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Low-x improved TMD approach to the lepto- and hadroproduction of a heavy-quark pair

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  • Published: 14 June 2021
  • Volume 2021, article number 85, (2021)
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Low-x improved TMD approach to the lepto- and hadroproduction of a heavy-quark pair
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  • Tolga Altinoluk1,
  • Cyrille Marquet2 &
  • Pieter Taels  ORCID: orcid.org/0000-0001-9252-60232 
  • 229 Accesses

  • 19 Citations

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A preprint version of the article is available at arXiv.

Abstract

We study the lepto- and hadroproduction of a heavy-quark pair in the ITMD factorization framework for dilute-dense collisions. Due to the presence of a nonzero quark mass and/or nonzero photon virtuality, new contributions appear compared to the cases of photo- and hadroproduction of dijets, for which the ITMD framework was originally derived. These extra terms are sensitive to gluons that are not fully linearly polarized. At small x, those gluons emerge only when all saturation effects are carefully taken into account. Therefore, the resulting contributions are absent in linear small-x frameworks, where gluons are fully linearly polarized. We show, however, that even for large gluon transverse momentum, these contributions are not always negligible, due to the behavior of the off-shell hard factors.

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References

  1. P. Kotko, K. Kutak, C. Marquet, E. Petreska, S. Sapeta and A. van Hameren, Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions, JHEP 09 (2015) 106 [arXiv:1503.03421] [INSPIRE].

    Article  ADS  Google Scholar 

  2. A. van Hameren, P. Kotko, K. Kutak, C. Marquet, E. Petreska and S. Sapeta, Forward di-jet production in p+Pb collisions in the small-x improved TMD factorization framework, JHEP 12 (2016) 034 [Erratum ibid. 02 (2019) 158] [arXiv:1607.03121] [INSPIRE].

  3. F. Gelis, E. Iancu, J. Jalilian-Marian and R. Venugopalan, The Color Glass Condensate, Ann. Rev. Nucl. Part. Sci. 60 (2010) 463 [arXiv:1002.0333] [INSPIRE].

    Article  ADS  Google Scholar 

  4. T. Altinoluk, R. Boussarie and P. Kotko, Interplay of the CGC and TMD frameworks to all orders in kinematic twist, JHEP 05 (2019) 156 [arXiv:1901.01175] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. T. Altinoluk and R. Boussarie, Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation, JHEP 10 (2019) 208 [arXiv:1902.07930] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. R. Boussarie and Y. Mehtar-Tani, Gauge invariance of transverse momentum dependent distributions at small x, Phys. Rev. D 103 (2021) 094012 [arXiv:2001.06449] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. F. Dominguez, B.-W. Xiao and F. Yuan, kt-factorization for Hard Processes in Nuclei, Phys. Rev. Lett. 106 (2011) 022301 [arXiv:1009.2141] [INSPIRE].

    Article  ADS  Google Scholar 

  8. F. Dominguez, C. Marquet, B.-W. Xiao and F. Yuan, Universality of Unintegrated Gluon Distributions at small x, Phys. Rev. D 83 (2011) 105005 [arXiv:1101.0715] [INSPIRE].

    Article  ADS  Google Scholar 

  9. E. Iancu and J. Laidet, Gluon splitting in a shockwave, Nucl. Phys. A 916 (2013) 48 [arXiv:1305.5926] [INSPIRE].

    Article  ADS  Google Scholar 

  10. C. Marquet, E. Petreska and C. Roiesnel, Transverse-momentum-dependent gluon distributions from JIMWLK evolution, JHEP 10 (2016) 065 [arXiv:1608.02577] [INSPIRE].

    Article  ADS  Google Scholar 

  11. C. Marquet, C. Roiesnel and P. Taels, Linearly polarized small-x gluons in forward heavy-quark pair production, Phys. Rev. D 97 (2018) 014004 [arXiv:1710.05698] [INSPIRE].

    Article  ADS  Google Scholar 

  12. S. Catani, M. Ciafaloni and F. Hautmann, High-energy factorization and small x heavy flavor production, Nucl. Phys. B 366 (1991) 135 [INSPIRE].

    Article  ADS  Google Scholar 

  13. M. Deak, F. Hautmann, H. Jung and K. Kutak, Forward Jet Production at the Large Hadron Collider, JHEP 09 (2009) 121 [arXiv:0908.0538] [INSPIRE].

    Article  ADS  Google Scholar 

  14. R. Angeles-Martinez et al., Transverse Momentum Dependent (TMD) parton distribution functions: status and prospects, Acta Phys. Polon. B 46 (2015) 2501 [arXiv:1507.05267] [INSPIRE].

    Article  ADS  Google Scholar 

  15. J. C. Collins, Foundations of Perturbative QCD, Cambridge University Press (2013).

  16. C. J. Bomhof, P. J. Mulders and F. Pijlman, The Construction of gauge-links in arbitrary hard processes, Eur. Phys. J. C 47 (2006) 147 [hep-ph/0601171] [INSPIRE].

    Article  ADS  Google Scholar 

  17. C. Marquet, Forward inclusive dijet production and azimuthal correlations in p(A) collisions, Nucl. Phys. A 796 (2007) 41 [arXiv:0708.0231] [INSPIRE].

    Article  ADS  Google Scholar 

  18. H. Fujii, C. Marquet and K. Watanabe, Comparison of improved TMD and CGC frameworks in forward quark dijet production, JHEP 12 (2020) 181 [arXiv:2006.16279] [INSPIRE].

    Article  ADS  Google Scholar 

  19. P. Kotko, K. Kutak, S. Sapeta, A. M. Stasto and M. Strikman, Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC, Eur. Phys. J. C 77 (2017) 353 [arXiv:1702.03063] [INSPIRE].

    Article  ADS  Google Scholar 

  20. M. Bury, A. van Hameren, P. Kotko and K. Kutak, Forward trijet production in p-p and p-Pb collisions at LHC, JHEP 09 (2020) 175 [arXiv:2006.13175] [INSPIRE].

    Article  ADS  Google Scholar 

  21. I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].

    Article  ADS  Google Scholar 

  22. Y. V. Kovchegov, Small x F(2) structure function of a nucleus including multiple Pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [INSPIRE].

    Article  ADS  Google Scholar 

  23. L. N. Lipatov, Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian Gauge Theories, Sov. J. Nucl. Phys. 23 (1976) 338 [INSPIRE].

    Google Scholar 

  24. E. A. Kuraev, L. N. Lipatov and V. S. Fadin, Multi-Reggeon Processes in the Yang-Mills Theory, Sov. Phys. JETP 44 (1976) 443 [INSPIRE].

    ADS  Google Scholar 

  25. I. I. Balitsky and L. N. Lipatov, The Pomeranchuk Singularity in Quantum Chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [INSPIRE].

    Google Scholar 

  26. A. Metz and J. Zhou, Distribution of linearly polarized gluons inside a large nucleus, Phys. Rev. D 84 (2011) 051503 [arXiv:1105.1991] [INSPIRE].

    Article  ADS  Google Scholar 

  27. F. Dominguez, J.-W. Qiu, B.-W. Xiao and F. Yuan, On the linearly polarized gluon distributions in the color dipole model, Phys. Rev. D 85 (2012) 045003 [arXiv:1109.6293] [INSPIRE].

    Article  ADS  Google Scholar 

  28. E. Akcakaya, A. Schäfer and J. Zhou, Azimuthal asymmetries for quark pair production in pA collisions, Phys. Rev. D 87 (2013) 054010 [arXiv:1208.4965] [INSPIRE].

    Article  ADS  Google Scholar 

  29. D. Boer, P. J. Mulders, C. Pisano and J. Zhou, Asymmetries in Heavy Quark Pair and Dijet Production at an EIC, JHEP 08 (2016) 001 [arXiv:1605.07934] [INSPIRE].

    Article  ADS  Google Scholar 

  30. L. D. McLerran and R. Venugopalan, Computing quark and gluon distribution functions for very large nuclei, Phys. Rev. D 49 (1994) 2233 [hep-ph/9309289] [INSPIRE].

    Article  ADS  Google Scholar 

  31. L. D. McLerran and R. Venugopalan, Gluon distribution functions for very large nuclei at small transverse momentum, Phys. Rev. D 49 (1994) 3352 [hep-ph/9311205] [INSPIRE].

    Article  ADS  Google Scholar 

  32. L. D. McLerran and R. Venugopalan, Green’s functions in the color field of a large nucleus, Phys. Rev. D 50 (1994) 2225 [hep-ph/9402335] [INSPIRE].

    Article  ADS  Google Scholar 

  33. J. Jalilian-Marian, A. Kovner, A. Leonidov and H. Weigert, The BFKL equation from the Wilson renormalization group, Nucl. Phys. B 504 (1997) 415 [hep-ph/9701284] [INSPIRE].

    Article  ADS  Google Scholar 

  34. J. Jalilian-Marian, A. Kovner, A. Leonidov and H. Weigert, The Wilson renormalization group for low x physics: Towards the high density regime, Phys. Rev. D 59 (1998) 014014 [hep-ph/9706377] [INSPIRE].

    Article  ADS  Google Scholar 

  35. J. Jalilian-Marian, A. Kovner and H. Weigert, The Wilson renormalization group for low x physics: Gluon evolution at finite parton density, Phys. Rev. D 59 (1998) 014015 [hep-ph/9709432] [INSPIRE].

    Article  ADS  Google Scholar 

  36. E. Iancu, A. Leonidov and L. D. McLerran, Nonlinear gluon evolution in the color glass condensate. 1, Nucl. Phys. A 692 (2001) 583 [hep-ph/0011241] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  37. E. Iancu, A. Leonidov and L. D. McLerran, The Renormalization group equation for the color glass condensate, Phys. Lett. B 510 (2001) 133 [hep-ph/0102009] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  38. E. Ferreiro, E. Iancu, A. Leonidov and L. McLerran, Nonlinear gluon evolution in the color glass condensate. 2, Nucl. Phys. A 703 (2002) 489 [hep-ph/0109115] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  39. H. Weigert, Unitarity at small Bjorken x, Nucl. Phys. A 703 (2002) 823 [hep-ph/0004044] [INSPIRE].

    Article  ADS  Google Scholar 

  40. R. Boussarie, H. Mäntysaari, F. Salazar and B. Schenke, in preparation.

  41. M. Bury, P. Kotko and K. Kutak, TMD gluon distributions for multiparton processes, Eur. Phys. J. C 79 (2019) 152 [arXiv:1809.08968] [INSPIRE].

    Article  ADS  Google Scholar 

  42. T. Altinoluk, N. Armesto, A. Kovner, M. Lublinsky and E. Petreska, Soft photon and two hard jets forward production in proton-nucleus collisions, JHEP 04 (2018) 063 [arXiv:1802.01398] [INSPIRE].

    Article  ADS  Google Scholar 

  43. T. Altinoluk, R. Boussarie, C. Marquet and P. Taels, TMD factorization for dijets + photon production from the dilute-dense CGC framework, JHEP 07 (2019) 079 [arXiv:1810.11273] [INSPIRE].

    Article  ADS  Google Scholar 

  44. T. Altinoluk, R. Boussarie, C. Marquet and P. Taels, Photoproduction of three jets in the CGC: gluon TMDs and dilute limit, JHEP 07 (2020) 143 [arXiv:2001.00765] [INSPIRE].

    Article  ADS  Google Scholar 

  45. P. J. Mulders and J. Rodrigues, Transverse momentum dependence in gluon distribution and fragmentation functions, Phys. Rev. D 63 (2001) 094021 [hep-ph/0009343] [INSPIRE].

    Article  ADS  Google Scholar 

  46. S. Meissner, A. Metz and K. Goeke, Relations between generalized and transverse momentum dependent parton distributions, Phys. Rev. D 76 (2007) 034002 [hep-ph/0703176] [INSPIRE].

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. National Centre for Nuclear Research, 02-093, Warsaw, Poland

    Tolga Altinoluk

  2. Centre de Physique Théorique, École polytechnique, CNRS, I.P. Paris, F-91128, Palaiseau, France

    Cyrille Marquet & Pieter Taels

Authors
  1. Tolga Altinoluk
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  2. Cyrille Marquet
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  3. Pieter Taels
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Correspondence to Pieter Taels.

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ArXiv ePrint: 2103.14495

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Altinoluk, T., Marquet, C. & Taels, P. Low-x improved TMD approach to the lepto- and hadroproduction of a heavy-quark pair. J. High Energ. Phys. 2021, 85 (2021). https://doi.org/10.1007/JHEP06(2021)085

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  • Received: 23 April 2021

  • Accepted: 24 May 2021

  • Published: 14 June 2021

  • DOI: https://doi.org/10.1007/JHEP06(2021)085

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Keywords

  • Heavy Ion Phenomenology
  • Deep Inelastic Scattering (Phenomenology)
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