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Photoproduction of three jets in the CGC: gluon TMDs and dilute limit

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  • Published: 21 July 2020
  • Volume 2020, article number 143, (2020)
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Photoproduction of three jets in the CGC: gluon TMDs and dilute limit
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  • Tolga Altinoluk1,
  • Renaud Boussarie2,
  • Cyrille Marquet3 &
  • …
  • Pieter Taels  ORCID: orcid.org/0000-0001-9252-60233,4 

  • 358 Accesses

  • 22 Citations

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A preprint version of the article is available at arXiv.

Abstract

We study the process γA → \( q\overline{q}g \) + X in the Color Glass Condensate (CGC) effective theory. After obtaining the cross section, we consider two kinematic limits which are encompassed in our result. In the so-called correlation limit, the vector sum of the transverse momenta of the three outgoing particles is small with respect to the individual transverse momenta; the cross section then simplifies considerably and can be written in a factorized form, sensitive to both the unpolarized and linearly-polarized Weizsäcker-Williams transverse momentum dependent gluon distribution function (gluon TMD). The second limit of the CGC cross section that we consider is the dilute limit, which we obtain after performing a weak-field expansion; we recover a typical linear-regime expression, involving a single unintegrated gluon distribution function. Using numerical simulations of the small-x QCD evolution of the TMDs, we investigate the rapidity dependence of the cross section in the correlation limit.

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References

  1. E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk Singularity in Nonabelian Gauge Theories, Sov. Phys. JETP. 45 (1977) 199 [Zh. Eksp. Teor. Fiz. 72 (1977) 377] [INSPIRE].

  2. I.I. Balitsky and L.N. Lipatov, The Pomeranchuk Singularity in Quantum Chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [Yad. Fiz. 28 (1978) 1597] [INSPIRE].

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

  4. I.I. Balitsky, Factorization for high-energy scattering, Phys. Rev. Lett. 81 (1998) 2024 [hep-ph/9807434] [INSPIRE].

  5. I.I. Balitsky, Factorization and high-energy effective action, Phys. Rev. D 60 (1999) 014020 [hep-ph/9812311] [INSPIRE].

  6. Y.V. Kovchegov, Small x F2 structure function of a nucleus including multiple Pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [INSPIRE].

  7. Y.V. Kovchegov, Unitarization of the BFKL Pomeron on a nucleus, Phys. Rev. D 61 (2000) 074018 [hep-ph/9905214] [INSPIRE].

  8. 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].

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

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

  11. A. Kovner and J.G. Milhano, Vector potential versus color charge density in low x evolution, Phys. Rev. D 61 (2000) 014012 [hep-ph/9904420] [INSPIRE].

  12. A. Kovner, J.G. Milhano and H. Weigert, Relating different approaches to nonlinear QCD evolution at finite gluon density, Phys. Rev. D 62 (2000) 114005 [hep-ph/0004014] [INSPIRE].

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

  14. 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].

  15. 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].

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

  17. 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].

  18. 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].

    ADS  Google Scholar 

  19. 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].

  20. 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].

  21. 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 

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

  23. 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  ADS  MathSciNet  Google Scholar 

  24. 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  ADS  MathSciNet  Google Scholar 

  25. A. Dumitru, T. Lappi and V. Skokov, Distribution of Linearly Polarized Gluons and Elliptic Azimuthal Anisotropy in Deep Inelastic Scattering Dijet Production at High Energy, Phys. Rev. Lett. 115 (2015) 252301 [arXiv:1508.04438] [INSPIRE].

    Article  ADS  Google Scholar 

  26. 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 

  27. 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].

    ADS  Google Scholar 

  28. 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].

  29. 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].

  30. 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].

  31. 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].

    Article  ADS  Google Scholar 

  32. 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].

    Article  ADS  Google Scholar 

  33. J.C. Collins, Foundations of perturbative QCD, Cambridge University Press, Cambridge U.K. (2013).

    Google Scholar 

  34. A.H. Mueller, B.-W. Xiao and F. Yuan, Sudakov Resummation in Small-x Saturation Formalism, Phys. Rev. Lett. 110 (2013) 082301 [arXiv:1210.5792] [INSPIRE].

    Article  ADS  Google Scholar 

  35. A.H. Mueller, B.-W. Xiao and F. Yuan, Sudakov double logarithms resummation in hard processes in the small-x saturation formalism, Phys. Rev. D 88 (2013) 114010 [arXiv:1308.2993] [INSPIRE].

    ADS  Google Scholar 

  36. A. Stasto, S.-Y. Wei, B.-W. Xiao and F. Yuan, On the Dihadron Angular Correlations in Forward pA collisions, Phys. Lett. B 784 (2018) 301 [arXiv:1805.05712] [INSPIRE].

    Article  ADS  Google Scholar 

  37. C. Marquet, S.-Y. Wei and B.-W. Xiao, Probing parton saturation with forward Z 0 -boson production at small transverse momentum in p + p and p + A collisions, Phys. Lett. B 802 (2020) 135253 [arXiv:1909.08572] [INSPIRE].

    Article  Google Scholar 

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

    ADS  Google Scholar 

  39. 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].

    ADS  Google Scholar 

  40. 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].

    ADS  Google Scholar 

  41. E. Petreska, TMD gluon distributions at small x in the CGC theory, Int. J. Mod. Phys. E 27 (2018) 1830003 [arXiv:1804.04981] [INSPIRE].

    Article  ADS  Google Scholar 

  42. 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 

  43. 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 

  44. 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 

  45. S. Frixione, M.L. Mangano, P. Nason and G. Ridolfi, Improving the Weizsäcker-Williams approximation in electron-proton collisions, Phys. Lett. B 319 (1993) 339 [hep-ph/9310350] [INSPIRE].

  46. 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 

  47. A. Ayala, M. Hentschinski, J. Jalilian-Marian and M.E. Tejeda-Yeomans, Polarized 3 parton production in inclusive DIS at small x, Phys. Lett. B 761 (2016) 229 [arXiv:1604.08526] [INSPIRE].

    Article  ADS  Google Scholar 

  48. G. Beuf, Dipole factorization for DIS at NLO: Loop correction to the \( {\gamma}_{T,L}^{\ast}\to q\overline{q} \) light-front wave functions, Phys. Rev. D 94 (2016) 054016 [arXiv:1606.00777] [INSPIRE].

    ADS  Google Scholar 

  49. G. Beuf, Dipole factorization for DIS at NLO: Combining the \( q\overline{q} \) and \( q\overline{q}g \) contributions, Phys. Rev. D 96 (2017) 074033 [arXiv:1708.06557] [INSPIRE].

    ADS  Google Scholar 

  50. 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 

  51. 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].

  52. C.A. Bertulani, S.R. Klein and J. Nystrand, Physics of ultra-peripheral nuclear collisions, Ann. Rev. Nucl. Part. Sci. 55 (2005) 271 [nucl-ex/0502005] [INSPIRE].

  53. J.B. Kogut and D.E. Soper, Quantum Electrodynamics in the Infinite Momentum Frame, Phys. Rev. D 1 (1970) 2901 [INSPIRE].

    ADS  Google Scholar 

  54. J.D. Bjorken, J.B. Kogut and D.E. Soper, Quantum Electrodynamics at Infinite Momentum: Scattering from an External Field, Phys. Rev. D 3 (1971) 1382 [INSPIRE].

    ADS  Google Scholar 

  55. S.J. Brodsky, H.-C. Pauli and S.S. Pinsky, Quantum chromodynamics and other field theories on the light cone, Phys. Rept. 301 (1998) 299 [hep-ph/9705477] [INSPIRE].

  56. E. Iancu, Physics of the Color Glass Condensate, Thesis, Institut de Physique Théorique, Saclay France (2005) [INSPIRE].

  57. K. Kutak and A.M. Stasto, Unintegrated gluon distribution from modified BK equation, Eur. Phys. J. C 41 (2005) 343 [hep-ph/0408117] [INSPIRE].

  58. E. Avsar and J.C. Collins, Inability to find justification of a kT -factorization formula by following chains of citations, arXiv:1209.1675 [INSPIRE].

  59. E. Iancu and Y. Mulian, Forward trijet production in proton-nucleus collisions, Nucl. Phys. A 985 (2019) 66 [arXiv:1809.05526] [INSPIRE].

    Article  ADS  Google Scholar 

  60. S. Benić, K. Fukushima, O. Garcia-Montero and R. Venugopalan, Probing gluon saturation with next-to-leading order photon production at central rapidities in proton-nucleus collisions, JHEP 01 (2017) 115 [arXiv:1609.09424] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  61. S. Benić and A. Dumitru, Prompt photon-jet angular correlations at central rapidities in p+A collisions, Phys. Rev. D 97 (2018) 014012 [arXiv:1710.01991] [INSPIRE].

    ADS  Google Scholar 

  62. S. Benić, K. Fukushima, O. Garcia-Montero and R. Venugopalan, Constraining unintegrated gluon distributions from inclusive photon production in proton-proton collisions at the LHC, Phys. Lett. B 791 (2019) 11 [arXiv:1807.03806] [INSPIRE].

    Article  ADS  Google Scholar 

  63. K. Roy and R. Venugopalan, Inclusive prompt photon production in electron-nucleus scattering at small x, JHEP 05 (2018) 013 [arXiv:1802.09550] [INSPIRE].

    Article  ADS  Google Scholar 

  64. K. Roy and R. Venugopalan, NLO impact factor for inclusive photon + dijet production in e + A DIS at small x, Phys. Rev. D 101 (2020) 034028 [arXiv:1911.04530] [INSPIRE].

    ADS  Google Scholar 

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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Authors and Affiliations

  1. Theoretical Physics Division, National Centre for Nuclear Research, Pasteura 7, 02-093, Warsaw, Poland

    Tolga Altinoluk

  2. Physics Department, Brookhaven National Laboratory, Upton, NY, 11973, USA

    Renaud Boussarie

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

    Cyrille Marquet & Pieter Taels

  4. INFN, Sezione di Cagliari, Cittadella Universitaria, Monserrato, I-09042, Cagliari, Italy

    Pieter Taels

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  1. Tolga Altinoluk
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Correspondence to Pieter Taels.

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Altinoluk, T., Boussarie, R., Marquet, C. et al. Photoproduction of three jets in the CGC: gluon TMDs and dilute limit. J. High Energ. Phys. 2020, 143 (2020). https://doi.org/10.1007/JHEP07(2020)143

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  • Received: 14 January 2020

  • Revised: 20 May 2020

  • Accepted: 25 May 2020

  • Published: 21 July 2020

  • DOI: https://doi.org/10.1007/JHEP07(2020)143

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Keywords

  • Heavy Ion Phenomenology
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