Isospin Violation in Low-energy Hadronic Physics

Abstract

Isospin violation in pionic and nuclear systems is studied at energies comparable to the pion mass using the general effective chiral Lagrangian. It is shown that the smallness of observed isospin breaking arises naturally from QCD (with electromagnetic interactions included). Except for process that involve two neutral pions where one expects an O $$\left( \frac{{{m}_{d}}-{{m}_{u}}}{{{m}_{d}}+{{m}_{u}}} \right)$$ effect, isospin in violation from the quark mass difference is further suppressed by powers of the pion mass over the characteristic scale of QCD. As a result, the pion mass difference tends to be the dominant effect. Pion-pion, pion-nucleon scattering and the nucleon-nucleon interaction are considered. The implications for the latter case are: i) charge dependent forces due to the pion mass difference in one pion exchange are the largest; ii) charge asymmetric forces arise from sub-leading operators, which are related to meson mixing.