Quark anomalous magnetic moment and its effects on the ρ 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 ρ meson properties: mass and decay constants, electromagnetic form factors, and valencequark distribution amplitudes.

Pion and Kaon box contribution to aμHLbL

“…Once the 1 and 2-body kernels have been specified (i.e., a truncation scheme has been defined), gap and Bethe-Salpeter equations can be solved. In fact, ½K ð1Þ and ½K ð2Þ are related via vector and axial-vector Ward-Green-Takahashi identities (WGTIs) [91][92][93], implying charge conservation and the appearance of pions and kaons (in the chiral limit) as Nambu-Goldstone bosons of dynamical chiral symmetry breaking [94].…”

Pion and Kaon box contribution to $a_μ^{\text{HLbL}}$

“…Once the 1 and 2-body kernels have been specified (that is, a truncation has been defined), gap and Bethe-Salpeter equations can be solved. In fact, [K (1) ] and [K (2) ] are related via vector and axial-vector Ward-Green-Takahashi identities (WGTIs) [91][92][93], implying charge conservation and the appearance of pions and Kaons (in the chiral limit) as Nambu-Goldstone bosons of dynamical chiral symmetry breaking [94].…”