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  • Open Access

Data-driven analysis of the γγ*→π0 system using mathematical models and the role of feedback-loop dynamics

N. G. Stefanis*

  • *Contact author: stefanis@tp2.ruhr-uni-bochum.de
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Phys. Rev. D 112, 074042 – Published 30 October, 2025

DOI: https://doi.org/10.1103/jq1w-yb7x

Abstract

The data behavior of the pion-photon transition form factor (TFF) is discussed using a nonlinear mathematical model with two parameters B and C. Analysis shows that the model’s inherent inhibition provides a precondition for the asymptotic saturation of the TFF in agreement with perturbative quantum chromodynamics (QCD). Integral to this derivation is the use of a novel fundamental relation between the half-saturated TFF and its asymptotic limit given by B. This helps avoid the determination of the location of the TFF at infinite momentum by estimating instead the maximum slope of the curve at Q2=C. In conjunction with the 1σ(B,C) confidence ellipse, this framework provides an improved fit to the Belle data by setting stronger constraints on the fitting parameters and taking into account the sensitivity to third-party events below Belle’s kinematic coverage. Without inhibition, the slope of the TFF curve would continue to grow so that saturation toward the asymptotic QCD limit would not be achieved. In order to compare the key features of TFF fit models to upcoming high-precision data in a standardized way, a conformity protocol in terms of QCD-based criteria is worked out. Adopting a broader perspective, we show that the asymptotic saturation of an inhibited TFF fit curve is analogous to a mechanical system driven by a feedback-loop mechanism in control theory.

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References (44)

  1. G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980).
  2. S. J. Brodsky and G. P. Lepage, Phys. Rev. D 24, 1808 (1981).
  3. P. A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
  4. H. J. Behrend et al. (CELLO Collaboration), Z. Phys. C 49, 401 (1991).
  5. J. Gronberg et al. (CLEO Collaboration), Phys. Rev. D 57, 33 (1998).
  6. B. Aubert et al. (BABAR Collaboration), Phys. Rev. D 80, 052002 (2009).
  7. S. Uehara et al. (Belle Collaboration), Phys. Rev. D 86, 092007 (2012).
  8. C. F. Redmer (BESIII Collaboration), EPJ Web Conf. 212, 04004 (2019).
  9. M. Ablikim et al., Chin. Phys. C 44, 040001 (2020).
  10. N. G. Stefanis, Phys. Rev. D 102, 034022 (2020).
  11. P. Masjuan, Phys. Rev. D 86, 094021 (2012).
  12. G. Eichmann, C. S. Fischer, E. Weil, and R. Williams, Phys. Lett. B 774, 425 (2017).
  13. R. Escribano and S. Gonzàlez-Solís, Chin. Phys. C 42, 023109 (2018).
  14. N. G. Stefanis, A. P. Bakulev, S. V. Mikhailov, and A. V. Pimikov, Phys. Rev. D 87, 094025 (2013).
  15. N. Wiener, Cybernetics; or, Control and Communication in the Animal and the Machine (M.I.T. Press, New York, 1961).
  16. V. M. Braun, A. N. Manashov, S. Moch, and J. Schoenleber, Phys. Rev. D 104, 094007 (2021).
  17. J. Gao, T. Huber, Y. Ji, and Y.-M. Wang, Phys. Rev. Lett. 128, 062003 (2022).
  18. G. P. Lepage and S. J. Brodsky, Phys. Lett. 87B, 359 (1979).
  19. L. Michaelis and M. L. Menten, Biochemische Zeitschrift 49, 339 (1913).
  20. L. Michaelis and M. M. L. Menten, FEBS Lett. 587, 2712 (2013).
  21. S. J. Brodsky, F.-G. Cao, and G. F. de Téramond, Phys. Rev. D 84, 033001 (2011).
  22. A. P. Bakulev, S. V. Mikhailov, A. V. Pimikov, and N. G. Stefanis, Phys. Rev. D 86, 031501(R) (2012).
  23. S. V. Mikhailov, A. V. Pimikov, and N. G. Stefanis, Phys. Rev. D 103, 096003 (2021).
  24. A. V. Efremov and A. V. Radyushkin, Theor. Math. Phys. 42, 97 (1980).
  25. V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112, 173 (1984).
  26. A. P. Bakulev, S. V. Mikhailov, and N. G. Stefanis, Phys. Lett. B 508, 279 (2001); 590, 309(E) (2004).
  27. S. S. Agaev, V. M. Braun, N. Offen, and F. A. Porkert, Phys. Rev. D 83, 054020 (2011).
  28. N. G. Stefanis, Phys. Lett. B 738, 483 (2014).
  29. G. S. Bali, V. M. Braun, S. Bürger, M. Göckeler, M. Gruber, F. Hutzler, P. Korcyl, A. Schäfer, A. Sternbeck, and P. Wein (RQCD Collaboration), J. High Energy Phys. 08 (2019) 065; 11 (2020) 37(A).
  30. J. Hua et al. (Lattice Parton Collaboration), Phys. Rev. Lett. 129, 132001 (2022).
  31. X. Gao, A. D. Hanlon, N. Karthik, S. Mukherjee, P. Petreczky, P. Scior, S. Syritsyn, and Y. Zhao, Phys. Rev. D 106, 074505 (2022).
  32. L. Chang, I. C. Cloet, J. J. Cobos-Martinez, C. D. Roberts, S. M. Schmidt, and P. C. Tandy, Phys. Rev. Lett. 110, 132001 (2013).
  33. V. M. Braun, A. N. Manashov, S. Moch, and M. Strohmaier, J. High Energy Phys. 06 (2017) 037.
  34. W. Altmannshofer et al. (Belle-II Collaboration), Prog. Theor. Exp. Phys. 2019, 123C01 (2019); 2020, 029201(E) (2020).
  35. N. G. Stefanis and A. V. Pimikov, Nucl. Phys. A945, 248 (2016).
  36. V. M. Braun and I. E. Filyanov, Z. Phys. C 44, 157 (1989) [Yad. Fiz. 50, 818 (1989)].
  37. N. G. Stefanis, S. V. Mikhailov, and A. V. Pimikov, Few Body Syst. 56, 295 (2015).
  38. B. Melić, D. Müller, and K. Passek-Kumerički, Phys. Rev. D 68, 014013 (2003).
  39. S. V. Mikhailov, A. V. Pimikov, and N. G. Stefanis, Phys. Rev. D 93, 114018 (2016).
  40. I. I. Balitsky, V. M. Braun, and A. V. Kolesnichenko, Nucl. Phys. B312, 509 (1989).
  41. A. Khodjamirian, Eur. Phys. J. C 6, 477 (1999).
  42. C. Ayala, S. V. Mikhailov, and N. G. Stefanis, Phys. Rev. D 98, 096017 (2018); 101, 059901(E) (2020).
  43. S. Mikhailov, A. Pimikov, and N. G. Stefanis, EPJ Web Conf. 258, 03003 (2022).
  44. A. Rohatgi, Webplotdigitizer: Version 4.4 (2020), https://automeris.io/WebPlotDigitizer.

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Phys. Rev. D 112, 074042– Published 30 October, 2025
  • Received 15 January 2025
  • Accepted 6 October 2025
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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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