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New tool for kinematic regime estimation in semi-inclusive deep-inelastic scattering

A preprint version of the article is available at arXiv.

Abstract

We introduce a new phenomenological tool based on momentum region indicators to guide the analysis and interpretation of semi-inclusive deep-inelastic scattering measurements. The new tool, referred to as “affinity”, is devised to help visualize and quantify the proximity of any experimental kinematic bin to a particular hadron production region, such as that associated with transverse momentum dependent factorization. We apply the affinity estimator to existing HERMES and COMPASS data and expected data from Jefferson Lab and the future Electron-Ion Collider. We also provide an interactive notebook based on Machine Learning for fast evaluation of affinity.

References

  1. A. Kotzinian, New quark distributions and semiinclusive electroproduction on the polarized nucleons, Nucl. Phys. B 441 (1995) 234 [hep-ph/9412283] [INSPIRE].

    ADS  Article  Google Scholar 

  2. P. J. Mulders and R. D. Tangerman, The complete tree level result up to order 1/Q for polarized deep inelastic leptoproduction, Nucl. Phys. B 461 (1996) 197 [Erratum ibid. 484 (1997) 538] [hep-ph/9510301] [INSPIRE].

  3. A. Bacchetta, M. Diehl, K. Goeke, A. Metz, P. J. Mulders and M. Schlegel, Semi-inclusive deep inelastic scattering at small transverse momentum, JHEP 02 (2007) 093 [hep-ph/0611265] [INSPIRE].

    ADS  Article  Google Scholar 

  4. D. Boer, R. Jakob and P. J. Mulders, Asymmetries in polarized hadron production in e+ e annihilation up to order 1/Q, Nucl. Phys. B 504 (1997) 345 [hep-ph/9702281] [INSPIRE].

    ADS  Article  Google Scholar 

  5. D. Boer, Sudakov suppression in azimuthal spin asymmetries, Nucl. Phys. B 603 (2001) 195 [hep-ph/0102071] [INSPIRE].

    ADS  Article  Google Scholar 

  6. D. Boer, Angular dependences in inclusive two-hadron production at BELLE, Nucl. Phys. B 806 (2009) 23 [arXiv:0804.2408] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  7. R. D. Tangerman and P. J. Mulders, Intrinsic transverse momentum and the polarized Drell-Yan process, Phys. Rev. D 51 (1995) 3357 [hep-ph/9403227] [INSPIRE].

    ADS  Article  Google Scholar 

  8. J. C. Collins and D. E. Soper, Parton distribution and decay functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].

    ADS  Article  Google Scholar 

  9. J. C. Collins, D. E. Soper and G. F. Sterman, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys. B 250 (1985) 199 [INSPIRE].

    ADS  Article  Google Scholar 

  10. X.-D. Ji, J.-P. Ma and F. Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D 71 (2005) 034005 [hep-ph/0404183] [INSPIRE].

    ADS  Article  Google Scholar 

  11. J. Collins, Foundations of perturbative QCD, Cambridge University Press, Cambridge, U.K. (2009).

    Google Scholar 

  12. D. Boer and P. J. Mulders, Time reversal odd distribution functions in leptoproduction, Phys. Rev. D 57 (1998) 5780 [hep-ph/9711485] [INSPIRE].

    ADS  Article  Google Scholar 

  13. E. L. Berger, Semi-inclusive inelastic electron scattering from nuclei, in NPAS workshop on electronuclear physics with internal targets, SLAC, U.S.A. (1987), p. 82.

  14. L. Trentadue and G. Veneziano, Fracture functions: an improved description of inclusive hard processes in QCD, Phys. Lett. B 323 (1994) 201 [INSPIRE].

    ADS  Article  Google Scholar 

  15. M. Grazzini, L. Trentadue and G. Veneziano, Fracture functions from cut vertices, Nucl. Phys. B 519 (1998) 394 [hep-ph/9709452] [INSPIRE].

    ADS  Article  Google Scholar 

  16. M. Anselmino, V. Barone and A. Kotzinian, SIDIS in the target fragmentation region: polarized and transverse momentum dependent fracture functions, Phys. Lett. B 699 (2011) 108 [arXiv:1102.4214] [INSPIRE].

    ADS  Article  Google Scholar 

  17. X. P. Chai, K. B. Chen, J. P. Ma and X. B. Tong, Fracture functions in different kinematic regions and their factorizations, JHEP 10 (2019) 285 [arXiv:1903.00809] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  18. P. J. Mulders, Current fragmentation in semiinclusive leptoproduction, AIP Conf. Proc. 588 (2001) 75 [hep-ph/0010199] [INSPIRE].

    ADS  Article  Google Scholar 

  19. S. J. Joosten, Fragmentation and nucleon structure in semi-inclusive deep-inelastic scattering at the HERMES experiment, Ph.D. thesis, Illinois U., Urbana, IL, U.S.A. (2013).

  20. M. Boglione, J. Collins, L. Gamberg, J. O. Gonzalez-Hernandez, T. C. Rogers and N. Sato, Kinematics of current region fragmentation in semi-inclusive deeply inelastic scattering, Phys. Lett. B 766 (2017) 245 [arXiv:1611.10329] [INSPIRE].

    ADS  Article  Google Scholar 

  21. J. Collins and T. C. Rogers, Graphical structure of hadronization and factorization in hard collisions, arXiv:1801.02704 [INSPIRE].

  22. M. Boglione et al., Mapping the kinematical regimes of semi-inclusive deep inelastic scattering, JHEP 10 (2019) 122 [arXiv:1904.12882] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  23. M. Anselmino, M. Boglione, J. O. Gonzalez Hernandez, S. Melis and A. Prokudin, Unpolarised transverse momentum dependent distribution and fragmentation functions from SIDIS multiplicities, JHEP 04 (2014) 005 [arXiv:1312.6261] [INSPIRE].

    ADS  Article  Google Scholar 

  24. A. Bacchetta, F. Delcarro, C. Pisano, M. Radici and A. Signori, Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production, JHEP 06 (2017) 081 [Erratum ibid. 06 (2019) 051] [arXiv:1703.10157] [INSPIRE].

  25. I. Scimemi and A. Vladimirov, Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum, JHEP 06 (2020) 137 [arXiv:1912.06532] [INSPIRE].

    ADS  Article  Google Scholar 

  26. A. Bacchetta et al., Transverse-momentum-dependent parton distributions up to N3 LL from Drell-Yan data, JHEP 07 (2020) 117 [arXiv:1912.07550] [INSPIRE].

    ADS  Article  Google Scholar 

  27. HERMES collaboration, Azimuthal single- and double-spin asymmetries in semi-inclusive deep-inelastic lepton scattering by transversely polarized protons, JHEP 12 (2020) 010 [arXiv:2007.07755] [INSPIRE].

  28. J. Collins, L. Gamberg, A. Prokudin, T. C. Rogers, N. Sato and B. Wang, Relating transverse momentum dependent and collinear factorization theorems in a generalized formalism, Phys. Rev. D 94 (2016) 034014 [arXiv:1605.00671] [INSPIRE].

    ADS  Article  Google Scholar 

  29. J. C. Collins and D. E. Soper, Back-to-back jets in QCD, Nucl. Phys. B 193 (1981) 381 [Erratum ibid. 213 (1983) 545] [INSPIRE].

  30. J. C. Collins and D. E. Soper, Back-to-back jets: Fourier transform from B to K -transverse, Nucl. Phys. B 197 (1982) 446 [INSPIRE].

    ADS  Article  Google Scholar 

  31. R. Meng, F. I. Olness and D. E. Soper, Semiinclusive deeply inelastic scattering at small qT, Phys. Rev. D 54 (1996) 1919 [hep-ph/9511311] [INSPIRE].

    ADS  Article  Google Scholar 

  32. S. M. Aybat and T. C. Rogers, TMD parton distribution and fragmentation functions with QCD evolution, Phys. Rev. D 83 (2011) 114042 [arXiv:1101.5057] [INSPIRE].

    ADS  Article  Google Scholar 

  33. J. Collins and T. Rogers, Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel, Phys. Rev. D 91 (2015) 074020 [arXiv:1412.3820] [INSPIRE].

    ADS  Article  Google Scholar 

  34. M. G. Echevarria, A. Idilbi and I. Scimemi, Factorization theorem for Drell-Yan at low qT and transverse momentum distributions on-the-light-cone, JHEP 07 (2012) 002 [arXiv:1111.4996] [INSPIRE].

    ADS  Article  Google Scholar 

  35. M. G. Echevarria, A. Idilbi and I. Scimemi, Unified treatment of the QCD evolution of all (un-)polarized transverse momentum dependent functions: Collins function as a study case, Phys. Rev. D 90 (2014) 014003 [arXiv:1402.0869] [INSPIRE].

    ADS  Article  Google Scholar 

  36. G. Altarelli, R. K. Ellis, M. Greco and G. Martinelli, Vector boson production at colliders: a theoretical reappraisal, Nucl. Phys. B 246 (1984) 12 [INSPIRE].

    ADS  Article  Google Scholar 

  37. J. Collins, Do fragmentation functions in factorization theorems correctly treat non-perturbative effects?, PoS QCDEV2016 (2017) 003 [arXiv:1610.09994] [INSPIRE].

  38. T. Sjöstrand, S. Mrenna and P. Z. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  39. G. Corcella et al., HERWIG 6: an event generator for hadron emission reactions with interfering gluons (including supersymmetric processes), JHEP 01 (2001) 010 [hep-ph/0011363] [INSPIRE].

    ADS  Article  Google Scholar 

  40. B. Andersson, The Lund model, volume 7, Cambridge University Press, Cambridge, U.K. (2005) [INSPIRE].

  41. A. Signori, A. Bacchetta, M. Radici and G. Schnell, Investigations into the flavor dependence of partonic transverse momentum, JHEP 11 (2013) 194 [arXiv:1309.3507] [INSPIRE].

    ADS  Article  Google Scholar 

  42. R. Abdul Khalek et al., Science requirements and detector concepts for the electron-ion collider: EIC yellow report, arXiv:2103.05419 [INSPIRE].

  43. M. Boglione and A. Simonelli, Kinematic regions in the e+ e → hX factorized cross section in a 2-jet topology with thrust, arXiv:2109.11497 [INSPIRE].

  44. Jefferson Lab Angular Momentum collaboration, Origin of single transverse-spin asymmetries in high-energy collisions, Phys. Rev. D 102 (2020) 054002 [arXiv:2002.08384] [INSPIRE].

  45. COMPASS collaboration, Transverse-momentum-dependent multiplicities of charged hadrons in muon-deuteron deep inelastic scattering, Phys. Rev. D 97 (2018) 032006 [arXiv:1709.07374] [INSPIRE].

  46. HERMES collaboration, Multiplicities of charged pions and kaons from semi-inclusive deep-inelastic scattering by the proton and the deuteron, Phys. Rev. D 87 (2013) 074029 [arXiv:1212.5407] [INSPIRE].

  47. B. Wang, J. O. Gonzalez-Hernandez, T. C. Rogers and N. Sato, Large transverse momentum in semi-inclusive deeply inelastic scattering beyond lowest order, Phys. Rev. D 99 (2019) 094029 [arXiv:1903.01529] [INSPIRE].

    ADS  Article  Google Scholar 

  48. J. O. Gonzalez-Hernandez, T. C. Rogers, N. Sato and B. Wang, Challenges with large transverse momentum in semi-inclusive deeply inelastic scattering, Phys. Rev. D 98 (2018) 114005 [arXiv:1808.04396] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  49. A. Bacchetta, G. Bozzi, M. Lambertsen, F. Piacenza, J. Steiglechner and W. Vogelsang, Difficulties in the description of Drell-Yan processes at moderate invariant mass and high transverse momentum, Phys. Rev. D 100 (2019) 014018 [arXiv:1901.06916] [INSPIRE].

    ADS  Article  Google Scholar 

  50. A. Kulesza, G. F. Sterman and W. Vogelsang, Joint resummation for Higgs production, Phys. Rev. D 69 (2004) 014012 [hep-ph/0309264] [INSPIRE].

    ADS  Article  Google Scholar 

  51. J. C. Collins, D. E. Soper and G. F. Sterman, Factorization of hard processes in QCD, Adv. Ser. Direct. High Energy Phys. 5 (1989) 1 [hep-ph/0409313] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  52. M. G. Echevarria, T. Kasemets, J.-P. Lansberg, C. Pisano and A. Signori, Matching factorization theorems with an inverse-error weighting, Phys. Lett. B 781 (2018) 161 [arXiv:1801.01480] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  53. A. Berera and D. E. Soper, Behavior of diffractive parton distribution functions, Phys. Rev. D 53 (1996) 6162 [hep-ph/9509239] [INSPIRE].

    ADS  Article  Google Scholar 

  54. T. Sjöstrand, Status and developments of event generators, PoS LHCP2016 (2016) 007 [arXiv:1608.06425] [INSPIRE].

  55. B. Andersson, G. Gustafson, G. Ingelman and T. Sjöstrand, Parton fragmentation and string dynamics, Phys. Rept. 97 (1983) 31 [INSPIRE].

    ADS  Article  Google Scholar 

  56. A. Kerbizi, X. Artru, Z. Belghobsi, F. Bradamante and A. Martin, Recursive model for the fragmentation of polarized quarks, Phys. Rev. D 97 (2018) 074010 [arXiv:1802.00962] [INSPIRE].

    ADS  Article  Google Scholar 

  57. T. Ito, W. Bentz, I. C. Cloet, A. W. Thomas and K. Yazaki, The NJL-jet model for quark fragmentation functions, Phys. Rev. D 80 (2009) 074008 [arXiv:0906.5362] [INSPIRE].

    ADS  Article  Google Scholar 

  58. H. H. Matevosyan, A. Kotzinian and A. W. Thomas, Monte Carlo implementation of polarized hadronization, Phys. Rev. D 95 (2017) 014021 [arXiv:1610.05624] [INSPIRE].

    ADS  Article  Google Scholar 

  59. M. Abadi et al., TensorFlow: large-scale machine learning on heterogeneous distributed systems, arXiv:1603.04467 [INSPIRE].

  60. T. O’Malley et al., Keras tuner github repository, https://github.com/keras-team/keras-tuner, (2019).

  61. M. Boglione et al., Affinity github repository, https://github.com/QCDHUB/SIDIS-Affinity, (2022).

  62. M. Boglione et al., Affinity tool, https://colab.research.google.com/github/QCDHUB/SIDIS-Affinity/blob/main/interactive_affinity_tool.ipynb, (2022).

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Correspondence to A. Prokudin.

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ArXiv ePrint: 2201.12197

On sabbatical leave at Temple University, Philadelphia, PA, U.S.A. (A. Prokudin)

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The Jefferson Lab Angular Momentum (JAM) collaboration., Boglione, M., Diefenthaler, M. et al. New tool for kinematic regime estimation in semi-inclusive deep-inelastic scattering. J. High Energ. Phys. 2022, 84 (2022). https://doi.org/10.1007/JHEP04(2022)084

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  • DOI: https://doi.org/10.1007/JHEP04(2022)084

Keywords

  • Specific QCD Phenomenology
  • Deep Inelastic Scattering or Small-X Physics