Timelike form factor for the anomalous process ${\gamma }^{\ast }\pi \to \pi \pi$

Abstract

The form factor $F_{3\pi }(s,t,u)$ for the anomalous process ${\gamma }^{\ast }\pi \to \pi \pi$ 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 rho meson resonance, the form factor $F_{3\pi }(s,t,u)$ is determined for timelike Mandelstam s. In particular, predictions are made for the kinematics relevant for the Primakoff reaction studied with COMPASS/AMBER at CERN.

9 pages, 5 figures; Added references, matches the published version plus additional remark on quark mass effect

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