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Journal of High Energy Physics

, 2017:114 | Cite as

General formulae for dipole Wilson line correlators with the Color Glass Condensate

  • Kenji Fukushima
  • Yoshimasa Hidaka
Open Access
Regular Article - Theoretical Physics

Abstract

We present general formulae to compute Wilson line correlators with the Color Glass Condensate described by the McLerran-Venugopalan model. We explicitly construct a complete and non-orthogonal set of color-singlet bases and write matrix elements down, so that the exponential of the matrix leads to the Wilson line correlators. We further develop a systematic perturbative expansion of dipole Wilson line correlators in terms of 1/Nc where Nc is the color number. As a phenomenological application we calculate the flow harmonics vn{m} in the dipole model and discuss the Nc scaling.

Keywords

Resummation Perturbative QCD Quark-Gluon Plasma 

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]
    A.H. Mueller, Soft gluons in the infinite momentum wave function and the BFKL Pomeron, Nucl. Phys. B 415 (1994) 373 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    A.H. Mueller and B. Patel, Single and double BFKL Pomeron exchange and a dipole picture of high-energy hard processes, Nucl. Phys. B 425 (1994) 471 [hep-ph/9403256] [INSPIRE].
  3. [3]
    I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
  4. [4]
    I. Balitsky, Effective field theory for the small x evolution, Phys. Lett. B 518 (2001) 235 [hep-ph/0105334] [INSPIRE].
  5. [5]
    Y.V. Kovchegov, Small xF 2 structure function of a nucleus including multiple Pomeron exchanges, Phys. Rev. D 60 (1999) 034008 [hep-ph/9901281] [INSPIRE].
  6. [6]
    F. Gelis, Color glass condensate and glasma, Int. J. Mod. Phys. A 28 (2013) 1330001 [arXiv:1211.3327] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    J.-P. Blaizot, High gluon densities in heavy ion collisions, Rept. Prog. Phys. 80 (2017) 032301 [arXiv:1607.04448] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    A.M. Stasto, K.J. Golec-Biernat and J. Kwiecinski, Geometric scaling for the total γ p cross-section in the low x region, Phys. Rev. Lett. 86 (2001) 596 [hep-ph/0007192] [INSPIRE].
  9. [9]
    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].
  10. [10]
    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].
  11. [11]
    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].
  12. [12]
    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].
  13. [13]
    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].
  14. [14]
    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].
  15. [15]
    Y.V. Kovchegov, Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus, Phys. Rev. D 54 (1996) 5463 [hep-ph/9605446] [INSPIRE].
  16. [16]
    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].
  17. [17]
    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].
  18. [18]
    H. Weigert, Unitarity at small Bjorken x, Nucl. Phys. A 703 (2002) 823 [hep-ph/0004044] [INSPIRE].
  19. [19]
    K. Rummukainen and H. Weigert, Universal features of JIMWLK and BK evolution at small x, Nucl. Phys. A 739 (2004) 183 [hep-ph/0309306] [INSPIRE].
  20. [20]
    T. Lappi and H. Mäntysaari, Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next to leading order, Phys. Rev. D 91 (2015) 074016 [arXiv:1502.02400] [INSPIRE].ADSGoogle Scholar
  21. [21]
    E. Iancu, K. Itakura and L. McLerran, A Gaussian effective theory for gluon saturation, Nucl. Phys. A 724 (2003) 181 [hep-ph/0212123] [INSPIRE].
  22. [22]
    T. Lappi and H. Mantysaari, Forward dihadron correlations in deuteron-gold collisions with the Gaussian approximation of JIMWLK, Nucl. Phys. A 908 (2013) 51 [arXiv:1209.2853] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A. Kovner and U.A. Wiedemann, Eikonal evolution and gluon radiation, Phys. Rev. D 64 (2001) 114002 [hep-ph/0106240] [INSPIRE].
  24. [24]
    Y.V. Kovchegov and K. Tuchin, Inclusive gluon production in DIS at high parton density, Phys. Rev. D 65 (2002) 074026 [hep-ph/0111362] [INSPIRE].
  25. [25]
    J.P. Blaizot, F. Gelis and R. Venugopalan, High-energy pA collisions in the color glass condensate approach. 1. Gluon production and the Cronin effect, Nucl. Phys. A 743 (2004) 13 [hep-ph/0402256] [INSPIRE].
  26. [26]
    J.P. Blaizot, F. Gelis and R. Venugopalan, High-energy pA collisions in the color glass condensate approach. 2. Quark production, Nucl. Phys. A 743 (2004) 57 [hep-ph/0402257] [INSPIRE].
  27. [27]
    R. Baier, A. Kovner, M. Nardi and U.A. Wiedemann, Particle correlations in saturated QCD matter, Phys. Rev. D 72 (2005) 094013 [hep-ph/0506126] [INSPIRE].
  28. [28]
    C. Marquet, Forward inclusive dijet production and azimuthal correlations in pA collisions, Nucl. Phys. A 796 (2007) 41 [arXiv:0708.0231] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    K. Fukushima and Y. Hidaka, Two gluon production and longitudinal correlations in the color glass condensate, Nucl. Phys. A 813 (2008) 171 [arXiv:0806.2143] [INSPIRE].ADSGoogle Scholar
  30. [30]
    J.L. Albacete and C. Marquet, Azimuthal correlations of forward di-hadrons in d+Au collisions at RHIC in the color glass condensate, Phys. Rev. Lett. 105 (2010) 162301 [arXiv:1005.4065] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    A. Kovner, M. Lublinsky and V. Skokov, Exploring correlations in the CGC wave function: odd azimuthal anisotropy, Phys. Rev. D 96 (2017) 016010 [arXiv:1612.07790] [INSPIRE].ADSGoogle Scholar
  32. [32]
    F. Gelis and J. Jalilian-Marian, Photon production in high-energy proton nucleus collisions, Phys. Rev. D 66 (2002) 014021 [hep-ph/0205037] [INSPIRE].
  33. [33]
    F. Gelis and J. Jalilian-Marian, Dilepton production from the color glass condensate, Phys. Rev. D 66 (2002) 094014 [hep-ph/0208141] [INSPIRE].
  34. [34]
    J. Jalilian-Marian, Electromagnetic signatures of the color glass condensate: dileptons, Nucl. Phys. A 739 (2004) 319 [nucl-th/0402014] [INSPIRE].
  35. [35]
    S. Benic and K. Fukushima, Photon from the annihilation process with CGC in the pA collision, Nucl. Phys. A 958 (2017) 1 [arXiv:1602.01989] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    S. Benic, 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].ADSCrossRefzbMATHGoogle Scholar
  37. [37]
    A. Dumitru, F. Gelis, L. McLerran and R. Venugopalan, Glasma flux tubes and the near side ridge phenomenon at RHIC, Nucl. Phys. A 810 (2008) 91 [arXiv:0804.3858] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    A. Dumitru, K. Dusling, F. Gelis, J. Jalilian-Marian, T. Lappi and R. Venugopalan, The ridge in proton-proton collisions at the LHC, Phys. Lett. B 697 (2011) 21 [arXiv:1009.5295] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    C. Loizides, Experimental overview on small collision systems at the LHC, Nucl. Phys. A 956 (2016) 200 [arXiv:1602.09138] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    V. Skokov, High order cumulants of the azimuthal anisotropy in the dilute-dense limit: connected graphs, Phys. Rev. D 91 (2015) 054014 [arXiv:1412.5191] [INSPIRE].ADSGoogle Scholar
  41. [41]
    T. Lappi, B. Schenke, S. Schlichting and R. Venugopalan, Tracing the origin of azimuthal gluon correlations in the color glass condensate, JHEP 01 (2016) 061 [arXiv:1509.03499] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    K. Dusling, M. Mace and R. Venugopalan, Multiparticle collectivity from initial state correlations in high energy proton-nucleus collisions, arXiv:1705.00745 [INSPIRE].
  43. [43]
    K. Dusling, M. Mace and R. Venugopalan, Parton model description of multiparticle azimuthal correlations in pA collisions, arXiv:1706.06260 [INSPIRE].
  44. [44]
    Y. Shi, C. Zhang and E. Wang, Multipole scattering amplitudes in the color glass condensate formalism, Phys. Rev. D 95 (2017) 116014 [arXiv:1704.00266] [INSPIRE].ADSGoogle Scholar
  45. [45]
    K. Fukushima and Y. Hidaka, Light projectile scattering off the color glass condensate, JHEP 06 (2007) 040 [arXiv:0704.2806] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    A. Dumitru and V. Skokov, Fluctuations of the gluon distribution from the small-x effective action, Phys. Rev. D 96 (2017) 056029 [arXiv:1704.05917] [INSPIRE].ADSGoogle Scholar
  47. [47]
    H. Kowalski, L. Motyka and G. Watt, Exclusive diffractive processes at HERA within the dipole picture, Phys. Rev. D 74 (2006) 074016 [hep-ph/0606272] [INSPIRE].
  48. [48]
    N. Borghini, P.M. Dinh and J.-Y. Ollitrault, Flow analysis from multiparticle azimuthal correlations, Phys. Rev. C 64 (2001) 054901 [nucl-th/0105040] [INSPIRE].

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of PhysicsThe University of TokyoTokyoJapan
  2. 2.Theoretical Research DivisionNishina Center, RIKENWakoJapan

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