Light Quark Mass Spectrum in Quantum Chromodynamics

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