Light-quark masses and isospin violation

Abstract

Isospin-violating effects arising from a nonvanishing quark mass difference ${m}_{d}\ensuremath{-}{m}_{u}$ are discussed, in particular for the ${\ensuremath{\pi}}^{+}\ensuremath{-}{\ensuremath{\pi}}^{0}$ mass-difference question and for ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}3\ensuremath{\pi}$ and $\ensuremath{\Sigma}\ensuremath{\rightarrow}\ensuremath{\Lambda}+e+\ensuremath{\nu}$ decays. The role of the strong anomaly is emphasized, and exploited to bring out certain relations among heavy-quark, light-quark, and gluon operator matrix elements. The anomaly suppresses isospin-violating effects that might otherwise be substantial for the Bjorken electroproduction sum rule.