Abstract
We develop a new approximation scheme aiming at extracting higher-point correlation functions from the JIMWLK evolution, in the limit where the number of colors is large. Namely, we show that by exploiting the structure of the ‘virtual’ terms in the Balitsky-JIMWLK equations, one can derive functional relations expressing arbitrary n-point functions of the Wilson lines in terms of the 2-point function (the scattering amplitude for a color dipole). These approximations are correct not only in the regime of strong scattering, where the evolution is indeed controlled by the ‘virtual’ terms, but also in the regime of weak scattering, where they reduce to the corresponding BFKL solutions. This last feature follows from the fact that the JIMWLK Hamiltonian is a linear combination of the pieces responsible for the ‘real’ and ‘virtual’ terms, respectively. We apply this scheme to two examples: the ‘color quadrupole’ (the 4-point function of the Wilson lines which enters the cross-section for the production of a pair of jets at forward rapidities) and the ‘color sextupole’ (the 6-point function). For particular configurations of the quadrupole, our general formula reduces to relatively simple expressions that have been previously proposed on the basis of the McLerran-Venugopalan model and which were recently shown to agree quite well with exact, numerical, solutions to the JIMWLK equation.
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References
I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B 463 (1996) 99 [hep-ph/9509348] [INSPIRE].
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].
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 (1999) 014014 [hep-ph/9706377] [INSPIRE].
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 (1999) 014015 [hep-ph/9709432] [INSPIRE].
A. Kovner, J. 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].
H. Weigert, Unitarity at small Bjorken x, Nucl. Phys. A 703 (2002) 823 [hep-ph/0004044] [INSPIRE].
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].
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].
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].
E. Iancu, A. Leonidov and L. McLerran, The color glass condensate: an introduction, hep-ph/0202270 [INSPIRE].
E. Iancu and R. Venugopalan, The color glass condensate and high-energy scattering in QCD, hep-ph/0303204 [INSPIRE].
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].
E. Braidot, Two-particle azimuthal correlations at forward rapidity in STAR, arXiv:1102.0931 [INSPIRE].
J. Jalilian-Marian and Y.V. Kovchegov, Inclusive two-gluon and valence quark-gluon production in DIS and pA, Phys. Rev. D 70 (2004) 114017 [Erratum ibid. D 71 (2005) 079901] [hep-ph/0405266] [INSPIRE].
N. Nikolaev, W. Schafer, B. Zakharov and V. Zoller, Nonlinear k-perpendicular-factorization for quark-gluon dijet production off nuclei, Phys. Rev. D 72 (2005) 034033 [hep-ph/0504057] [INSPIRE].
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].
C. Marquet, Forward inclusive dijet production and azimuthal correlations in pA collisions, Nucl. Phys. A 796 (2007) 41 [arXiv:0708.0231] [INSPIRE].
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].
A. Dumitru and J. Jalilian-Marian, Forward dijets in high-energy collisions: evolution of QCD n-point functions beyond the dipole approximation, Phys. Rev. D 82 (2010) 074023 [arXiv:1008.0480] [INSPIRE].
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].
F. Dominguez, A. Mueller, S. Munier and B.-W. Xiao, On the small-x evolution of the color quadrupole and the Weizsácker-Williams gluon distribution, Phys. Lett. B 705 (2011) 106 [arXiv:1108.1752] [INSPIRE].
A. Dumitru, J. Jalilian-Marian, T. Lappi, B. Schenke and R. Venugopalan, Renormalization group evolution of multi-gluon correlators in high energy QCD, arXiv:1108.4764 [INSPIRE].
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].
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].
A.H. Mueller, Soft gluons in the infinite momentum wave function and the BFKL Pomeron, Nucl. Phys. B 415 (1994) 373 [INSPIRE].
J. Jalilian-Marian, private communication.
G.A. Chirilli, private communication.
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].
J.-P. Blaizot, E. Iancu and H. Weigert, Nonlinear gluon evolution in path integral form, Nucl. Phys. A 713 (2003) 441 [hep-ph/0206279] [INSPIRE].
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].
Y.V. Kovchegov, J. Kuokkanen, K. Rummukainen and H. Weigert, Subleading-N c corrections in non-linear small-x evolution, Nucl. Phys. A 823 (2009) 47 [arXiv:0812.3238] [INSPIRE].
T. Lappi, Gluon spectrum in the glasma from JIMWLK evolution, Phys. Lett. B 703 (2011) 325 [arXiv:1105.5511] [INSPIRE].
Y. Hatta, E. Iancu, K. Itakura and L. McLerran, Odderon in the color glass condensate, Nucl. Phys. A 760 (2005) 172 [hep-ph/0501171] [INSPIRE].
D. Triantafyllopoulos, Pomeron loops in high energy QCD, Acta Phys. Polon. B 36 (2005) 3593 [hep-ph/0511226] [INSPIRE].
E. Levin and K. Tuchin, Solution to the evolution equation for high parton density QCD, Nucl. Phys. B 573 (2000) 833 [hep-ph/9908317] [INSPIRE].
E. Iancu and A. Mueller, Rare fluctuations and the high-energy limit of the S matrix in QCD, Nucl. Phys. A 730 (2004) 494 [hep-ph/0309276] [INSPIRE].
E. Iancu and D. Triantafyllopoulos, A Langevin equation for high energy evolution with Pomeron loops, Nucl. Phys. A 756 (2005) 419 [hep-ph/0411405] [INSPIRE].
A. Mueller, A. Shoshi and S. Wong, Extension of the JIMWLK equation in the low gluon density region, Nucl. Phys. B 715 (2005) 440 [hep-ph/0501088] [INSPIRE].
E. Iancu and D. Triantafyllopoulos, Non-linear QCD evolution with improved triple-Pomeron vertices, Phys. Lett. B 610 (2005) 253 [hep-ph/0501193] [INSPIRE].
A. Kovner and M. Lublinsky, In pursuit of Pomeron loops: the JIMWLK equation and the Wess-Zumino term, Phys. Rev. D 71 (2005) 085004 [hep-ph/0501198] [INSPIRE].
E. Iancu, K. Itakura and L. McLerran, Geometric scaling above the saturation scale, Nucl. Phys. A 708 (2002) 327 [hep-ph/0203137] [INSPIRE].
A. Mueller and D. Triantafyllopoulos, The energy dependence of the saturation momentum, Nucl. Phys. B 640 (2002) 331 [hep-ph/0205167] [INSPIRE].
S. Munier and R.B. Peschanski, Geometric scaling as traveling waves, Phys. Rev. Lett. 91 (2003) 232001 [hep-ph/0309177] [INSPIRE].
K.J. Golec-Biernat and M. Wusthoff, Saturation effects in deep inelastic scattering at low Q 2 and its implications on diffraction, Phys. Rev. D 59 (1998) 014017 [hep-ph/9807513] [INSPIRE].
K.J. Golec-Biernat and M. Wusthoff, Saturation in diffractive deep inelastic scattering, Phys. Rev. D 60 (1999) 114023 [hep-ph/9903358] [INSPIRE].
D. Binosi and L. Theussl, JaxoDraw: a graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
D. Binosi, J. Collins, C. Kaufhold and L. Theussl, JaxoDraw: a graphical user interface for drawing Feynman diagrams. Version 2.0 release notes, Comput. Phys. Commun. 180 (2009) 1709 [arXiv:0811.4113] [INSPIRE].
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ArXiv ePrint: 1109.0302
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Iancu, E., Triantafyllopoulos, D.N. Higher-point correlations from the JIMWLK evolution. J. High Energ. Phys. 2011, 105 (2011). https://doi.org/10.1007/JHEP11(2011)105
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DOI: https://doi.org/10.1007/JHEP11(2011)105