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

Víctor Martínez-Fernández1,2,* and Cédric Mezrag1,†

  • *Contact author: victor.martinezfernandez@cea.fr
  • †Contact author: cedric.mezrag@cea.fr

Phys. Rev. D 113, 094004 – Published 4 May, 2026

DOI: https://doi.org/10.1103/6kny-88yg

Abstract

In this paper we include kinematic power corrections up to twist-four to the deeply virtual Compton scattering dispersion relation. We demonstrate that, both for (pseudo)scalar and spin-1/2 targets, the formal expression of the n-subtracted leading-twist dispersion relations is preserved. However, the expression of the subtracted constants is modified by the kinematic powers. Importantly, the minimal-subtracted dispersion relation for the helicity-conserving amplitude, previously thought to depend only on the Polyakov-Weiss D-term, now also depends on the double distributions F and K. These results are consistent with the ones obtained previously in the literature. Such a mixing may be critical for the Jefferson Lab kinematic range, as it is not suppressed for typical values of t and Q2 in the valence region. We therefore expect a strong impact on the attempts to extract pressure forces from deeply virtual Compton scattering data.

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Physics Subject Headings (PhySH)

See Also

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

Víctor Martínez-Fernández, Daniele Binosi, Cédric Mezrag, and Zhao-Qian Yao (姚照千)
Phys. Rev. D 113, 094003 (2026)

Article Text

References (84)

  1. Maxim V. Polyakov and Peter Schweitzer, Forces inside hadrons: Pressure, surface tension, mechanical radius, and all that, Int. J. Mod. Phys. A 33, 1830025 (2018).
  2. Cédric Lorcé, Hervé Moutarde, and Arkadiusz P. Trawiński, Revisiting the mechanical properties of the nucleon, Eur. Phys. J. C 79, 89 (2019).
  3. V. D. Burkert, L. Elouadrhiri, and F. X. Girod, The pressure distribution inside the proton, Nature (London) 557, 396 (2018).
  4. Krešimir Kumerički, Measurability of pressure inside the proton, Nature (London) 570, E1 (2019).
  5. 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).
  6. Adam Freese, Noether’s theorems and the energy-momentum tensor in quantum gauge theories, Phys. Rev. D 106, 125012 (2022).
  7. 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).
  8. C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, A. Vaquero Avilés-Casco, and C. Wiese, Nucleon spin and momentum decomposition using lattice QCD simulations, Phys. Rev. Lett. 119, 142002 (2017).
  9. C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou, H. Panagopoulos, and G. Spanoudes, Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass, Phys. Rev. D 101, 094513 (2020).
  10. Gen Wang, Yi-Bo Yang, Jian Liang, Terrence Draper, and Keh-Fei Liu, Proton momentum and angular momentum decompositions with overlap fermions, Phys. Rev. D 106, 014512 (2022).
  11. 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).
  12. Sreeraj Nair, Chandan Mondal, Siqi Xu, Xingbo Zhao, Asmita Mukherjee, and James P. Vary, Gravitational form factors and mechanical properties of quarks in protons: A basis light-front quantization approach, Phys. Rev. D 110, 056027 (2024).
  13. 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).
  14. Xiang-Dong Ji, Gauge-invariant decomposition of nucleon spin, Phys. Rev. Lett. 78, 610 (1997).
  15. 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).
  16. Xiang-Dong Ji, Deeply virtual Compton scattering, Phys. Rev. D 55, 7114 (1997).
  17. A. V. Radyushkin, Asymmetric gluon distributions and hard diffractive electroproduction, Phys. Lett. B 385, 333 (1996).
  18. A. V. Radyushkin, Nonforward parton distributions, Phys. Rev. D 56, 5524 (1997).
  19. John C. Collins, Leonid Frankfurt, and Mark Strikman, Factorization for hard exclusive electroproduction of mesons in QCD, Phys. Rev. D 56, 2982 (1997).
  20. John C. Collins and Andreas Freund, Proof of factorization for deeply virtual Compton scattering in QCD, Phys. Rev. D 59, 074009 (1999).
  21. Edgar R. Berger, M. Diehl, and B. Pire, Time—like Compton scattering: Exclusive photoproduction of lepton pairs, Eur. Phys. J. C 23, 675 (2002).
  22. Dieter Müller, Tobias Lautenschlager, Kornelija Passek-Kumericki, and Andreas Schaefer, Towards a fitting procedure to deeply virtual meson production—the next-to-leading order case, Nucl. Phys. B884, 438 (2014).
  23. V. Bertone, H. Dutrieux, C. Mezrag, H. Moutarde, and P. Sznajder, The deconvolution problem of deeply virtual Compton scattering, Phys. Rev. D 103, 114019 (2021).
  24. Eric Moffat, Adam Freese, Ian Cloët, Thomas Donohoe, Leonard Gamberg, Wally Melnitchouk, Andreas Metz, Alexei Prokudin, and Nobuo Sato, Shedding light on shadow generalized parton distributions, Phys. Rev. D 108, 036027 (2023).
  25. Andrei V. Belitsky and Dieter Mueller, Probing generalized parton distributions with electroproduction of lepton pairs off the nucleon, Phys. Rev. D 68, 116005 (2003).
  26. M. Guidal and M. Vanderhaeghen, Double deeply virtual Compton scattering off the nucleon, Phys. Rev. Lett. 90, 012001 (2003).
  27. 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).
  28. J. S. Alvarado, M. Hoballah, and E. Voutier, Sensitivity of double deeply virtual Compton-scattering observables to generalized parton distributions, Phys. Rev. C 111, 065205 (2025).
  29. 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; 10 (2018) 29.
  30. G. Duplančić, K. Passek-Kumerički, B. Pire, L. Szymanowski, and S. Wallon, Probing axial quark generalized parton distributions through exclusive photoproduction of a γπ± pair with a large invariant mass, J. High Energy Phys. 11 (2018) 179.
  31. Oskar Grocholski, Bernard Pire, Paweł Sznajder, Lech Szymanowski, and Jakub Wagner, Collinear factorization of diphoton photoproduction at next to leading order, Phys. Rev. D 104, 114006 (2021).
  32. Jian-Wei Qiu and Zhite Yu, Exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions for extracting generalized parton distributions, J. High Energy Phys. 08 (2022) 103.
  33. Jian-Wei Qiu and Zhite Yu, Single diffractive hard exclusive processes for the study of generalized parton distributions, Phys. Rev. D 107, 014007 (2023).
  34. Jian-Wei Qiu and Zhite Yu, Extraction of the parton momentum-fraction dependence of generalized parton distributions from exclusive photoproduction, Phys. Rev. Lett. 131, 161902 (2023).
  35. F. X. Girod et al., Measurement of deeply virtual Compton scattering beam-spin asymmetries, Phys. Rev. Lett. 100, 162002 (2008).
  36. A. Airapetian et al., Beam-helicity and beam-charge asymmetries associated with deeply virtual Compton scattering on the unpolarised proton, J. High Energy Phys. 07 (2012) 032.
  37. H. S. Jo et al., Cross sections for the exclusive photon electroproduction on the proton and generalized parton distributions, Phys. Rev. Lett. 115, 212003 (2015).
  38. 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).
  39. M. Defurne et al., A glimpse of gluons through deeply virtual compton scattering on the proton, Nat. Commun. 8, 1408 (2017).
  40. R. Akhunzyanov et al., Transverse extension of partons in the proton probed in the sea-quark range by measuring the DVCS cross section, Phys. Lett. B 793, 188 (2019); 800, 135129(E) (2020).
  41. F. Georges et al., Deeply virtual Compton scattering cross section at high Bjorken xB, Phys. Rev. Lett. 128, 252002 (2022).
  42. G. Christiaens et al., First CLAS12 measurement of deeply virtual Compton scattering beam-spin asymmetries in the extended valence region, Phys. Rev. Lett. 130, 211902 (2023).
  43. V. M. Braun, A. N. Manashov, S. Moch, and J. Schoenleber, Two-loop coefficient function for DVCS: Vector contributions, J. High Energy Phys. 09 (2020) 117.
  44. Andrei V. Belitsky and Dieter Mueller, Twist- three effects in two photon processes, Nucl. Phys. B589, 611 (2000).
  45. 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).
  46. 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).
  47. 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).
  48. 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.
  49. 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.
  50. 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.
  51. V. Martinez-Fernandez, B. Pire, P. Sznajder, and J. Wagner, Timelike Compton scattering on a spin-0 target with kinematic twist-four precision, Phys. Rev. D 111, 074034 (2025).
  52. I. V. Anikin and O. V. Teryaev, Dispersion relations and subtractions in hard exclusive processes, Phys. Rev. D 76, 056007 (2007).
  53. Maxim V. Polyakov and C. Weiss, Skewed and double distributions in pion and nucleon, Phys. Rev. D 60, 114017 (1999).
  54. B. L. G. Bakker, E. Leader, and T. L. Trueman, A Critique of the angular momentum sum rules and a new angular momentum sum rule, Phys. Rev. D 70, 114001 (2004).
  55. E. Leader and C. Lorcé, The angular momentum controversy: What’s it all about and does it matter?, Phys. Rep. 541, 163 (2014).
  56. M. V. Polyakov, Generalized parton distributions and strong forces inside nucleons and nuclei, Phys. Lett. B 555, 57 (2003).
  57. M. Diehl, Generalized parton distributions, Phys. Rep. 388, 41 (2003).
  58. O. V. Teryaev, Crossing and radon tomography for generalized parton distributions, Phys. Lett. B 510, 125 (2001).
  59. 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).
  60. N. Chouika, C. Mezrag, H. Moutarde, and J. Rodríguez-Quintero, A Nakanishi-based model illustrating the covariant extension of the pion GPD overlap representation and its ambiguities, Phys. Lett. B 780, 287 (2018).
  61. P. Dall’Olio, F. De Soto, C. Mezrag, J. M. Morgado Chávez, H. Moutarde, J. Rodríguez-Quintero, P. Sznajder, and J. Segovia, Unraveling generalized parton distributions through Lorentz symmetry and partial DGLAP knowledge, Phys. Rev. D 109, 096013 (2024).
  62. A. V. Belitsky and A. V. Radyushkin, Unraveling hadron structure with generalized parton distributions, Phys. Rep. 418, 1 (2005).
  63. A. V. Radyushkin, Modeling Nucleon Generalized Parton Distributions, Phys. Rev. D 87, 096017 (2013).
  64. C. Mezrag, H. Moutarde, and F. Sabatié, Test of two new parametrizations of the generalized parton distribution H, Phys. Rev. D 88, 014001 (2013).
  65. 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).
  66. O. V. Teryaev, Analytic properties of hard exclusive amplitudes, in 11th International Conference on Elastic and Diffractive Scattering: Towards High Energy Frontiers: The 20th Anniversary of the Blois Workshops, 17th Rencontre de Blois (2005), arXiv:hep-ph/0510031.
  67. M. Diehl and D. Yu. Ivanov, Dispersion representations for hard exclusive processes: Beyond the Born approximation, Eur. Phys. J. C 52, 919 (2007).
  68. Daniela Amrath, Markus Diehl, and Jean-Philippe Lansberg, Deeply virtual Compton scattering on a virtual pion target, Eur. Phys. J. C 58, 179 (2008).
  69. 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).
  70. José Manuel Morgado Chávez, Valerio Bertone, Feliciano De Soto Borrero, Maxime Defurne, Cédric Mezrag, Hervé Moutarde, José Rodríguez-Quintero, and Jorge Segovia, Accessing the pion 3D structure at U.S. and China electron-ion colliders, Phys. Rev. Lett. 128, 202501 (2022).
  71. Abigail R. Castro, Cédric Mezrag, Jose M. Morgado Chávez, and Bernard Pire, Backward DVCS in a Sullivan process, Phys. Rev. D 112, 034009 (2025).
  72. Sara Fucini, Mohammad Hattawy, Matteo Rinaldi, and Sergio Scopetta, Deeply virtual Compton scattering off helium nuclei with positron beams, Eur. Phys. J. A 57, 273 (2021).
  73. S. V. Goloskokov and P. Kroll, The Longitudinal cross-section of vector meson electroproduction, Eur. Phys. J. C 50, 829 (2007).
  74. 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).
  75. 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).
  76. Peter Kroll, Herve Moutarde, and Franck Sabatie, From hard exclusive meson electroproduction to deeply virtual Compton scattering, Eur. Phys. J. C 73, 2278 (2013).
  77. B. Berthou, D. Binosi, N. Chouika, L. Colaneri, M. Guidal, C. Mezrag, H. Moutarde, J. Rodríguez-Quintero, F. Sabatié, P. Sznajder et al., PARTONS: Partonic Tomography of Nucleon Software. A computing framework for the phenomenology of generalized parton distributions, Eur. Phys. J. C 78, 478 (2018).
  78. V. Bertone, S. Carrazza, and J. Rojo, APFEL: A PDF Evolution Library with QED corrections, Comput. Phys. Commun. 185, 1647 (2014).
  79. V. Bertone, S. Carrazza, and N. P. Hartland, APFELgrid: A high performance tool for parton density determinations, Comput. Phys. Commun. 212, 205 (2017).
  80. Valerio Bertone, APFEL++: A new PDF evolution library in C++, Proc. Sci., DIS2017 (2018) 201.
  81. Valerio Bertone, Hervé Dutrieux, Cédric Mezrag, José M. Morgado, and Hervé Moutarde, Revisiting evolution equations for generalised parton distributions, Eur. Phys. J. C 82, 888 (2022).
  82. Víctor Martínez-Fernández, Daniele Binosi, Cédric Mezrag, and Zhao-Qian Yao, preceding article, Constraining the energy-momentum tensor through the DVCS dispersion relation beyond leading power, Phys. Rev. D 113, 094003 (2026).
  83. H. Moutarde, B. Pire, F. Sabatie, L. Szymanowski, and J. Wagner, On timelike and spacelike deeply virtual Compton scattering at next to leading order, Phys. Rev. D 87, 054029 (2013).
  84. V. M. Braun and A. N. Manashov, Operator product expansion in QCD in off-forward kinematics: Separation of kinematic and dynamical contributions, J. High Energy Phys. 01 (2012) 085.

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