Light-quark mass spectrum in quantum chromodynamics

Abstract

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 $\eta \to 3\pi$ 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 $\eta \to 3\pi$ decay we obtain $\frac{m_u}{m_d}=0.38\mathrm{}\pm 0.13$ and $\frac{m_d}{m_s}=0.045\mathrm{}\pm 0.011$. 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.