https://doi.org/10.1140/epjs/s11734-026-02304-z
Regular Article
Neutral and charged pion form factors in the intermediate-energy region from double-dilaton HQCD model
Grup de Física Teòrica, Departament de Física, Universitat Autònoma de Barcelona, and Institut de Física d’Altes Energies (IFAE), and The Barcelona Institute of Science and Technology (BIST), Campus UAB, 08193, Bellaterra, Barcelona, Spain
a
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Received:
12
December
2025
Accepted:
30
March
2026
Published online:
9
April
2026
Abstract
We compute the form factors of both neutral and charged pion using a non-perturbative running of the strong coupling constant 
obtained using a double-dilaton holographic QCD model. These form factors remain poorly understood in the intermediate-energy region, which marks the transition between low- and high-energy physics. In particular, experimental data for the neutral pion form factor exhibits a deviation from the expected asymptotic behavior, and the charged pion form factor remains comparatively less explored. To address these issues, we employ the pion distribution amplitude formalism to investigate the form factor behavior in this intermediate regime. Our results suggests that non-perturbative physics of the strong interaction is relevant even at energy scales traditionally considered perturbative, implying that the perturbative regime could occur at higher energies than previously thought. Finally, our approach allows us to study isospin-breaking effects through the quadratic pion mass difference.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
