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Coherent deeply virtual Compton scattering on He4 beyond leading power

V. Martínez-Fernández1,2, B. Pire3, P. Sznajder4, and J. Wagner4

Phys. Rev. C 114, 035203 – Published 9 September, 2026

DOI: https://doi.org/10.1103/h7kn-ql7j

Abstract

Coherent hard exclusive reactions on light nuclei provide access to their quark and gluon structure and enable three-dimensional tomography of these complex systems. We study deeply virtual Compton scattering on a helium-4 target, including both kinematic twist-3 and twist-4 corrections, as well as next-to-leading-order corrections to the twist-2 amplitude in the strong coupling αs. We show that these contributions are crucial for achieving a precise description of the data and, as a result, obtain the first tomographic image of the helium-4 nucleus at the quark-gluon level.

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Physics Subject Headings (PhySH)

See Also

Quark and Gluon Tomography of the Helium-4 Nucleus

V. Martínez-Fernández, B. Pire, P. Sznajder, and J. Wagner
Phys. Rev. Lett. 137, 111905 (2026)

Article Text

References (57)

  1. E. R. Berger, F. Cano, M. Diehl, and B. Pire, Generalized parton distributions in the deuteron, Phys. Rev. Lett. 87, 142302 (2001).
  2. A. Kirchner and D. Mueller, Deeply virtual Compton scattering off nuclei, Eur. Phys. J. C 32, 347 (2003).
  3. V. Guzey and M. Strikman, Deeply virtual Compton scattering on spinless nuclear targets in the impulse approximation, Phys. Rev. C 68, 015204 (2003).
  4. F. Cano and B. Pire, Deep electroproduction of photons and mesons on the deuteron, Eur. Phys. J. A 19, 423 (2004).
  5. S. Scopetta, Generalized parton distributions of He3, Phys. Rev. C 70, 015205 (2004).
  6. A. V. Belitsky, D. Mueller, and A. Kirchner, Theory of deeply virtual Compton scattering on the nucleon, Nucl. Phys. B 629, 323 (2002).
  7. X. Ji, Gauge-invariant decomposition of nucleon spin, Phys. Rev. Lett. 78, 610 (1997).
  8. A. V. Belitsky and A. V. Radyushkin, Unraveling hadron structure with generalized parton distributions, Phys. Rep. 418, 1 (2005).
  9. M. Diehl, Generalized parton distributions, Phys. Rep. 388, 41 (2003).
  10. V. M. Braun, Y. Ji, and A. N. Manashov, Kinematic power corrections to deeply virtual Compton scattering to twist-six accuracy, Phys. Rev. D 111, 076011 (2025).
  11. V. Martinez-Fernandez, B. Pire, P. Sznajder, and J. Wagner, Timelike Compton scattering on a spin-0 target with kinematic twist-4 precision, Phys. Rev. D 111, 074034 (2025).
  12. M. Burkardt, Impact parameter space interpretation for generalized parton distributions, Int. J. Mod. Phys. A 18, 173 (2003).
  13. J. P. Ralston and B. Pire, Femtophotography of protons to nuclei with deeply virtual Compton scattering, Phys. Rev. D 66, 111501 (2002).
  14. M. Diehl, Generalized parton distributions in impact parameter space, Eur. Phys. J. C 25, 223 (2002); Erratum: 31, 277 (2003).
  15. C. Lorcé, H. Moutarde, and A. P. Trawiński, Revisiting the mechanical properties of the nucleon, Eur. Phys. J. C 79, 89 (2019).
  16. V. Martínez-Fernández and C. Mezrag, Dispersion relations of deeply virtual Compton scattering: investigating twist-4 kinematic power corrections, Phys. Rev. D 113, 094004 (2026).
  17. V. Martínez-Fernández, D. Binosi, C. Mezrag, and Z.-Q. Yao, Constraining the energy-momentum tensor through the DVCS dispersion relation beyond leading power, Phys. Rev. D 113, 094003 (2026).
  18. B. Pire, L. Szymanowski, and J. Wagner, Next-to-leading order corrections to timelike, spacelike, and double deeply virtual Compton scattering, Phys. Rev. D 83, 034009 (2011).
  19. A. V. Belitsky and D. Mueller, Off-forward gluonometry, Phys. Lett. B 486, 369 (2000).
  20. V. Martínez-Fernández, B. Pire, P. Sznajder, and J. Wagner, companion paper, Quark and gluon tomography of the helium-4 nucleus, Phys. Rev. Lett. 137, 111905 (2026).
  21. M. Hattawy, N. A. Baltzell, R. Dupré, K. Hafidi, S. Stepanyan, S. Bültmann, R. De Vita, A. El Alaoui, L. El Fassi, H. Egiyan, et al. (CLAS Collaboration), First exclusive measurement of deeply virtual Compton scattering off He4: Toward the 3D tomography of nuclei, Phys. Rev. Lett. 119, 202004 (2017).
  22. R. Dupré, M. Hattawy, N. A. Baltzell, S. Bültmann, R. De Vita, A. El Alaoui, L. El Fassi, H. Egiyan, F. X. Girod, M. Guidal, et al. (CLAS Collaboration), Measurement of deeply virtual Compton scattering off He4 with the CEBAF large acceptance spectrometer at Jefferson lab, Phys. Rev. C 104, 025203 (2021).
  23. S. Fucini, S. Scopetta, and M. Viviani, Coherent deeply virtual Compton scattering off He4, Phys. Rev. C 98, 015203 (2018).
  24. R. Kleiss, The cross section for e+ee+ee+e, Nucl. Phys. B 241, 61 (1984).
  25. R. Kleiss and W. Stirling, Spinor techniques for calculating, Nucl. Phys. B 262, 235 (1985).
  26. A. Bacchetta, U. D'Alesio, M. Diehl, and C. A. Miller, Single-spin asymmetries: The Trento conventions, Phys. Rev. D 70, 117504 (2004).
  27. V. M. Braun, A. N. Manashov, and B. Pirnay, Finite- t and target mass corrections to deeply virtual Compton scattering on a scalar target, Phys. Rev. D 86, 014003 (2012).
  28. X.-D. Ji and J. Osborne, One-loop corrections and all order factorization in deeply virtual Compton scattering, Phys. Rev. D 58, 094018 (1998).
  29. V. M. Braun, A. N. Manashov, D. Müller, and B. M. Pirnay, Deeply virtual Compton scattering to the twist-four accuracy: Impact of finite- t and target mass corrections, Phys. Rev. D 89, 074022 (2014).
  30. S. V. Goloskokov and P. Kroll, The longitudinal cross section of vector meson electroproduction, Eur. Phys. J. C 50, 829 (2007).
  31. A. V. Radyushkin, Double distributions and evolution equations, Phys. Rev. D 59, 014030 (1998).
  32. R. A. Khalek, R. Gauld, T. Giani, E. R. Nocera, T. R. Rabemananjara, and J. Rojo, nNNPDF3.0: Evidence for a modified partonic structure in heavy nuclei, Eur. Phys. J. C 82, 507 (2022).
  33. M. V. Polyakov and C. Weiss, Skewed and double distributions in the pion and the nucleon, Phys. Rev. D 60, 114017 (1999).
  34. V. Bertone, H. Dutrieux, C. Mezrag, J. M. Morgado, and H. Moutarde, Revisiting evolution equations for generalised parton distributions, Eur. Phys. J. C 82, 888 (2022).
  35. V. Bertone, APFEL++: A new PDF evolution library in C++, arXiv:1708.00911.
  36. B. Pire, J. Soffer, and O. Teryaev, Positivity constraints for off-forward parton distributions, Eur. Phys. J. C 8, 103 (1999).
  37. M. Kirch, P. V. Pobylitsa, and K. Goeke, Inequalities for nucleon generalized parton distributions with helicity flip, Phys. Rev. D 72, 054019 (2005).
  38. V. M. Braun, Y. Ji, and A. N. Manashov, Next-to-leading-power kinematic corrections to DVCS: A scalar target, J. High Energy Phys. 01 (2023) 078.
  39. J. P. Repellin, P. Lehmann, J. Lefrançois, and D. B. Isabelle, Elastic electron scattering on helium 4, Phys. Lett. 16, 169 (1965).
  40. R. F. Frosch, J. S. McCarthy, R. E. Rand, and M. R. Yearian, Structure of the He4 nucleus from elastic electron scattering, Phys. Rev. 160, 874 (1967).
  41. R. G. Arnold et al., Elastic electron scattering from He3 and He4 at high momentum transfer, Phys. Rev. Lett. 40, 1429 (1978).
  42. C. R. Ottermann, G. Kobschall, K. Maurer, K. Rohrich, C. Schmitt, and V. H. Walther, Elastic electron scattering from He3 and He4, Nucl. Phys. A 436, 688 (1985).
  43. A. Camsonne et al. (Jefferson Lab Hall A Collaboration), JLab measurement of the He4 charge form factor at large momentum transfers, Phys. Rev. Lett. 112, 132503 (2014).
  44. W. Armstrong et al., Partonic structure of light nuclei, arXiv:1708.00888.
  45. R. Abdul Khalek et al., Science requirements and detector concepts for the electron-ion collider, Nucl. Phys. A 1026, 122447 (2022).
  46. D. P. Anderle et al., Electron-ion collider in China, Front. Phys. 16, 64701 (2021).
  47. E. R. Berger, M. Diehl, and B. Pire, Timelike Compton scattering: Exclusive photoproduction of lepton pairs, Eur. Phys. J. C 23, 675 (2002).
  48. O. Grocholski, H. Moutarde, B. Pire, P. Sznajder, and J. Wagner, Data-driven study of timelike Compton scattering, Eur. Phys. J. C 80, 171 (2020).
  49. D. Mueller, B. Pire, L. Szymanowski, and J. Wagner, Timelike and spacelike hard exclusive reactions, Phys. Rev. D 86, 031502 (2012).
  50. H. Moutarde, B. Pire, F. Sabatie, L. Szymanowski, and J. Wagner, Timelike and spacelike deeply virtual Compton scattering at next-to-leading order, Phys. Rev. D 87, 054029 (2013).
  51. K. Deja, V. Martinez-Fernandez, B. Pire, P. Sznajder, and J. Wagner, Phenomenology of double deeply virtual Compton scattering in the era of new experiments, Phys. Rev. D 107, 094035 (2023).
  52. A. Pedrak, B. Pire, L. Szymanowski, and J. Wagner, Hard photoproduction of a diphoton with a large invariant mass, Phys. Rev. D 96, 074008 (2017); 100, 039901(E) (2019).
  53. A. Pedrak, B. Pire, L. Szymanowski, and J. Wagner, Electroproduction of a large invariant mass photon pair, Phys. Rev. D 101, 114027 (2020).
  54. O. Grocholski, B. Pire, P. Sznajder, L. Szymanowski, and J. Wagner, Phenomenology of diphoton photoproduction at next-to-leading order, Phys. Rev. D 105, 094025 (2022).
  55. R. Boussarie, B. Pire, L. Szymanowski, and S. Wallon, Exclusive photoproduction of a γρ pair with a large invariant mass, J. High Energy Phys. 02 (2017) 054; Erratum: 10 (2018) 029.
  56. G. Duplančić, S. Nabeebaccus, K. Passek-Kumerički, B. Pire, L. Szymanowski, and S. Wallon, Probing chiral-even and chiral-odd leading twist quark generalized parton distributions through the exclusive photoproduction of a γρ pair, Phys. Rev. D 107, 094023 (2023).
  57. A. V. Belitsky and D. Mueller, Exclusive electroproduction of lepton pairs as a probe of nucleon structure, Phys. Rev. Lett. 90, 022001 (2003).

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