I present a brief review of the recent phenomenological analyses of RHIC data
based on the the Color Glass Condensate, including the use of non-linear
evolution equations with running coupling. In particular, I focus in the study
of the total multiplicities in Au+Au collisions, and in the single inclusive
and double inclusive forward spectra in d+Au collisions. Predictions for the
LHC are also discussed.Comment: 4 pages, 5 figures. Contributed to the proceedings of the XLVth
  Rencontres de Moriond, QCD session. March 13th - 20th, La Thuile, Ital

Albacete, Javier L.

English

arXiv

I present a brief review of the recent phenomenological analyses of RHIC data based on the the Color Glass Condensate, including the use of non-linear evolution equations with running coupling. In particular, I focus in the study of the total multiplicities in Au+Au collisions, and in the single inclusive and double inclusive forward spectra in d+Au collisions. Predictions for the LHC are also discussed.I present a brief review of the recent phenomenological analyses of RHIC data based on the the Color Glass Condensate, including the use of non-linear evolution equations with running coupling. In particular, I focus in the study of the total multiplicities in Au+Au collisions, and in the single inclusive and double inclusive forward spectra in d+Au collisions. Predictions for the LHC are also discussed.I present a brief review of the recent phenomenological analyses of RHIC data based on the the Color Glass Condensate, including the use of non-linear evolution equations with running coupling. In particular, I focus in the study of the total multiplicities in Au+Au collisions, and in the single inclusive and double inclusive forward spectra in d+Au collisions. Predictions for the LHC are also discussed

CERN Document Server

CGC phenomenology at RHIC and the LHCJ. L. AlbaceteInstitut de Physique The´orique, CEA/Saclay, 91191 Gif-sur-Yvette cedex, FranceURA 2306, unite´ de recherche associe´e au CNRSI present a brief review of the recent phenomenological analyses of RHIC data based on thethe Color Glass Condensate, including the use of non-linear evolution equations with runningcoupling. In particular, I focus in the study of the total multiplicities in Au+Au collisions, andin the single inclusive and double inclusive forward spectra in d+Au collisions. Predictionsfor the LHC are also discussedAt high energies, QCD scattering enters a novel regime governed by large gluon densitiesand coherent, non-linear phenomena, including saturation of the hadronic wave functions, knownas the Color Glass Condensate (CGC) (see e.g., the review 1 and references therein). Nuclearcollisions performed at RHIC provide a good opportunity to explore the CGC regime, since thegluon densities in a nucleus are already large even at moderate energies. The recent calculation ofrunning coupling corrections 2,3,4,5 to the BK-JIMWLK evolution equations of the CGC allowsfor a good quantitative description of several experimental measurements, thus reducing thedegree of modelization required in phenomenological studies. Here I present a brief review ofthe phenomenological analyses of RHIC data based on the use of Balitsky-Kovchegov equation6,7 including running coupling correction (rcBK) for the description of the small-x degrees offreedom of the wavefunction of the colliding nuclei. We also discuss predictions for the LHC.The rcBK equation for the small-x evolution of the dipole scattering amplitude reads∂N (x, r)∂ ln(x0/x)=∫d2r1 Krun(r, r1, r2) [N (x, r1) +N (x, r2)−N (x, r)−N (x, r1)N (x, r2)] , (1)where ri refers to the dipoles tranverse sizes and x0 is the starting point for the evolution. Therunning coupling kernel Krun is evaluated according to Balitsly’s prescription 2. In the analysespresented below, the rcBK equation is supplemented with MV initial conditions at the startingevolution point, x0, NF (A)(r, x0) = 1 − exp[− r2Q2s04 ln(1Λ r + e)], with Qs0 the initial quark(gluon) saturation scale and Λ=0.241 GeV.1 Multiplicity densities in nucleus-nucleus collisions a RHIC and the LHC.The total number of particles produced per unit rapidity in RHIC Au+Au collisions turned outto be significantly lower than predicted assuming incoherent superposition of nucleon-nucleonscattering, signaling the importance of coherence effects. Such reduced multiplicities are inter-preted in the CGC as a consequence of a reduced flux of scattering centers, i.e. gluons, enteringthe collision due to saturation effects in the wave function of the colliding nuclei. Thus, thefinal number of produced particles rises proportional to the number of gluons in the incomingwavefunction, whose growth can be described by the rcBK equation. Even if its applicability tonucleus-nucleus collisions is not completely justified, such idea is realized in the kT -factorizationframework, as proposed in 8, where the multiplicity distributions can be written as :dNchdy d2b= C4piNcN2c − 1∫d2ptp2t∫ ptd2kt αs(Q)ϕ(x1,|kt + pt|2)ϕ(x2,|kt − pt|2), (2)where pt and y are the transverse momentum and rapidity of the produced particle, x1,2 =(pt/√s) e±y. ϕ(x, kt) =∫d2r2pi r2ei kt·rN (x, r) is the nuclear unintegrated gluon distribution. ThearXiv:1005.4892v1  [hep-ph]  26 May 2010-4 -2 0 2 42004006008001000120014001600ηdchdNη=200 GeVNNsAu-Au 0-6%, =130 GeVNNsAu-Au 0-6%, =5.5 TeVNNsPb-Pb Figure 1: Multiplicity densities as a functiion of pseudorapidity in RHIC Au+Au collisions at√s = 200 and 130GeV (data by the PHOBOS Coll.). Uppermost curves correspond to predictions for Pb+Pb collisions at the LHC(√s = 5.5 TeV).lack of impact parameter integration in this calculation and the gluon to charged hadron ratio areaccounted for by the constant C, which sets the normalization. As shown in Fig. 1, the use of Eq.(2) together with rcBK equation for the small-x dynamics of the nuclear ugd provides 9 a gooddescription of the energy and pseudorapidity dependence of data ? for the multiplicity densitiesin Au+Au collisions at the highest collision energies at RHIC. With all the parameters in thecalculation constrained by RHIC data, the extrapolation to Pb+Pb collisions at the LHC is nowcompletely driven by the small-x dynamics, yieldingdNPb−Pbchdη (√s=5.5 TeV, η = 0) ∼ 1290÷1480.2 Forward single inclusive spectra in p+p, d+Au and p+Pb collisions.The experimentally observed suppression of forward hadron yields in d+Au collisions comparedto those measured in p+p collisions was predicted in CGC base calculations, albeit at a qual-itative level10,11. Thanks to the new theoretical tools available, now it is also possible to get agood quantitative description of such suppression 12. At forward rapidities, where the projectileis probed at large-x and the target nucleus at small-x, single inclusive hadron production canbe calculated as 13:dNhdyh d2pt=K(2pi)2∑q∫ 1xFdzz2[x1fq / p(x1, p2t ) N˜F(x2,ptz)Dh / q(z, p2t )+ x1fg / p(x1, p2t ) N˜A(x2,ptz)Dh / g(z, p2t )], (3)where pt and yh are the transverse momentum and rapidity of the produced hadron, and fi/p andDh/i refer to the parton distribution function of the incoming proton and to the fragmentationfunction respectively. The gluon distributions representing the target are given by the Fouriertransforms of the dipole amplitude: N˜F (A)(x, k) =∫d2r e−ik·r[1−NF (A)(r, x)], where F(A)stands for fundamental (adjoint) representation.With Q2s0 = 0.4 ÷ 0.5 GeV2 (for quarks) and 0.005< x0 <0.025, we 12 obtain a very gooddescription of the forward negative charged hadrons at y= 2.2 and 3.2 (data by the BRAHMSCollaboration 17) and neutral pion production at y = 4 (data by the STAR collaboration 18)in minimum bias d+Au collisions, as shown in Fig. 2 (left). An equally good description is                                        (GeV)Tp0.5 1 1.5 2 2.5 3 3.5 4 4.5 5)−2 (GeVTp2/dηN/d2 d−610−510−410−310−210−110110210 BRAHMS=2.2; K=1η(x20); −h=3.2; K=1η(x4); −hSTAR=4; K=0.3η; 0pi                (GeV)Tp0 5 10 15 20 25          ± h pPbR0.10.20.30.40.50.60.70.80.91=8.8 TeVNNs =2, 4, 6hyhybrid formalismkt−factorization=3.6collNFigure 2: Left: Charged hadron (y = 2.2 and 3.2) and neutral pion (y = 4) spectra in d+Au collisions. Right:Predicted nuclear modification factor for charged hadron spectra in p+Pb collisions at the LHC.obtained for proton-proton data at the same collision energy with Q2s0 = 0.2 GeV2. Remarkably,the description of negative charged hadrons does not require any K-factors, i.e. K = 1. However,for neutral pion production we get K = 0.3 (0.4) in d+Au (p+p) collisions. In agreement withother CGC calculations, we predict a sizable (∼ 0.5) suppression for the nuclear modificationfactor RpPb = (dNpPbh± /dyd2pt)/(dNpph±/dyd2pt)/Ncoll where, following the experimental analysesat RHIC, we have taken Ncoll=3.6.3 Di-hadron azimuthal correlations at forward rapidities in d+Au collisions.Recent measurements of azimuthal forward di-hadron correlations in d+Au collisions by theSTAR Collaboration 15 exhibit the feature of monojet production, i.e., the suppression of theaway-side peak characteristic of approximate back-to-back correlations. Following 16, we calcu-lated the forward double inclusive pion production in d+Au collisions in the CGC framework14. More specifically, we are interested in the coincidence probability, which is the experimentalmeasured quantity. It is given by CP (∆φ) = Npair(∆φ)/Ntrig withNpair(∆φ) =∫yi,|pi⊥|dNdAu→h1h2Xd3p1d3p2, Ntrig =∫y, p⊥dNdAu→hXd3p, (4)and it has the meaning of the probability of, given a trigger hadron h1 in a certain momentumrange, produce an associated hadron h2 in another momentum range and with a differencebetween the azimuthal angles of the two particles equal to ∆φ. Following the experimentalanalysis by the STAR collaboration 15, we set |p1⊥| > 2 GeV, 1 GeV < |p2⊥| < |p1⊥| and2.4 < y1,2 < 4 for the transverse momenta and rapidity of the produced pions. Our results,shifted by an arbitrary offset, are shown in Fig 3, together with the corresponding preliminarydata by the STAR collaboration. The disappearance of the away-side peak around ∆φ ∼ piin d+Au collisions exhibited by data is quantitatively well described by our CGC calculation.In our approach, the angular decorrelation is due to the the momentum broadening inducedby the propagation of the projectile (or its Fock states) through the nucleus. The momentum                                       φ∆0 1 2 3 4 5 6)   φ∆CP(00.0010.0020.0030.0040.0050.0060.0070.008X0pi0pi →dAuT,L<pT,S>2 GeV/c,  1 GeV/c < pT,Lpb=0 fmb=3 fmb=4.4 fmb=5.1 fmFigure 3: Left: CP (∆φ) for forward pions in d+Au collisions (preliminary data by the STAR Coll.) and CGCtheoretical results (blue dots). Right: CP (∆φ) for various collision centralities.broadening, in turn, is related to the saturation scale of the target nucleus, which is large in theforward region. Fig 3 (right) shows the centrality dependence of our calculation. We predictthat the away peak should reappear for more peripheral collisions or, at a fixed rapidity, forlarger momenta of the detected particles.AcknowledgmentsThis work is supported by a Marie Curie Intra-European Fellowship (FP7- PEOPLE-IEF-2008),contract number 236376.References1. F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan. arXiv:1002.0333 [hep-ph].2. I. I. Balitsky. Phys. Rev. D, 75:014001, 2007.3. Y. Kovchegov and H. Weigert. Nucl. Phys. A, 784:188–226, 2007.4. E. Gardi, J. Kuokkanen, K. Rummukainen and H. Weigert, Nucl. Phys. A 784 (2007) 2825. Javier L. Albacete and Yuri V. Kovchegov. Phys. Rev., D75:125021, 2007.6. I. Balitsky, Nucl. Phys. B 463, 99 (1996).7. Y. V. Kovchegov, Phys. Rev. D 60, 034008 (1999).8. Dmitri Kharzeev, Eugene Levin, and Marzia Nardi. Phys. Rev., C71:054903, 2005.9. Javier L. Albacete. Phys. Rev. Lett., 99:262301, 2007.10. Javier L. Albacete, Nestor Armesto, Alex Kovner, Carlos A. Salgado, and Urs AchimWiedemann. Phys. Rev. Lett., 92:082001, 2004.11. Dmitri Kharzeev, Yuri V. Kovchegov, and Kirill Tuchin. Phys. Rev., D68:094013, 2003.12. Javier L. Albacete and Cyrille Marquet. Phys. Lett., B687:174–179, 2010.13. Adrian Dumitru, Arata Hayashigaki, and Jamal Jalilian-Marian. Nucl. Phys., A765:464–482, 2006.14. Javier L. Albacete and Cyrille Marquet. arXiv:1005.4065 [hep-ph].15. Ermes Braidot for the STAR collaboration. arXiv:1005.2378 [hep-ph]. In these proceed-ings.16. Cyrille Marquet. Nucl. Phys., A796:41–60, 2007.17. I. Arsene et al. [BRAHMS Collaboration], Phys. Rev. Lett. 93 (2004) 24230318. J. Adams et al. [STAR Collaboration], Phys. Rev. Lett. 97, 152302 (2006)

CGC phenomenology at RHIC and the LHC

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