Light-quark masses and isospin violation

Abstract

Isospin-violating effects arising from a nonvanishing quark mass difference $m_d-m_u$ are discussed, in particular for the ${\pi }^{+}-{\pi }^0$ mass-difference question and for ${\eta }^{\prime }\to 3\pi$ and $\Sigma \to \Lambda +e+\nu$ 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.