalization-group invariants up to small and controllable corrections from flavor interactions. We calculate the mass ratios of the light u, d, and s quarks using the pseudoscalar-meson mass spectrum, the baryon mass spectrum, and the η→3π decay. The main theoretical assumptions are that low-lying-resonance and Born terms correctly estimate the photonic contribution to isotopic mass splitting and that chiral perturbation theory—equivalently kaon partial convervation of axialvector current—correctly estimates chiral-symmetry breaking. Taking account of all leading-order chiral corrections to the meson spectrum and from the baryon spectrum and η→3π decay we obtain mumd=0.38±0.13 and mdms=0.045±0.011. We conclude that while a vanishing up-quark mass is not rigorously ruled out it is unattractive from the standpoint of the presently consistent phenomenology of hadronic symmetry breaking