Contribution of higher meson resonances to the electromagnetic $π$-meson mass difference

Abstract

Modifications of the DGMLY relation for calculation of electromagnetic $π$-meson mass difference based on the Chiral Symmetry Restoration phenomenon at high energies as well as the Operator Product Expansion of quark densities for vector ($ρ$) and axial-vector ($a_1$) meson fields difference are proposed. In the calculations higher meson resonances in vector and axial-vector channels are taken into account. It is shown that the inclusion of the first $ρ$ and $a_1$ radial excitations improves the results for electromagnetic $π$-meson mass difference as compared with the previous ones. Estimations on the electromagnetic $ρ$ and $a_1$-meson decay constants and the constant $L_{10}$ of effective chiral Lagrangian are obtained from the generalized Weinberg sum rules.