Advertisement

Gluon TMD in particle production from low to moderate x

  • I. Balitsky
  • A. Tarasov
Open Access
Regular Article - Theoretical Physics

Abstract

We study the rapidity evolution of gluon transverse momentum dependent distributions appearing in processes of particle production and show how this evolution changes from small to moderate Bjorken x.

Keywords

Deep Inelastic Scattering (Phenomenology) QCD Phenomenology 

Notes

Open Access

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.

References

  1. [1]
    J.C. Collins and D.E. Soper, Parton Distribution and Decay Functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].ADSGoogle Scholar
  2. [2]
    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].
  3. [3]
    J.C. Collins, Foundations of Perturbative QCD, Cambridge University Press, Cambridge, U.K. (2011).CrossRefGoogle Scholar
  4. [4]
    HERMES collaboration, A. Airapetian et al., Single-spin asymmetries in semi-inclusive deep-inelastic scattering on a transversely polarized hydrogen target, Phys. Rev. Lett. 94 (2005) 012002 [hep-ex/0408013] [INSPIRE].
  5. [5]
    COMPASS collaboration, V.Yu. Alexakhin et al., First measurement of the transverse spin asymmetries of the deuteron in semi-inclusive deep inelastic scattering, Phys. Rev. Lett. 94 (2005) 202002 [hep-ex/0503002] [INSPIRE].
  6. [6]
    COMPASS collaboration, E.S. Ageev et al., A new measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target, Nucl. Phys. B 765 (2007) 31 [hep-ex/0610068] [INSPIRE].
  7. [7]
    M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin, Extracting the Sivers function from polarized SIDIS data and making predictions, Phys. Rev. D 72 (2005) 094007 [Erratum ibid. D 72 (2005) 099903] [hep-ph/0507181] [INSPIRE].
  8. [8]
    M. Anselmino et al., Transversity and Collins functions from SIDIS and e + e data, Phys. Rev. D 75 (2007) 054032 [hep-ph/0701006] [INSPIRE].
  9. [9]
    COMPASS collaboration, C. Adolph et al., Transverse spin effects in hadron-pair production from semi-inclusive deep inelastic scattering, Phys. Lett. B 713 (2012) 10 [arXiv:1202.6150] [INSPIRE].
  10. [10]
    COMPASS collaboration, C. Adolph et al., II — Experimental investigation of transverse spin asymmetries in μ-p SIDIS processes: Sivers asymmetries, Phys. Lett. B 717 (2012) 383 [arXiv:1205.5122] [INSPIRE].
  11. [11]
    G.A. Ladinsky and C.P. Yuan, The Nonperturbative regime in QCD resummation for gauge boson production at hadron colliders, Phys. Rev. D 50 (1994) 4239 [hep-ph/9311341] [INSPIRE].
  12. [12]
    C. Balázs, J.-w. Qiu and C.P. Yuan, Effects of QCD resummation on distributions of leptons from the decay of electroweak vector bosons, Phys. Lett. B 355 (1995) 548 [hep-ph/9505203] [INSPIRE].
  13. [13]
    C. Balázs and C.P. Yuan, Soft gluon effects on lepton pairs at hadron colliders, Phys. Rev. D 56 (1997) 5558 [hep-ph/9704258] [INSPIRE].
  14. [14]
    F. Landry, R. Brock, G. Ladinsky and C.P. Yuan, New fits for the nonperturbative parameters in the CSS resummation formalism, Phys. Rev. D 63 (2001) 013004 [hep-ph/9905391] [INSPIRE].
  15. [15]
    J.-w. Qiu and X.-f. Zhang, Role of the nonperturbative input in QCD resummed Drell-Yan Q T distributions, Phys. Rev. D 63 (2001) 114011 [hep-ph/0012348] [INSPIRE].
  16. [16]
    G.I. Fai, J.-w. Qiu and X.-f. Zhang, Full transverse momentum spectra of low mass Drell-Yan pairs at LHC energies, Phys. Lett. B 567 (2003) 243 [hep-ph/0303021] [INSPIRE].
  17. [17]
    F. Landry, R. Brock, P.M. Nadolsky and C.P. Yuan, Tevatron Run-1 Z boson data and Collins-Soper-Sterman resummation formalism, Phys. Rev. D 67 (2003) 073016 [hep-ph/0212159] [INSPIRE].
  18. [18]
    A.V. Konychev and P.M. Nadolsky, Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production, Phys. Lett. B 633 (2006) 710 [hep-ph/0506225] [INSPIRE].
  19. [19]
    T.C. Rogers, An Overview of Transverse Momentum Dependent Factorization and Evolution, arXiv:1509.04766 [INSPIRE].
  20. [20]
    C.A. Aidala, S.D. Bass, D. Hasch and G.K. Mallot, The Spin Structure of the Nucleon, Rev. Mod. Phys. 85 (2013) 655 [arXiv:1209.2803] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    J.-P. Chen, QCD evolution and TMD/spin experiments, Int. J. Mod. Phys. Conf. Ser. 20 (2012) 45.CrossRefGoogle Scholar
  22. [22]
    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].ADSCrossRefGoogle Scholar
  23. [23]
    I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
  24. [24]
    I. Balitsky, Factorization and high-energy effective action, Phys. Rev. D 60 (1999) 014020 [hep-ph/9812311] [INSPIRE].
  25. [25]
    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].
  26. [26]
    Y.V. Kovchegov, Unitarization of the BFKL Pomeron on a nucleus, Phys. Rev. D 61 (2000) 074018 [hep-ph/9905214] [INSPIRE].
  27. [27]
    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].
  28. [28]
    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].
  29. [29]
    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].
  30. [30]
    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].
  31. [31]
    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].
  32. [32]
    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].
  33. [33]
    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].
  34. [34]
    Y.V. Kovchegov and M.D. Sievert, Calculating TMDs of a Large Nucleus: Quasi-Classical Approximation and Quantum Evolution, Nucl. Phys. B 903 (2016) 164 [arXiv:1505.01176] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    Y.V. Kovchegov, D. Pitonyak and M.D. Sievert, Helicity Evolution at Small-x, JHEP 01 (2016) 072 [arXiv:1511.06737] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    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].
  37. [37]
    M.G. Echevarria, A. Idilbi and I. Scimemi, Factorization Theorem For Drell-Yan At Low q T And Transverse Momentum Distributions On-The-Light-Cone, JHEP 07 (2012) 002 [arXiv:1111.4996] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    J.C. Collins, Leading twist single transverse-spin asymmetries: Drell-Yan and deep inelastic scattering, Phys. Lett. B 536 (2002) 43 [hep-ph/0204004] [INSPIRE].
  39. [39]
    M.G.A. Buffing, A. Mukherjee and P.J. Mulders, Generalized Universality of Definite Rank Gluon Transverse Momentum Dependent Correlators, Phys. Rev. D 88 (2013) 054027 [arXiv:1306.5897] [INSPIRE].ADSGoogle Scholar
  40. [40]
    I. Balitsky and A. Tarasov, Rapidity evolution of gluon TMD from low to moderate x, JHEP 10 (2015) 017 [arXiv:1505.02151] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    I. Balitsky and G.A. Chirilli, Photon impact factor in the next-to-leading order, Phys. Rev. D 83 (2011) 031502 [arXiv:1009.4729] [INSPIRE].ADSGoogle Scholar
  42. [42]
    I. Balitsky and G.A. Chirilli, Photon impact factor and k T -factorization for DIS in the next-to-leading order, Phys. Rev. D 87 (2013) 014013 [arXiv:1207.3844] [INSPIRE].ADSGoogle Scholar
  43. [43]
    R.L. Jaffe, Parton Distribution Functions for Twist Four, Nucl. Phys. B 229 (1983) 205 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    I. Balitsky, High-energy QCD and Wilson lines, hep-ph/0101042 [INSPIRE].
  45. [45]
    I. Balitsky, High-energy amplitudes in the next-to-leading order, arXiv:1004.0057 [INSPIRE].
  46. [46]
    I. Balitsky, Factorization and high-energy effective action, Phys. Rev. D 60 (1999) 014020 [hep-ph/9812311] [INSPIRE].
  47. [47]
    F. Dominguez, A.H. Mueller, S. Munier and B.-W. Xiao, On the small-x evolution of the color quadrupole and the Weizsäcker-Williams gluon distribution, Phys. Lett. B 705 (2011) 106 [arXiv:1108.1752] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    M. Ciafaloni, Coherence Effects in Initial Jets at Small Q 2 /s, Nucl. Phys. B 296 (1988) 49 [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    S. Catani, F. Fiorani and G. Marchesini, QCD Coherence in Initial State Radiation, Phys. Lett. B 234 (1990) 339 [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    S. Catani, F. Fiorani and G. Marchesini, Small x Behavior of Initial State Radiation in Perturbative QCD, Nucl. Phys. B 336 (1990) 18 [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    H.-n. Li and J.-L. Lim, Soft gluons in logarithmic summations, Eur. Phys. J. C 10 (1999) 319 [hep-ph/9903267] [INSPIRE].
  52. [52]
    S. Marzani, Combining Q T and small-x resummations, Phys. Rev. D 93 (2016) 054047 [arXiv:1511.06039] [INSPIRE].ADSGoogle Scholar
  53. [53]
    J. Zhou, The evolution of the small x gluon TMD, arXiv:1603.07426 [INSPIRE].
  54. [54]
    I. Balitsky, Quark contribution to the small-x evolution of color dipole, Phys. Rev. D 75 (2007) 014001 [hep-ph/0609105] [INSPIRE].
  55. [55]
    I. Balitsky and G.A. Chirilli, Next-to-leading order evolution of color dipoles, Phys. Rev. D 77 (2008) 014019 [arXiv:0710.4330] [INSPIRE].ADSGoogle Scholar
  56. [56]
    I. Balitsky and G.A. Chirilli, NLO evolution of color dipoles in N = 4 SYM, Nucl. Phys. B 822 (2009) 45 [arXiv:0903.5326] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  57. [57]
    Y.V. Kovchegov and H. Weigert, Triumvirate of Running Couplings in Small-x Evolution, Nucl. Phys. A 784 (2007) 188 [hep-ph/0609090] [INSPIRE].
  58. [58]
    Y.V. Kovchegov and H. Weigert, Quark loop contribution to BFKL evolution: Running coupling and leading-N f NLO intercept, Nucl. Phys. A 789 (2007) 260 [hep-ph/0612071] [INSPIRE].
  59. [59]
    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].ADSGoogle Scholar
  60. [60]
    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].ADSCrossRefGoogle Scholar
  61. [61]
    A.H. Mueller, L. Szymanowski, S. Wallon, B.-W. Xiao and F. Yuan, Sudakov Resummations in Mueller-Navelet Dijet Production, JHEP 03 (2016) 096 [arXiv:1512.07127] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    I.I. Balitsky and V.M. Braun, Nonlocal Operator Expansion for Structure Functions of e + e Annihilation, Phys. Lett. B 222 (1989) 123 [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    I.I. Balitsky and V.M. Braun, The nonlocal operator expansion for inclusive particle production in e + e annihilation, Nucl. Phys. B 361 (1991) 93 [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    I.I. Balitsky and V.M. Braun, Valleys in Minkowski space and instanton induced cross-sections, Nucl. Phys. B 380 (1992) 51 [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    I.I. Balitsky and A.V. Belitsky, Nonlinear evolution in high density QCD, Nucl. Phys. B 629 (2002) 290 [hep-ph/0110158] [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of PhysicsOld Dominion UniversityNorfolkU.S.A.
  2. 2.Theory Group, Jefferson LabNewport NewsU.S.A.

Personalised recommendations