Timelike form factor for the anomalous process γ⁎π → ππ

The form factor F 3 π ( s , t , u ) for the anomalous process γ ⁎ π → π π is calculated in the isospin limit for several values of the light current-quark mass (i.e., the pion mass) using Dyson–Schwinger and Bethe–Salpeter equations. Beyond a quark interaction kernel representing gluon-mediated interactions, leading beyond-rainbow-ladder effects at low energies are incorporated by back-coupling pions as explicit degrees of freedom. Building upon an earlier calculation of the quark-photon vertex that captures the branch cut associated with the two-pion threshold and the ρ -meson resonance, the form factor F 3 π ( s , t , u ) is determined for timelike Mandelstam s . In particular, predictions are made for the kinematics relevant to the Primakoff reaction studied with COMPASS/AMBER at CERN.