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Next-to-leading order corrections to radiative pion pair production via dispersion relations

Carlo M. Carloni Calame ^1,*, Marco Ghilardi ^2,1,†, Andrea Gurgone ^3,‡, Guido Montagna ^2,1,§, Mauro Moretti ^4,5,∥, Oreste Nicrosini^1,¶, Fulvio Piccinini ^1,6,**, and Francesco P. Ucci ^2,1,††

¹INFN, Sezione di Pavia, Via A. Bassi 6, 27100, Pavia, Italy
²Dipartimento di Fisica “Alessandro Volta,” Università di Pavia, Via Agostino Bassi 6, 27100, Pavia, Italy
³Division of Theoretical Physics, Ruđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
⁴Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
⁵INFN, Sezione di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
⁶INFN, Galileo Galilei Institute for Theoretical Physics, Largo Enrico Fermi 2, 50125 Firenze, Italy

^*Contact author: carlo.carloni.calame@pv.infn.it
^†Contact author: marco.ghilardi01@universitadipavia.it
^‡Contact author: andrea.gurgone@irb.hr
^§Contact author: guido.montagna@unipv.it
^∥Contact author: mauro.moretti@fe.infn.it
^¶Contact author: oreste.nicrosini@pv.infn.it
^**Contact author: fulvio.piccinini@pv.infn.it
^††Contact author: francesco.ucci@pv.infn.it

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Phys. Rev. D 114, 076022 – Published 21 October, 2026

DOI: https://doi.org/10.1103/8zd9-sytq

Abstract

We compute the next-to-leading order corrections to the radiative return process $e^{+} e^{-} \to π^{+} π^{-} γ$ using a dispersive representation of the pion form factor for the calculation of loop integrals. We compare our results with those of the factorized scalar QED approach, as well as with previous predictions obtained by us in the generalized vector meson dominance model. We show the numerical impact of the structure-dependent corrections on various observables of interest for radiative return experiments at flavor factories. Following recent input from the literature, we include in our calculation also corrections due to neutral pseudoscalar poles, and we provide a first estimate of such contributions. We also investigate additional mechanisms contributing to final-state radiation at center-of-mass energies around the $ϕ$ -meson resonance, such as radiative $ϕ$ decays, presenting numerical results that are relevant for the KLOE experiment. These novel features are implemented in the Monte Carlo event generator babayaga@nlo, which can now be used to evaluate the impact of the modeling of pion-photon interaction in radiative return measurements.

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Phys. Rev. D 114, 076022– Published 21 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 5 August 2026
Accepted 2 October 2026

DOI: https://doi.org/10.1103/8zd9-sytq

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Next-to-leading order corrections to radiative pion pair production via dispersion relations

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