Timelike form factor for the anomalous process $\gamma^\ast \pi \rightarrow \pi \pi$

Angel S. Miramontes; Gernot Eichmann; Reinhard Alkofer

doi:10.1016/j.physletb.2025.139659

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arXiv · 2504.20899

Timelike form factor for the anomalous process $\gamma^\ast \pi \rightarrow \pi \pi$

Angel S. Miramontes·Gernot Eichmann·Reinhard Alkofer

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Abstract

The form factor $F_{3\pi}(s,t,u)$ for the anomalous process $\gamma^\ast \pi \rightarrow \pi \pi$ 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.

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Angel S. Miramontes, Gernot Eichmann, Reinhard Alkofer. 2025-04-29. Timelike form factor for the anomalous process $\gamma^\ast \pi \rightarrow \pi \pi$. https://doi.org/10.1016/j.physletb.2025.139659

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