Quark anomalous magnetic moment and its effects on the $\rho$ meson properties

Abstract

A symmetry-preserving treatment of mesons, within a Dyson-Schwinger and Bethe-Salpeter equations approach, demands an interconnection between the kernels of the quark gap equation and meson Bethe-Salpeter equation. Appealing to those symmetries expressed by the vector and axial-vector Ward-Green-Takahashi identitiges (WGTI), we construct a two-body Bethe-Salpeter kernel and study its implications in the vector channel; particularly, we analyze the structure of the quark-photon vertex, which explicitly develops a vector meson pole in the timelike axis and the quark anomlaous magnetic moment term, as well as a variety of $\rho$ meson properties: mass and decay constants, electromagnetic form factors, and valence-quark distribution amplitudes.