We consider a novel mechanism for J/Psi production in nuclear collisions
arising due to the high density of gluons. We calculate the resulting J/Psi
production cross section as a function of rapidity and centrality. We evaluate
the nuclear modification factor and show that the rapidity distribution of the
produced J/Psi's is significantly more narrow in AA collisions due to the gluon
saturation effects. Our results indicate that gluon saturation in the colliding
nuclei is a significant source of J/Psi suppression that can be disentangled
from the quark-gluon plasma effects.Comment: 5 pages, 3 figures; v2: typos corrected; presentation improve

D. Kharzeev

Dmitri Kharzeev

E. M. Levin

Eugene Levin

Kirill Tuchin

Marzia Nardi

English

arXiv

We discuss a novel mechanism for J/ψ production in nuclear collisions arising due to the high density of gluons. We demonstrate that gluon saturation in the colliding nuclei is a dominant source of J/Psi suppression and can explain its experimentally observed rapidity and centrality dependence.NOTICE: This is the author's version of a work that was accepted for publication in Nuclear Physics A. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nuclear Physics A, v.830 (2009): doi: 10.1016/j.nuclphysa.2009.09.025.</p

Kharzeev, Dmitri

Levin, Eugene

Nardi, Marzia

Tuchin, Kirill

Digital Repository @ Iowa State University (ISU)

Gluon saturation effects on J/Psi production in heavy ion collisions

We consider a novel mechanism for J/Psi production in nuclear collisions arising due to the high density of gluons. The resulting J/Psi production cross section is evaluated as a function of rapidity and centrality. We compute the nuclear modification factor and show that the rapidity distribution of the produced J/Psi ’s is significantly more narrow in AA collisions due to the gluon saturation effects. Our results indicate that gluon saturation in the colliding nuclei is a significant source of J/Psi suppression and can explain the experimentally observed rapidity and centrality dependencies of the effect.This article is from Physical Review Letters 102 (2009): 152301, doi: 10.1103/PhysRevLett.102.152301. Posted with permission.</p

Gluon Saturation Effects on J=c Production in Heavy Ion CollisionsDmitri Kharzeev,1 Eugene Levin,2 Marzia Nardi,3 and Kirill Tuchin4,51Department of Physics, Brookhaven National Laboratory, Upton, New York 11973-5000, USA2HEP Department, School of Physics, Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University,Tel Aviv 69978, Israel3Istituto Nazionale di Fisica Nucleare, Sezione di Torino, via P.Giuria 1, I-10125 Torino, Italy4Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA5RIKEN BNL Research Center, Upton, New York 11973-5000, USA(Received 22 August 2008; revised manuscript received 5 November 2008; published 14 April 2009)We consider a novel mechanism for J=c production in nuclear collisions arising due to the high densityof gluons. The resulting J=c production cross section is evaluated as a function of rapidity and centrality.We compute the nuclear modification factor and show that the rapidity distribution of the produced J=c ’sis significantly more narrow in AA collisions due to the gluon saturation effects. Our results indicate thatgluon saturation in the colliding nuclei is a significant source of J=c suppression and can explain theexperimentally observed rapidity and centrality dependencies of the effect.DOI: 10.1103/PhysRevLett.102.152301 PACS numbers: 25.75.qIntroduction.—The mechanism of J=c production inhigh-energy nuclear collisions can be expected to differfrom that in hadron-hadron collisions. Consider first theJ=c production in hadron-hadron collisions. The lead-ing contribution is given by the two-gluon fusion(i) GþG ! J=c þ soft gluon; see Fig. 1(a). This pro-cess is of the order Oð5sÞ. The three-gluon fusion(ii) GþGþG ! J=c [see Fig. 1(b)] is parametricallysuppressed as it is proportional to Oð6sÞ. However, inhadron-nucleus collisions, an additional gluon can be at-tached to the nucleus. This brings in an additional enhance-ment by a factor A1=3. If the collision energy is highenough, the coherence length becomes much larger thanthe size of the interaction region. In this case, all A nu-cleons interact coherently as a quasiclassical field [1–4]. Inthe quasiclassical approximation, 2sA1=3  1. Therefore,the three-gluon fusion is actually enhanced by 1=s ascompared to the two-gluon fusion process. A similar con-clusion holds for heavy-ion collisions (we do not considerany final state processes leading to a possible formation ofthe quark-gluon plasma).In this Letter, we calculate the rapidity and centralitydependence of J=c production in AA collisions taking intoaccount the gluon saturation effects [5,6]. The case of J=cproduction in dAu collisions was considered by two of ussome time ago [7], where exactly the same mechanism wasdiscussed, though the nuclear geometry was oversimpli-fied. We note a reasonable agreement of this earlier ap-proach with the dA data; a more definite conclusion can bereached once the higher statistics data become available inthe near future. Our goal is to understand to what extent thecold nuclear matter effects are responsible for the J=csuppression in AA collisions. In our calculation, we use thedipole model [8] and take into account realistic nucleargeometry. In Ref. [7], detailed arguments were given whichjustify the application of the dipole model to the calcula-tion of J=c production at the Relativistic Heavy IonCollider (RHIC). We argued the following. (i) The coher-ence length for the production of the c c pair is sufficientlylarger than the longitudinal extent of the interaction region.This means that the development of the light-cone ‘‘wavefunction’’ happens a long time before the collision. (ii) Theformation of J=c is characterized by a time scale on theorder of the inverse binding energy. This time is certainlymuch larger than the c c production coherence length (by afactor of 1=2s), implying that the formation processtakes place far away from the nucleus. Therefore, in thefollowing, we concentrate on the dynamics of c c pairinteractions with the nucleus.New mechanism of J=c production.—A particularlyhelpful insight into the nature of the new productionmechanism, depicted in Fig. 1(b), is obtained if we notethat the three-gluon contribution is suppressed as com-pared to the two-gluon fusion mechanism [Fig. 1(a)] byan additional factor r2, where r is c c transverse separationsuch that ð2mcÞ1 & r & ð2mcsÞ1. This factor arisessince we need to have three gluons in the area of the orderof r2. In other words, it means that this reaction is origi-nated from the next-twist contribution. However, in thehadron-nucleus interactions, the next-twist contributionappears always in the dimensionless combination r2Q2swith the saturation scale Qs. The saturation scale is pro-portional to A1=3 which compensates for the smallness of r.The dominance of the higher twist process is the main ideaof Ref. [7], and we develop it in this Letter in the case ofheavy-ion collisions.Figure 1(b) represents the contribution of the orderð2sA1=3Þ2. In general, there must be an odd number ofgluons connected to the charm fermion line because thequantum numbers of J=c and of gluon are 1. Therefore,each inelastic interaction of the c c pair must involve twonucleons and hence is of the order ð2sA1=3Þ2n, wherePRL 102, 152301 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending17 APRIL 20090031-9007=09=102(15)=152301(4) 152301-1  2009 The American Physical Societyn ¼ 1; 2; . . . ; A=2 is the number of nucleon pairs. To take this into account, we write the cross section as the sum over allinelastic processes (labeled by the index n). This sum involves only an even number of interactions. For a heavy nucleusA  1, we havedinðpAÞdYd2b¼ CFx1Gðx1; m2cÞZ 2RA0̂inðx2; r; r0Þdz0Zd2rc Gðl1; r; z ¼ 1=2Þc VðrÞ Zd2r0c Gðl1; r0; z ¼ 1=2Þ c Vðr0Þe½ðx2;r2Þþðx2;r02Þ2RAX1n¼0Z 2RAz0dz1Z 2RAz1dz2 . . .Z 2RAz2ndz2nþ12nþ1̂2nþ1in ðx2; r; r0Þ; (1)where c G  c V is the projection of the J=c light-cone wave function onto the virtual gluon one [7,9], zi’s are the nucleonlongitudinal coordinates in the nucleus, and̂ inðx2; r; r0Þ  ðx2; r2Þ þ ðx2; r02Þ  ½x2; ðr r0Þ2: (2)After integration over zi’s and summation over n, we obtain the following formula:dinðpAÞdYd2b¼ CFx1Gðx1; m2cÞZd2rc Gðl1; r; z ¼ 1=2Þc VðrÞ Zd2r0c Gðl1; r0; z ¼ 1=2Þc Vðr0Þ 12ð expf½x2; ðr r0Þ22RAg þ expf½ðx2; rÞ þ ðx2; r0Þþ ̂inðx2; r; r0Þ2RAg  2 expf½ðx2; rÞ þ ðx2; r0Þ2RAgÞ: (3)The color factor in (1) and (3) is calculated in the Nc  1limit.In the quasiclassical approximation, the gluon saturationis given by [8] Q2s;AðxÞ ¼ 422sTðbÞ, where  is thenucleon density in a nucleus, Nc is the number of colors,b is the impact parameter, and TðbÞ is the optical width ofthe nucleus. Qs;A determines the scale of the typical trans-verse momenta for inclusive gluon production [10]. Itsvalue was extracted from the fit of the multiplicities ofnuclear reactions at the RHIC [11,12] and from fits of theF2 structure function in deep inelastic scattering [13–16].To generalize (3) to the case of AA collisions, we use theapproach suggested by Kovchegov [17] and replace thelowest order gluon field correlation function by the full MVformula as follows:s23x1Gðx1; m2cÞ ! d2br21 exp r2Q2s;A18: (4)Furthermore, noting that the dominant contribution to theintegral over r0 in (3) comes from the region r  r0 [7], weobtain1SAdðAAÞdYd2b/Q2s;A1ðx1ÞQ2s;A2ðx2Þ½Q2s;A1ðx1ÞþQ2s;A2ðx2ÞZ 10d9K2ðÞe½2=ð8m2cÞ½Q2s;A1 ðx1ÞþQ2s;A2ðx2Þ:(5)Equation (5) is derived in the quasiclassical approximationwhich takes into account multiple scattering of the c c pairin the cold nuclear medium. At forward rapidities at theRHIC and at the LHC, the gluon distribution functions (4)evolve according to the evolution equations of the colorglass condensate. Inclusion of this evolution in the case ofJ=c production presents a formidable technical challenge.Therefore we adopt a phenomenological approach ofRef. [12] in which the quantum evolution is encoded inthe energy or rapidity dependence of the saturation scales.FIG. 1. The process of inclusive J=c production in hadron-hadron (a) and in hadron-nucleus collisions (b).PRL 102, 152301 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending17 APRIL 2009152301-2In our numerical calculations, we take explicit accountof the impact parameter dependence of the saturationscales of each nucleus. We employ the Glauber approxi-mation and assume that the nucleons are small compared tothe size of the nuclei. The number of J=c ’s inclusivelyproduced in ion-ion collisions at given rapidity Y andcentrality characterized by b readsdNAAðY; bÞdY¼ CdNppðYÞdYZd2sTA1ðsÞTA2ðb sÞ ½Q2s;A1ðx1; sÞ þQ2s;A2ðx2; b sÞ1m2cZ 10d9K2ðÞ exp 28m2c½Q2s;A1ðx1; sÞþQ2s;A2ðx2; b sÞ; (6)where x1=2 ¼ ðmJ=c ;t=ffiffisp ÞeY , with m2J=c ;t ¼ m2J=c þ p2t ,pt being the transverse momentum J=c . The overall nor-malization constant C includes the color and the geometricfactors C2F=ð42sSpÞ, where Sp is the interaction area inproton-proton collisions. C also includes the amplitude ofquark-antiquark annihilation into J=c and a soft gluon inthe case of pp collisions. This amplitude as well as themechanism of Fig. 1(a) have a significant theoretical un-certainty. Therefore, we decided to parameterize thesecontributions by an overall normalization constant in (6).The rapidity distribution of J=c ’s in pp collisions, thefactor dNpp=dY appearing in Eq. (6), is fitted to theexperimental data given in Ref. [18] with a singleGaussian. In Fig. 2(a), the results provided by Eq. (6) arethen compared to the experimental data from the PHENIXCollaboration [19] for Au-Au collisions atffiffisp ¼ 200 GeV.The global normalization factorC is found from the overallfit. There are no other free parameters. The agreement ofthe theoretical results with experimental data is reasonable.It is evident that the effect of the gluon saturation on theJ=c rapidity distribution in nucleus-nucleus collisions isto make its width a decreasing function of centrality. Thedistribution in the most central bin is significantly morenarrow than in the peripheral bin.It is important that we describe well the data in thesemiperipheral region. This ensures that our model givesa good description of the J=c production in dAu colli-sions.We also note that an earlier approach [7] in which thesame model was employed (albeit with an oversimplifiednuclear geometry) provided a reasonable description of thedata. Still a more detailed investigation is required whichtakes into account the exact deuteron and gold nucleardistributions. This will allow a model-independent fixingof the overall normalization constant C. Such an analysiswill be presented in the near future.Previously, the initial-state effects on the nuclear sup-pression of J=c ’s have been estimated [20,21] through theproduct of nuclear modification factors measured in dAucollisions. This estimate holds as long as the collinearfactorization holds for the process of J=c production(this would be true, for example, in the limit of smallcc-bar dipole size). Here we find that the effects beyondthe collinear factorization are strong and may account for alarge part of the suppression measured in Au-Au, espe-cially at forward rapidities (where the density of gluons inthe initial state, inside one of the colliding nuclei, is thelargest).To emphasize the nuclear dependence of the inclusivecross sections, it is convenient to introduce the nuclearmodification factorRAAðy; NpartÞ ¼dNAAdyNcolldNppdy: (7)It is normalized in such a way that no nuclear effect wouldcorrespond to RAA ¼ 1. In Fig. 2(b), we plot the result of050100150200250300350-6 -4 -2 0 2 4 6dN/dy x 10^6y0-20%20-40%40-60%60-92%00.20.40.60.811.21.40 50 100 150 200 250 300 350 400RAANparty=0y=1.7(b)(a)FIG. 2. (a) J=c rapidity distribution in Au-Au collisions for different centrality cuts. (b) Nuclear modification factor for J=cproduction in heavy-ion collisions for different rapidities. Experimental data from Ref. [19].PRL 102, 152301 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending17 APRIL 2009152301-3our calculation. The nuclear modification factor exhibitsthe following two important features: (i) Unlike the opencharm production, J=c is suppressed even at y ¼ 0;(ii) cold nuclear matter effects account for a significantpart of the ‘‘anomalous’’ J=c suppression in heavy-ioncollisions at both y ¼ 0 and y ¼ 2.Conclusions.—The main results of this Letter are exhib-ited in Fig. 2. It is seen that the rapidity and centralitydependence of J=c production are reproduced with areasonable accuracy even without taking into account anyhot nuclear medium effects. This observation allows us toconclude that a fair amount (and perhaps most) of the J=csuppression in high-energy heavy-ion collisions arisesfrom the cold nuclear matter effects. In other words, J=cis expected to be strongly suppressed even if there were nohot nuclear matter effect produced. In this sense, we cantalk about the separation of the cold and hot nuclearmedium effects as advertised in the introduction.A certain fraction of J=c suppression in the forwarddirection can be attributed to suppression of the constituentc and c quarks [22–25] which would lead to suppression ofDmesons [26]. However,Dmesons are not predicted to besuppressed at central rapidities [26].The reason for J=c suppression at midrapidities is thatthe multiple scattering of c c in the cold nuclear mediumincreases the relative momentum between the quark andantiquark, which makes the bound state formation lessprobable. It was proven in Ref. [27] that, unless quantumlogð1=xÞ corrections become important, the inclusive gluonproduction satisfies the sum rule that requires the nuclearmodification factor to be of order unity. A similar sum ruleholds for heavy quark production but fails in the case of abound states, such as J=c .We realize that, although our calculation gives the para-metrically leading result at high gluon density, other pro-duction channels involving the gluon radiation in the finalstate and the color octet mechanism of J=c productionmay give phenomenologically significant contributions.These are likely to become the leading mechanisms inthe peripheral collisions where the strength of the gluonfields is significantly diminished. However, we believe thatour main results are robust for central high-energy colli-sions of heavy ions. These results imply that the observedJ=c suppression is a result of an interplay between thecold and hot nuclear matter effects.The work of D.K. was supported by the U.S.Department of Energy under Contract No. DE-AC02-98CH10886. K. T. was supported in part by the U.S.Department of Energy under Grant No. DE-FG02-87ER40371; he thanks RIKEN, BNL, and the U.S.Department of Energy (Contract No. DE-AC02-98CH10886) for providing facilities essential for the com-pletion of this work. This research of E. L. was supportedin part by a grant from Ministry of Science, Culture &Sport, Israel and the Russian Foundation for BasicResearch of the Russian Federation and by BSF GrantNo. 20004019.[1] L. D. McLerran and R. Venugopalan, Phys. Rev. D 49,2233 (1994); 49, 3352 (1994).[2] J. Jalilian-Marian, A. Kovner, A. Leonidov, and H.Weigert, Phys. Rev. D 59, 014014 (1998); Nucl. Phys.B504, 415 (1997); E. Iancu, A. Leonidov, and L.D.McLerran, Phys. Lett. B 510, 133 (2001); Nucl. Phys.A692, 583 (2001).[3] Y. V. Kovchegov, Phys. Rev. D 60, 034008 (1999).[4] Y. V. Kovchegov, Phys. Rev. D 54, 5463 (1996).[5] L. V. Gribov, E.M. Levin, and M.G. Ryskin, Phys. Rep.100, 1 (1983).[6] A. H. Mueller and J. Qiu, Nucl. Phys. B268, 427 (1986).[7] D. Kharzeev and K. Tuchin, Nucl. Phys. A770, 40 (2006).[8] A. H. Mueller, Nucl. Phys. B335, 115 (1990); B415, 373(1994).[9] E.M. Levin and M.G. Ryskin, Yad. Fiz. 45, 234 (1987)[Sov. J. Nucl. Phys. 45, 150 (1987)]; E. Gotsman, E.Levin, and U. Maor, Nucl. Phys. B464, 251 (1996).[10] Y. V. Kovchegov and K. Tuchin, Phys. Rev. D 65, 074026(2002).[11] D. Kharzeev and M. Nardi, Phys. Lett. B 507, 121 (2001);D. Kharzeev and E. Levin, Phys. Lett. B 523, 79 (2001).[12] D. Kharzeev, E. Levin, and M. Nardi, arXiv:0707.0811;Nucl. Phys. A747, 609 (2005); A730, 448 (2004); A743,329(E) (2004); Phys. Rev. C 71, 054903 (2005).[13] K. J. Golec-Biernat and M. Wusthoff, Phys. Rev. D 59,014017 (1998); 60, 114023 (1999).[14] E. Gotsman et al., J. Phys. G 27, 2297 (2001).[15] H. Kowalski and D. Teaney, Phys. Rev. D 68, 114005(2003).[16] J. Bartels, K. J. Golec-Biernat, and H. Kowalski, Phys.Rev. D 66, 014001 (2002).[17] Y. V. Kovchegov, Nucl. Phys. A692, 557 (2001).[18] A. Adare et al. (PHENIX Collaboration), Phys. Rev. Lett.98, 232002 (2007).[19] A. Adare et al. (PHENIX Collaboration), Phys. Rev. Lett.98, 232301 (2007).[20] F. Karsch, D. Kharzeev, and H. Satz, Phys. Lett. B 637, 75(2006).[21] R. Granier de Cassagnac, J. Phys. G 34, S955 (2007).[22] K. Tuchin, Phys. Lett. B 593, 66 (2004).[23] Y. V. Kovchegov and K. Tuchin, Phys. Rev. D 74, 054014(2006).[24] F. Gelis and R. Venugopalan, Phys. Rev. D 69, 014019(2004).[25] J. P. Blaizot, F. Gelis, and R. Venugopalan, Nucl. Phys.A743, 57 (2004).[26] K. Tuchin, Nucl. Phys. A798, 61 (2008).[27] D. Kharzeev, Y. V. Kovchegov, and K. Tuchin, Phys.Rev. D 68, 094013 (2003).PRL 102, 152301 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending17 APRIL 2009152301-4

Gluon Saturation Effects on J/Psi Production in Heavy Ion Collisions

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Gluon saturation effects on J/Psi production in heavy ion collisions

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