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Generalized Parton Distributions of Pions at the Forthcoming Electron-Ion Collider

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Abstract

We analyze deeply virtual Compton scattering on pions projected for a future electron-ion collider and conveyed in the Sullivan process. The relevant amplitude is known to be parametrized by generalized parton distributions. Hence taking advantage of state-of-the-art models for them, supplemented with effective leading-order scale evolution, we evaluate the amplitude for the process to occur and examine the pion’s structure from the perspective of electron-ion colliders. We estimate the expected event-rates for the Sullivan process showing: first, that deeply virtual Compton scattering on pions may be measurable at forthcoming experimental facilities. Second, that gluons may be decisive in the description of pions, driving the behavior of the relevant amplitudes and modulating the expected event-rates.

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Notes

  1. Some works exist on the nucleon side, e.g. [11, 12], but apart from [13] little can be said on the pion’s side.

References

  1. R. Abdul-Khalek, et al., Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report (2021). arXiv:2103.05419 [physics.ins-det]

  2. D.P. Anderle et al., Electron-ion collider in China. Front. Phys. (Beijing) 16(6), 64701 (2021). https://doi.org/10.1007/s11467-021-1062-0. arXiv:2102.09222 [nucl-ex]

    Article  ADS  Google Scholar 

  3. B. Adams, et al., Letter of Intent: A New QCD facility at the M2 beam line of the CERN SPS (COMPASS++/AMBER) (2018). arXiv:1808.00848 [hep-ex]

  4. A.C. Aguilar et al., Pion and kaon structure at the electron-ion collider. Eur. Phys. J. A 55(10), 190 (2019). https://doi.org/10.1140/epja/i2019-12885-0. arXiv:1907.08218 [nucl-ex]

    Article  ADS  MathSciNet  Google Scholar 

  5. C.D. Roberts, D.G. Richards, T. Horn, L. Chang, Insights into the emergence of mass from studies of pion and kaon structure. Prog. Part. Nucl. Phys. 120, 103883 (2021) https://doi.org/10.1016/j.ppnp.2021.103883, arXiv:2102.01765 [hep-ph]

  6. D. Amrath, M. Diehl, J.-P. Lansberg, Deeply virtual Compton scattering on a virtual pion target. Eur. Phys. J. C 58, 179–192 (2008). https://doi.org/10.1140/epjc/s10052-008-0769-1. arXiv:0807.4474 [hep-ph]

    Article  ADS  Google Scholar 

  7. J.M. Morgado Chávez, V. Bertone, F. De Soto, M. Defurne, C. Mezrag, H. Moutarde, J. Rodríguez-Quintero, J. Segovia, Accessing the pion 3D structure at US and China electron-ion colliders. Phys. Rev. Lett. 128(20), 202501 (2022). https://doi.org/10.1103/PhysRevLett.128.202501. arXiv:2110.09462 [hep-ph]

    Article  ADS  Google Scholar 

  8. M. Burkardt, Impact parameter dependent parton distributions and off forward parton distributions for \(\zeta \rightarrow 0\). Phys. Rev. D 62, 071503 (2000) https://doi.org/10.1103/PhysRevD.62.071503, https://doi.org/10.1103/PhysRevD.66.119903. arXiv:hep-ph/0005108 [hep-ph]. [Erratum: Phys. Rev.D66,119903(2002)]

  9. M. Diehl, Generalized parton distributions. Phys. Rep. 388, 41–277 (2003). https://doi.org/10.1016/j.physrep.2003.08.002. arXiv:hep-ph/0307382 [hep-ph]

    Article  ADS  Google Scholar 

  10. A.V. Belitsky, A.V. Radyushkin, Unraveling hadron structure with generalized parton distributions. Phys. Rep. 418, 1–387 (2005). https://doi.org/10.1016/j.physrep.2005.06.002. arXiv:hep-ph/0504030 [hep-ph]

    Article  ADS  Google Scholar 

  11. F.D. Aaron et al., Measurement of deeply virtual Compton scattering and its t-dependence at HERA. Phys. Lett. B 659, 796–806 (2008). https://doi.org/10.1016/j.physletb.2007.11.093. arXiv:0709.4114 [hep-ex]

    Article  ADS  Google Scholar 

  12. M. Defurne et al., A glimpse of gluons through deeply virtual compton scattering on the proton. Nat. Commun. 8(1), 1408 (2017). https://doi.org/10.1038/s41467-017-01819-3. arXiv:1703.09442 [hep-ex]

    Article  ADS  Google Scholar 

  13. S. Chekanov et al., Measurement of deeply virtual Compton scattering at HERA. Phys. Lett. B 573, 46–62 (2003). https://doi.org/10.1016/j.physletb.2003.08.048. arXiv:hep-ex/0305028 [hep-ex]

    Article  ADS  Google Scholar 

  14. E. Fermi, L. Marshall, On the interaction between neutrons and electrons. Phys. Rev. 72, 1139–1146 (1947). https://doi.org/10.1103/PhysRev.72.1139

    Article  ADS  Google Scholar 

  15. J.D. Sullivan, One pion exchange and deep inelastic electron–nucleon scattering. Phys. Rev. D 5, 1732–1737 (1972). https://doi.org/10.1103/PhysRevD.5.1732

    Article  ADS  Google Scholar 

  16. S.-X. Qin, C. Chen, C. Mezrag, C.D. Roberts, Off-shell persistence of composite pions and kaons. Phys. Rev. C 97(1), 015203 (2018). https://doi.org/10.1103/PhysRevC.97.015203. arXiv:1702.06100 [nucl-th]

    Article  ADS  Google Scholar 

  17. W. Broniowski, V. Shastry, E. Ruiz Arriola, Off-shell generalized parton distributions and form factors of the pion. Phys. Lett. B 840, 137872 (2023). https://doi.org/10.1016/j.physletb.2023.137872. arXiv:2211.11067 [hep-ph]

    Article  MATH  Google Scholar 

  18. W. Broniowski, V. Shastry, E. Ruiz Arriola, Off-shell generalized parton distributions of the pion, in 29th Cracow Epiphany Conference (2023)

  19. G.M. Huber, et al., Charged pion form-factor between \(Q^{2}=0.60~\text{GeV}^{2}\) and \(2.45~\text{ GeV}^{2}\). II. Determination of, and results for, the pion form-factor. Phys. Rev. C 78, 045203 (2008) https://doi.org/10.1103/PhysRevC.78.045203, arXiv:0809.3052 [nucl-ex]

  20. T. Horn et al., Scaling study of the pion electroproduction cross sections and the pion form factor. Phys. Rev. C 78, 058201 (2008). https://doi.org/10.1103/PhysRevC.78.058201. arXiv:0707.1794 [nucl-ex]

    Article  ADS  Google Scholar 

  21. T. Horn, et al., Determination of the charged pion form factor at \(Q^{2} = 1.60\) and \(2.45~\left(\text{ GeV }/c\right)^{2}\). Phys. Rev. Lett. 97, 192001 (2006) https://doi.org/10.1103/PhysRevLett.97.192001, arXiv:nucl-ex/0607005

  22. V. Tadevosyan, et al., Determination of the pion charge form-factor for \(Q^{2}=0.60~\text{ GeV}^{2}-1.60~\text{ GeV}^{2}\). Phys. Rev. C 75, 055205 (2007) https://doi.org/10.1103/PhysRevC.75.055205, arXiv:nucl-ex/0607007

  23. C.J. Bebek et al., Further measurements of forward-charged-pion electroproduction at large \(k^2\). Phys. Rev. D 9, 1229–1242 (1974). https://doi.org/10.1103/PhysRevD.9.1229

    Article  ADS  Google Scholar 

  24. C.N. Brown, C.R. Canizares, W.E. Cooper, A.M. Eisner, G.J. Feldmann, C.A. Lichtenstein, L. Litt, W. Loceretz, V.B. Montana, F.M. Pipkin, Coincidence electroproduction of charged pions and the pion form-factor. Phys. Rev. D 8, 92–135 (1973). https://doi.org/10.1103/PhysRevD.8.92

    Article  ADS  Google Scholar 

  25. E.B. Dally et al., Direct Measurement of the pi- Form-Factor. Phys. Rev. Lett. 39, 1176–1179 (1977). https://doi.org/10.1103/PhysRevLett.39.1176

    Article  ADS  Google Scholar 

  26. A.V. Radyushkin, Scaling limit of deeply virtual Compton scattering. Phys. Lett. B 380, 417–425 (1996). https://doi.org/10.1016/0370-2693(96)00528-X. arXiv:hep-ph/9604317 [hep-ph]

    Article  ADS  Google Scholar 

  27. J.C. Collins, A. Freund, Proof of factorization for deeply virtual Compton scattering in QCD. Phys. Rev. D 59, 074009 (1999). https://doi.org/10.1103/PhysRevD.59.074009. arXiv:hep-ph/9801262 [hep-ph]

    Article  ADS  Google Scholar 

  28. X. Ji, J. Osborne, One loop QCD corrections to deeply virtual Compton scattering: the Parton helicity independent case. Phys. Rev. D 57, 1337–1340 (1998). https://doi.org/10.1103/PhysRevD.57.1337. arXiv:hep-ph/9707254 [hep-ph]

    Article  ADS  Google Scholar 

  29. A.V. Belitsky, D. Mueller, A. Kirchner, A. Schafer, Twist three analysis of photon electroproduction off pion. Phys. Rev. D 64, 116002 (2001). https://doi.org/10.1103/PhysRevD.64.116002. arXiv:hep-ph/0011314 [hep-ph]

    Article  ADS  Google Scholar 

  30. A.V. Belitsky, D. Mueller, A. Kirchner, Theory of deeply virtual Compton scattering on the nucleon. Nucl. Phys. B 629, 323–392 (2002). https://doi.org/10.1016/S0550-3213(02)00144-X. arXiv:hep-ph/0112108 [hep-ph]

    Article  ADS  Google Scholar 

  31. A.V. Belitsky, D. Muller, Refined analysis of photon leptoproduction off spinless target. Phys. Rev. D 79, 014017 (2009). https://doi.org/10.1103/PhysRevD.79.014017. arXiv:0809.2890 [hep-ph]

    Article  ADS  Google Scholar 

  32. A. Bacchetta, U. D’Alesio, M. Diehl, C.A. Miller, Single-spin asymmetries: the Trento conventions. Phys. Rev. D 70, 117504 (2004). https://doi.org/10.1103/PhysRevD.70.117504. arXiv:hep-ph/0410050 [hep-ph]

    Article  ADS  Google Scholar 

  33. D. Muller, D. Robaschik, B. Geyer, F.M. Dittes, J. Hořeǰsi, Wave functions, evolution equations and evolution kernels from light ray operators of QCD. Fortsch. Phys. 42, 101–141 (1994) https://doi.org/10.1002/prop.2190420202, arXiv:hep-ph/9812448 [hep-ph]

  34. A.V. Radyushkin, Nonforward Parton distributions. Phys. Rev. D56, 5524–5557 (1997). https://doi.org/10.1103/PhysRevD.56.5524. arXiv:hep-ph/9704207 [hep-ph]

    Article  ADS  Google Scholar 

  35. X. Ji, Deeply virtual Compton scattering. Phys. Rev. D55, 7114–7125 (1997). https://doi.org/10.1103/PhysRevD.55.7114. arXiv:hep-ph/9609381 [hep-ph]

    Article  ADS  Google Scholar 

  36. B. Pire, L. Szymanowski, J. Wagner, NLO corrections to timelike, spacelike and double deeply virtual Compton scattering. Phys. Rev. D 83, 034009 (2011). https://doi.org/10.1103/PhysRevD.83.034009. arXiv:1101.0555 [hep-ph]

    Article  ADS  Google Scholar 

  37. K. Kumericki, S. Liuti, H. Moutarde, GPD phenomenology and DVCS fitting. Eur. Phys. J. A 52(6), 157 (2016). https://doi.org/10.1140/epja/i2016-16157-3. arXiv:1602.02763 [hep-ph]

    Article  ADS  Google Scholar 

  38. H. Moutarde, B. Pire, F. Sabatie, L. Szymanowski, J. Wagner, On timelike and spacelike deeply virtual Compton scattering at next to leading order. Phys. Rev. D 87, 054029 (2013). https://doi.org/10.1103/PhysRevD.87.054029. arXiv:1301.3819 [hep-ph]

    Article  ADS  Google Scholar 

  39. J.M. Morgado Chavez, V. Bertone, F. De Soto, M. Defurne, C. Mezrag, H. Moutarde, J. Rodríguez-Quintero, J. Segovia, Pion generalized parton distributions: a path toward phenomenology. Phys. Rev. D 105(9), 094012 (2022). https://doi.org/10.1103/PhysRevD.105.094012. arXiv:2110.06052 [hep-ph]

    Article  ADS  Google Scholar 

  40. M. Ding, K. Raya, D. Binosi, L. Chang, C.D. Roberts, S.M. Schmidt, Symmetry, symmetry breaking, and pion Parton distributions. Phys. Rev. D 101(5), 054014 (2020). https://doi.org/10.1103/PhysRevD.101.054014. arXiv:1905.05208 [nucl-th]

    Article  ADS  Google Scholar 

  41. Z.-F. Cui, M. Ding, F. Gao, K. Raya, D. Binosi, L. Chang, C.D. Roberts, J. Rodríguez-Quintero, S.M. Schmidt, Higgs modulation of emergent mass as revealed in kaon and pion Parton distributions. Eur. Phys. J. A 57(1), 5 (2021). https://doi.org/10.1140/epja/s10050-020-00318-2. arXiv:2006.14075 [hep-ph]

    Article  ADS  Google Scholar 

  42. Z.-F. Cui, M. Ding, J.M. Morgado, K. Raya, D. Binosi, L. Chang, F. De Soto, C.D. Roberts, J. Rodríguez-Quintero, S.M. Schmidt, Emergence of pion Parton distributions. Phys. Rev. D 105(9), 091502 (2022). https://doi.org/10.1103/PhysRevD.105.L091502. arXiv:2201.00884 [hep-ph]

    Article  ADS  Google Scholar 

  43. Z.-F. Cui, M. Ding, J.M. Morgado, K. Raya, D. Binosi, L. Chang, J. Papavassiliou, C.D. Roberts, J. Rodríguez-Quintero, S.M. Schmidt, Concerning pion Parton distributions. Eur. Phys. J. A 58(1), 10 (2022). https://doi.org/10.1140/epja/s10050-021-00658-7. arXiv:2112.09210 [hep-ph]

    Article  ADS  Google Scholar 

  44. K. Raya, Z.-F. Cui, L. Chang, J.-M. Morgado, C.D. Roberts, J. Rodriguez-Quintero, Revealing pion and kaon structure via generalised Parton distributions *. Chin. Phys. C 46(1), 013105 (2022). https://doi.org/10.1088/1674-1137/ac3071. arXiv:2109.11686 [hep-ph]

    Article  ADS  MATH  Google Scholar 

  45. V. Bertone, S. Carrazza, J. Rojo, APFEL: a PDF evolution library with QED corrections. Comput. Phys. Commun. 185, 1647–1668 (2014). https://doi.org/10.1016/j.cpc.2014.03.007. arXiv:1310.1394 [hep-ph]

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. V. Bertone, APFEL++: A new PDF evolution library in C++. PoS DIS2017, 201 (2018) https://doi.org/10.22323/1.297.0201, arXiv:1708.00911 [hep-ph]

  47. B. Berthou, D. Binosi, N. Chouika, L. Colaneri, M. Guidal, C. Mezrag, H. Moutarde, J. Rodríguez-Quintero, F. Sabatié, P. Sznajder, J. Wagner, PARTONS: PARtonic Tomography Of Nucleon Software. A computing framework for the phenomenology of Generalized Parton Distributions. Eur. Phys. J. C 78(6), 478 (2018) https://doi.org/10.1140/epjc/s10052-018-5948-0, arXiv:1512.06174 [hep-ph]

  48. V. Bertone, H. Dutrieux, C. Mezrag, J.M. Morgado, H. Moutarde, Revisiting evolution equations for generalised Parton distributions. Eur. Phys. J. C 82(10), 888 (2022). https://doi.org/10.1140/epjc/s10052-022-10793-0. arXiv:2206.01412 [hep-ph]

    Article  ADS  Google Scholar 

  49. M. Diehl, D.Y. Ivanov, Dispersion representations for hard exclusive processes: beyond the Born approximation. Eur. Phys. J. C 52, 919–932 (2007). https://doi.org/10.1140/epjc/s10052-007-0401-9. arXiv:0707.0351 [hep-ph]

    Article  ADS  Google Scholar 

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Acknowledgements

We would like to thank K. Raya, P. Dall’Olio, M. Riberdy, H. Dutrieux and P. Sznajder for stimulating discussions. F.S., J.R.Q. and J.S.’s work is supported by Ministerio de Ciencia e Innovación (Spain) under grant PID2019-107844GB-C22; Junta de Andalucía, under contract No. operativo FEDER Andalucía 2014-2020UHU-1264517 and P18-FR-5057 and PAIDI FQM-370. V.B., M.D., C.M and H.M acknowledge support from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No 824093. J.M.M.C.’s work has been supported by “P2IO LabEx (ANR-10-LABX-0038)”in the framework“Investissements d’Avenir (ANR-11-IDEX-0003-01)”managed by the Agence Nationale de la Recherche, France; and by the University of Huelva (EPIT-2019).

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Authors and Affiliations

  1. DPhN, Irfu/CEA-Saclay, 91191, Gif-sur-Yvette, France

    J. M. Morgado Chávez, V. Bertone, M. Defurne, C. Mezrag & H. Moutarde

  2. Departamento de Ciencias Integradas and CEAFMC, Universidad de Huelva, 21071, Huelva, Spain

    J. M. Morgado Chávez & J. Rodríguez Quintero

  3. Departamento de sistemas Físicos, Químicos y Naturales, Universidad Pablo de Olavide, 41013, Sevila, Spain

    F. De Soto & J. Segovia

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  1. J. M. Morgado Chávez
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  2. V. Bertone
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All listed authors identically contributed to the development of the research presented here as well as actively participated in writing and reviewing the manuscript. J.M.M.C. presented the work at Baryons2023.

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Correspondence to J. M. Morgado Chávez.

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Chávez, J.M.M., Bertone, V., De Soto, F. et al. Generalized Parton Distributions of Pions at the Forthcoming Electron-Ion Collider. Few-Body Syst 64, 38 (2023). https://doi.org/10.1007/s00601-023-01812-1

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