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Constraining the energy-momentum tensor through the DVCS dispersion relation beyond leading power

Víctor Martínez-Fernández1,2,*, Daniele Binosi3,†, Cédric Mezrag1,‡, and Zhao-Qian Yao (姚照千)4,5,§

  • *Contact author: victor.martinezfernandez@cea.fr
  • †Contact author: binosi@ectstar.eu
  • ‡Contact author: cedric.mezrag@cea.fr
  • §Contact author: zhaoqian.yao@dci.uhu.es

Phys. Rev. D 113, 094003 – Published 4 May, 2026

DOI: https://doi.org/10.1103/rqnd-gvlq

Abstract

In this paper, we analyze and interpret the kinematic power corrections to deeply virtual Compton scattering dispersion relation. We show that the kinematic corrections at twist-four can be connected to other form factors of the energy-momentum tensor beyond the pressure distribution involved at leading power, namely the ones related to momentum and total angular momentum distributions. In the nucleon case, these corrections are not negligible at presently accessible virtualities. The deeply virtual Compton scattering (DVCS) subtraction constant becomes an experimental constraint on momentum distributions, pressure forces distributions, and total angular momentum distributions. Finally, we use continuum and lattice-QCD results to predict the expected size of the DVCS subtraction constant, and conclude that momentum distributions are responsible of roughly one-third of the experimental signal at Q2=2  GeV2.

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Dispersion relations of deeply virtual Compton scattering: Investigating twist-four kinematic power corrections

Víctor Martínez-Fernández and Cédric Mezrag
Phys. Rev. D 113, 094004 (2026)

Article Text

References (40)

  1. M. V. Polyakov, Generalized parton distributions and strong forces inside nucleons and nuclei, Phys. Lett. B 555, 57 (2003).
  2. Cédric Lorcé and Peter Schweitzer, Pressure inside hadrons: Criticism, conjectures, and all that, Acta Phys. Pol. B 56, 3 (2025).
  3. Xiangdong Ji and Chen Yang, A journey of seeking pressures and forces in the nucleon, arxiv:2508.16727
  4. V. D. Burkert, L. Elouadrhiri, and F. X. Girod, The pressure distribution inside the proton, Nature (London) 557, 396 (2018).
  5. Krešimir Kumerički, Measurability of pressure inside the proton, Nature (London) 570, E1 (2019).
  6. H. Dutrieux, C. Lorcé, H. Moutarde, P. Sznajder, A. Trawiński, and J. Wagner, Phenomenological assessment of proton mechanical properties from deeply virtual Compton scattering, Eur. Phys. J. C 81, 300 (2021).
  7. Xiang-Dong Ji, Deeply virtual Compton scattering, Phys. Rev. D 55, 7114 (1997).
  8. Xiang-Dong Ji, Gauge-invariant decomposition of nucleon spin, Phys. Rev. Lett. 78, 610 (1997).
  9. I. V. Anikin and O. V. Teryaev, Dispersion relations and subtractions in hard exclusive processes, Phys. Rev. D 76, 056007 (2007).
  10. M. Diehl and D. Yu. Ivanov, Dispersion representations for hard exclusive processes: Beyond the born approximation, Eur. Phys. J. C 52, 919 (2007).
  11. Hervé Dutrieux, Thibaud Meisgny, Cédric Mezrag, and Hervé Moutarde, Proton internal pressure from deeply virtual Compton scattering on collider kinematics, Eur. Phys. J. C 85, 105 (2025).
  12. Maxim V. Polyakov and C. Weiss, Skewed and double distributions in pion and nucleon, Phys. Rev. D 60, 114017 (1999).
  13. Vladimir M. Braun, Alexander N. Manashov, Dieter Müller, and Bjoern 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).
  14. Víctor Martínez-Fernández and Cédric Mezrag, following article, Dispersion relations of deeply virtual Compton scattering: Investigating twist-four kinematic power corrections, Phys. Rev. D 113, 094004 (2026).
  15. Andrei V. Belitsky, Dieter Mueller, and A. Kirchner, Theory of deeply virtual Compton scattering on the nucleon, Nucl. Phys. B629, 323 (2002).
  16. Andrei V. Belitsky, Dieter Müller, and Yao Ji, Compton scattering: from deeply virtual to quasi-real, Nucl. Phys. B878, 214 (2014).
  17. Xiang-Dong Ji, Off forward parton distributions, J. Phys. G 24, 1181 (1998).
  18. A. V. Radyushkin, Symmetries and structure of skewed and double distributions, Phys. Lett. B 449, 81 (1999).
  19. Dieter Mueller, D. Robaschik, B. Geyer, F. M. Dittes, and J. Hořejši, Wave functions, evolution equations and evolution kernels from light ray operators of QCD, Fortschr. Phys. 42, 101 (1994).
  20. A. V. Radyushkin, Nonforward parton distributions, Phys. Rev. D 56, 5524 (1997).
  21. N. Chouika, C. Mezrag, H. Moutarde, and J. Rodríguez-Quintero, Covariant extension of the GPD overlap representation at low Fock states, Eur. Phys. J. C 77, 906 (2017).
  22. Cédric Mezrag, An introductory lecture on generalised parton distributions, Few Body Syst. 63, 62 (2022).
  23. V. M. Braun, A. N. Manashov, and B. Pirnay, Finite-t and target mass corrections to deeply virtual Compton scattering, Phys. Rev. Lett. 109, 242001 (2012).
  24. V. M. Braun, A. N. Manashov, and B. Pirnay, Finite-t and target mass corrections to DVCS on a scalar target, Phys. Rev. D 86, 014003 (2012).
  25. V. M. Braun, A. N. Manashov, S. Moch, and M. Strohmaier, Two-loop conformal generators for leading-twist operators in QCD, J. High Energy Phys. 03 (2016) 142.
  26. V. M. Braun, Yao Ji, and A. N. Manashov, Two-photon processes in conformal QCD: Resummation of the descendants of leading-twist operators, J. High Energy Phys. 03 (2021) 051.
  27. V. M. Braun, Yao Ji, and A. N. Manashov, Next-to-leading-power kinematic corrections to DVCS: A scalar target, J. High Energy Phys. 01 (2023) 078.
  28. V. M. Braun, Yao Ji, and A. N. Manashov, Kinematic power corrections to deeply virtual Compton scattering to twist-six accuracy, Phys. Rev. D 111, 076011 (2025).
  29. 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).
  30. José Manuel Morgado Chavez, Valerio Bertone, Feliciano De Soto Borrero, Maxime Defurne, Cédric Mezrag, Hervé Moutarde, José Rodríguez-Quintero, and Jorge Segovia, Pion generalized parton distributions: A path toward phenomenology, Phys. Rev. D 105, 094012 (2022).
  31. I. Novikov et al., Parton distribution functions of the charged pion within the xFitter framework, Phys. Rev. D 102, 014040 (2020).
  32. I. V. Musatov and A. V. Radyushkin, Evolution and models for skewed parton distributions, Phys. Rev. D 61, 074027 (2000).
  33. S. V. Goloskokov and P. Kroll, The longitudinal cross-section of vector meson electroproduction, Eur. Phys. J. C 50, 829 (2007).
  34. S. V. Goloskokov and P. Kroll, The role of the quark and gluon GPDs in hard vector-meson electroproduction, Eur. Phys. J. C 53, 367 (2008).
  35. S. V. Goloskokov and P. Kroll, The target asymmetry in hard vector-meson electroproduction and parton angular momenta, Eur. Phys. J. C 59, 809 (2009).
  36. Hervé Dutrieux, Robert G. Edwards, Colin Egerer, Joseph Karpie, Christopher Monahan, Kostas Orginos, Anatoly Radyushkin, David Richards, Eloy Romero, and Savvas Zafeiropoulos, Towards unpolarized GPDs from pseudo-distributions, J. High Energy Phys. 08 (2024) 162.
  37. Daniel C. Hackett, Dimitra A. Pefkou, and Phiala E. Shanahan, Gravitational form factors of the proton from lattice QCD, Phys. Rev. Lett. 132, 251904 (2024).
  38. Z. Q. Yao, Y. Z. Xu, D. Binosi, Z. F. Cui, M. Ding, K. Raya, C. D. Roberts, J. Rodríguez-Quintero, and S. M. Schmidt, Nucleon gravitational form factors, Eur. Phys. J. A 61, 92 (2025).
  39. Note the factor 4 difference in the definition of C between our convention and Refs. [37, 38].

  40. M. Defurne et al., E00-110 experiment at Jefferson Lab Hall A: Deeply virtual Compton scattering off the proton at 6 GeV, Phys. Rev. C 92, 055202 (2015).

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