Timelike behavior of the pion electromagnetic form factor in the functional formalism

The electromagnetic form factor of the pion is calculated within use functional formalism. We develop integral representation for minimal set Standard Model Green's functions and derive dispersion relation in two-flavor QCD isospin limit ${m}_{u}={m}_{d}$. dressed quark propagator as obtained from gap equation Minkowski space Dyson-Schwinger equations formalism to approximate first time. evaluate spacelike well timelike momentum presented A new Nakanishi-like proved on basis vector Bethe-Salpeter quark-photon with a ladder-rainbow kernel. gauge technique turns out be part entire structure vertex. In analytic approach here, it shown that large amount $\ensuremath{\rho}$-meson peak cross section ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ governed by invariance QED/QCD---i.e., gauge-technique-constructed This approximation naturally explains broad shape peak.