Isospin symmetry breaking and gluon anomaly

Abstract

The contribution of the electromagnetic interaction to the self-energy of pseudo-Goldstone bosons, as well as to the mixing angles and weak decay constants, is calculated in the first nonleading order in the simultaneous expansion in powers of $1/N_c$, momenta and quark masses. Particular attention is paid to the isospin symmetry breaking which is generated by means of $\eta$ and $\eta'$ admixtures to the pion. It is shown that the gluon anomaly enhances the electromagnetic contribution to the $\pi^0$-$\eta$ and $\pi^0$-$\eta'$ mixing angles, which facilitates the restoration of isospin symmetry in the spectrum of pseudo-Goldstone states at next-to-leading order. The contribution of the electromagnetic interaction to the $\eta$-$\eta'$ mixing angle is shown to be only about 3\%.