proton-proton and proton-nucleus collisions along with some perspectives. After reviewing recent experimental andtheoretical results on quarkonium production in pp and pA collisions, we discuss the emerging field of polarisationstudies. Afterwards, we report on issues related to heavy-quark production, both in pp and pA collisions, comple-mented by AA collisions. To put the work in broader perpectives, we emphasize the need for new observables toinvestigate the quarkonium production mechanisms and reiterate the qualities that make quarkonia a unique tool formany investigations in particle and nuclear physics.

Keywords: Quarkonium, production, proton, nucleus

Contents

1 Introduction

2 Quarkonium production in pp collisions

2.1 Current progress: Tevatron and RHIC .

4

2.2 First LHC results . . . . . . . . . . . .

5

2.3 What’s next ? . . . . . . . . . . . . . .

6

3 Quarkonium production in pA collisions

3.1 Basic phenomena and observables . . .3.2 Existing measurements and future per-

spectives . . . . . . . . . . . . . . . . . 1

4 Polarisation and feed-down in quarkonium

production 1

4.1 Frames and polarizations . . . . . . . . 14.2 Charmonium polarization . . . . . . . . 14.3 Bottomonium polarization . . . . . . . 14.4 Polarization in photoproduction and at

RHIC . . . . . . . . . . . . . . . . . .4.5 Perspectives on polarization studies . .

5 Open heavy-flavor production in pp and pAcollisions

5.1 Open heavy-flavor production at RHICand FONLL calculations . . . . . . . . 2

20

2

7

67

8

2020

4

9

87

9

Quarkonium production in high energyproton-proton and proton-nucleus collisions

Z. Conesa del Vallea,b, G. Corcellac, F. Fleuretd, E.G. Ferreiroe, V. Kartvelishvilif, B. Kopeliovichg,J.P. Lansbergh, C. Lourencob, G. Martinezi, V. Papadimitriouj, H. Satzk, E. Scomparinl, T. Ullrichm,

O. Teryaevn, R. Vogto,p, J.X. Wangq

aInstitut Pluridisciplinaire Hubert Curien (IPHC), Universite de Strasbourg, CNRS-IN2P3, Strasbourg, FrancebEuropean Organization for Nuclear Research (CERN), Geneva, Switzerland

cINFN, Laboratori Nazionali di Frascati, Via E.Fermi 40, I-00044, Frascati, ItalydLLR, Ecole polytechnique, CNRS/IN2P3, Palaiseau, France

eDepartamento de Fısica de Partıculas and IGFAE, Universidad de Santiago de Compostela, Santiago de Compostela, SpainfLancaster University, Lancaster LA1 4YB,United Kingdom

gDepartamento de Fısica Universidad Tecnica Federico Santa Marıa, Instituto de Estudios Avanzados en Ciencias e Ingenierıa and CentroCientıfico-Tecnologico de Valparaıso, Casilla 110-V, Valparaıso, ChilehIPNO, Universite Paris-Sud 11, CNRS/IN2P3, F-91406 Orsay, France

iSUBATECH, Ecole des Mines de Nantes, Universite de Nantes, CNRS-IN2P3, Nantes, FrancejFermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois, 60510, U.S.A

kFakultat fur Physik, Universitat Bielefeld, GermanylINFN Torino, Via P. Giuria 1, Torino, I-10125, Italy

mBrookhaven National Laboratory, Upton, New York 11973, USAnBogoliubov Laboratory of Theoretical Physics, JINR, Dubna 141980, Russia

oPhysics Divsion, Lawrence Livermore National Laboratory, Livermore, CA 94551pPhysics Department, University of California at Davis, Davis, CA 95616

qInstitute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918(4), Beijing, 100049, China

Abstract

We present a brief overview of the most relevant current issues related to quarkonium production in high energy

Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36

0920-5632/$ – see front matter © 2011 Elsevier B.V. All rights reserved.

www.elsevier.com/locate/npbps

doi:10.1016/j.nuclphysbps.2011.03.053

5.2 Properties of gluon radiation off heavyquarks . . . . . . . . . . . . . . . . . . 2

5.3 Heavy quarks and energy loss in densematter . . . . . . . . . . . . . . . . . . 2

5.4 Heavy quark plus photon production asa probe of the heavy quark PDF . . . . 2

6 Quarkonia as a Tool 25

6.1 Proton-Proton Collision Studies . . . . 25

3

6.2 Nuclear Collision Studies . . . . . . . . 26

4

7 New observables in quarkonium production 29

7.1 Hadronic activity around quarkonium .7.2 Associated production . . . . . . . . .

8 Conclusion

1. Introduction

The attention devoted to heavy quarkonium statesstarted with the discovery of the J/ψ charmonium me-son in 1974 followed by the Υ bottomonium mesonin 1977. From the theoretical point of view, quarko-nium bound states offer a solid ground to probe Quan-tum Chromodynamics (QCD), due to the high scale pro-vided by the large mass of the heavy quarks.

The application of perturbative techniques togetherwith the factorization principle gave birth to the Color-Singlet Model. Since then, the appearance of puzzlingmeasurements has never stopped and has led to newchallenges for theorists. These puzzles required the in-troduction of new ideas providing new probes for theunderstanding of QCD. Fifteen years ago, the observa-tion of an excess in charmonium production reported bythe CDF Collaboration, by orders of magnitude over thetheoretical predictions available at that time, gave rise tothe theory of Non-Relativistic QCD.

Data collected at the Tevatron, at HERA, and at lowenergy e+e− colliders has never ceased to challengethe existing theoretical models: the apparent violationof universality arising when comparing data from thehadron-hadron and the lepton-hadron colliders, the dis-agreement between the predictions for the polarizationof the J/ψ produced in hadronic collisions and the cur-rent data, as well as the excess of double charmoniumproduction first observed by Belle. The solution to thesepuzzles requires new theoretical developments on theunderlying production mechanism(s), as the computa-tion of higher-order corrections for characteristic pro-cesses and the study of new production processes, inaddition to investigations of new observables not ana-lyzed so far.

The interest in this field and its developments are notlimited to the issue of the production mechanisms. Theprogress in lattice calculations and effective field theo-ries have converted quarkonium physics into a power-ful tool to measure the mass of the heavy quarks andthe strength of the QCD coupling. The properties ofproduction and absorption of quarkonium in a nuclearmedium provide quantitative inputs for the study ofQCD at high density and temperature. In fact, charmo-nium production off nuclei is one of the most promisingprobes for studying properties of matter created in ul-trarelativistic heavy-ion collisions. Since quarkonium isheavy, it can be used as a probe of the properties of themedium created in these collisions, such as the intensityof interactions and possible thermalization.

Lattice QCD calculations predict that, at sufficientlylarge energy densities, hadronic matter undergoes aphase transition to a plasma of deconfined quarks andgluons. Since 1986, substantial efforts have been ded-icated to the research of high-energy heavy-ion colli-sions in order to reveal the existence of this phase tran-sition and to analyze the properties of strongly interact-ing matter in the new phase. The study of quarkoniumproduction and suppression is among the most interest-ing investigations in this field since calculations indi-cate that the QCD binding potential is screened in theQGP phase. The level of screening increases with theenergy density/temperature of the system. Given the ex-istence of several quarkonium states, each of them withdifferent binding energies, it is expected that they willsequentially melt into open charm or bottom mesonsabove succesive energy density thresholds. Moreover,the SPS and RHIC data on charmonium physics havebrought to light further interesting results, among thempuzzling features in proton-nucleus data, which high-lighted new aspects of charmonium physics in nuclearreactions, namely the role of cold nuclear matter effects.

The startup of the LHC and the opening of the newenergy frontier will offer new and challenging possibil-ities for the study of quarkonia.

All the above reasons have motivated the organizationof the Quarkonium 2010 workshop held at the EcolePolytechnique (Palaiseau, France) from July 29 to July31, 2010. This workshop, gathering both experimen-talists and theorists, was devoted to finding answers tothe numerous quarkonium-hadroproduction puzzles atthe dawn of the LHC era and the concurrent apogee ofthe Tevatron and RHIC. Introductory and review talksfocusing upon recent theoretical and experimental re-sults were presented, in addition to six topical WorkingGroup (WG) discussion sessions, each one devoted to aspecific issue:

4

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Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–364

• WG1: Quarkonium production in pp

• WG2: Quarkonium production in pA

• WG3: Polarisation and Feeddown

• WG4: Open Heavy Flavour (vs hidden)

• WG5: Quarkonium (production) as a tool

• WG6: New Observables in Quarkonium produc-tion

We present here a comprehensive review addressingall these matters. The following sections summarize theworking group discussions, together with the achievedconclusions. In section 8 we prioritize directions forongoing and future developments.

2. Quarkonium production in pp collisions

Among the wealth of quarkonium production mea-surements, the first CDF analyses of direct J/ψ andψ(2S ) production1 at

√s = 1.8 TeV [1, 2] are likely

the most important to date. They revealed that the mea-sured rates were more than an order of magnitude largerthan leading order (LO), color-singlet model (CSM) cal-culations [3], believed at that time – the mid 1990’s–to be the most straightforward application of perturba-tive QCD to quarkonium production. Both these dis-crepancies motivated a number of theoretical investiga-tions on quarkonium hadroproduction, including withinthe NRQCD factorization framework [4]. In the latterapproach, quarkonium production can also proceed viacreation of color-octet QQ pairs, present in higher-Fockstates, whose effects are believed to be suppressed bypowers of the relative QQ velocity, v.

Despite advances, there is still no clear picture of thequarkonium hadroproduction mechanisms. Such mech-anisms would have to explain both the cross section andpolarization measurements at the Tevatron [1, 2, 5, 6, 7,8, 9] and at RHIC [10, 11, 12, 13, 14, 15]. Obviously,the mechanisms involved in hadroproduction shouldalso comply with the constraints from photo/electro-production (see [16] and references therein) and pro-duction in e+e− annihiliation (see [17] and referencestherein). Here we discuss the hadroproduction crosssection only and leave the discussion of polarization

1“Prompt production” excludes quarkonium production fromweak decays of more massive states, such as the B meson. “Directproduction” further excludes quarkonium production from feeddown,via the electromagnetic and strong interactions, from more massivestates, such as higher-mass quarkonium states.

to Working Group 3 (Sec. 4). We only note thatthe NRQCD approach, based on the dominance of thecolor-octet transition, so far fails to provide a consistentdescription of production and polarization as well as in-clusive production in e+e− annihiliation. This failuremay be because the charmonium system is too light forrelativistic effects to be small and thus the velocity ex-pansion [4] may have been truncated at too low an order.If the convergence of the velocity expansion of NRQCDis the issue, then one would expect better agreement be-tween theory and data for theΥ. This could explain whyonly color-singlet contributions [18] (LO in v) appear tobe in better agreement with Υ [19, 20, 21, 22] than ψproduction [9].

At collider energies, quarkonium production occurspredominantly through gg channels. Higher order αS

corrections to the S states have only recently been cal-culated [23, 24, 25, 26, 27]. The results show that thetotal cross sections do not increase much when thesecorrections [24, 28] are included so that the perturba-tive series seems to converge, except perhaps at large√

s where initial-state radiation effect may need to beresummed [29]. However, the color-singlet correctionsat high pT are very large because the QCD correctionsto the CSM open new production channels important athigh pT . Similar behavior has also been seen in photo-production [30].

At LO (α2s), the cross section differential in p2

T scalesas p−8

T while several different diagrams which contributeat NLO decrease as p−6

T or p−4T . At NLO in color-octet

production, the higher-order corrections to S state pro-duction do not substantially harden the pT distributions.The LO color octet channel, gluon fragmentation, al-ready scales with the smallest possible power of pT ,p−4

T . However, there are substantial fragmentation con-tributions to 1S 0 production which enhance high pT pro-duction of these states. At NNLO (α5

s), important newchannels also appear. Color singlet gluon fragmenta-tion is relevant in the limit pT � m. Conversely, theexchange of two gluons in the t-channel in the high en-ergy limit s � s where s/s is the square of the four-momentum of the colliding hadrons/partons has beenstudied in the kT -factorization approach. In either limit,the expansion can be reorganized to simplify the eval-uation of the dominant contribution. Away from thisregime, corrections to each of these approaches may beimportant. Instead of calculating the full NNLO con-tributions to the CSM, NNLO� calculations consideronly real gluon emission at NNLO and control the di-vergences using a cutoff. This method has large uncer-tainties arising from the sensitivity to the cutoff and therenormalization scale [18]. We briefly summarize re-

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 5

cent developments here. For a more complete discus-sion, see Refs. [31, 32].

2.1. Current progress: Tevatron and RHICThe contributions of the NLO color-singlet correc-

tions reduce the discrepancy between the inclusive CSMcross sections and the CDF Υ data [9]. However, theNLO rate still falls too steeply at high pT to describethis region successfully. The NNLO� contribution maybe able to fill the gap between calculations and data athigh pT . While the large theoretical uncertainties do notplace strong constraints on the color-octet contribution,the data no longer require them [32].

Higher-order color singlet contributions to J/ψ andψ(2S ) production have also been calculated. The calcu-lation is simpler for the ψ(2S ) because there is no feed-down from higher charmonium states. CDF extracteddirect ψ(2S ) production [9]. The rates were compared tothe CSM calculations. While the higher order CSM cor-rections significantly reduce the discrepancy betweenthe calculation and the Tevatron data, they are insuffi-cient to remove it entirely. At intermediate pT , the up-per limit of the NNLO� calculation is in agreement withthe data while, for pT > 10 GeV, there is a gap betweenthe calculations and the data. The same is true for theJ/ψ [32].

NLO corrections to 1S 0 and 3S 1 color octet J/ψ [27]and Υ [33] production have been calculated. In bothcases, these corrections are small for pT < 20 GeV. Val-ues of the NRQCD 〈OJ/ψ(3S [8]

1)〉 and 〈OJ/ψ(1S [8]

0)〉 ma-

trix elements were obtained by fitting the prompt pro-duction rate measured by CDF [7] and were found to becompatible with those extracted at LO [27]. Feeddownwas ignored and the P state color octet contribution setto zero. Since a satisfactory fit could not be obtainedfor pT < 6 GeV, these points were not included in thefit. Note that NRQCD factorization may break down atlow pT so that resummation effects may be necessary todescribe the data in this region.

Two papers [34, 35] recently appeared with completecalculations of NLO αs color-octet production throughorder v4 for the 3S 1, 1S 0, and 3PJ channels. Althoughthe two calculations agree at the level of partonic crosssection, the values of the NRQCD matrix elements ex-tracted from the two different fitting procedures are in-consistent. In any case, all these computations fail tocomply with the constraint obtained in [36] by assum-ing that the e+e− → J/ψ + Xnon−cc rate measured byBelle [37] comes only from the color-octet processes:

〈0|OJ/ψ[1S (8)0 ]|0〉 + 4.0 〈0|OJ/ψ[3P(8)

0 ]|0〉/m2c

≤ (2.0 ± 0.6) × 10−2 GeV3(1)

at NLO in αs. If one keeps in mind that the color-singletcontribution –assumed to be zero in the equation above–saturates the experimental measurement by Belle, it isclear that this upper bound is in fact quite conservative,even though this measurement may be affected by the 4charged track requirement. The violation of this boundby these recent NLO analyses, where color-octets dom-inate, should be taken rather seriously, especially be-cause e+e− annihilation may be a cleaner probe of theinclusive charmonium production mechanisms.

On top of its earlier J/ψ analyses, PHENIX hasshown preliminary measurements of the pT dependenceof the ψ(2S ) cross section at 200 GeV [14]. This isthe first measurement of the pT dependence of an ex-cited charmonium state at RHIC. PHENIX measuredthe feeddown contribution of the ψ(2S ) to the J/ψ to be8.6 ± 2.3%, in good agreement with the world average.

STAR has recently published [13] measurements ofthe J/ψ cross section in 200 GeV pp collisions for5 < pT < 13 GeV/c. This greatly extends the pT rangeover which J/ψ data are available at RHIC. AlthoughPHENIX can trigger at all pT , it has so far been limitedto pT below about 9 GeV/c [14] because of its muchsmaller acceptance.

STAR has also recently presented a measurement ofthe fraction of J/ψ produced from B decays [13]. Theresults appear to be consistent with the CDF measure-ment at an order of magnitude higher energy.

Unfortunately, little is known about J/ψ feed downfrom higher charmonium resonances such as the χc atRHIC. These may significantly contribute to the yieldof J/ψ mesons observed by PHENIX and STAR. Forinstance, it is likely that the fraction of J/ψ from χc

should be independent of pT , y and√

s. This may berelevant for the interpretation of the high pT STAR data[13] which favor NRQCD over CSM production in cal-culations with NRQCD at LO [38] and CSM contribu-tions up to NNLO� (see [18]). Both these calculationsdo not include feeddown. At lower pT , PHENIX J/ψdata [14, 15] agrees with LO NRQCD including feed-down [39]. However, in the latter case, the low pT val-ues may call the validity of the perturbative calculationinto question, especially since the LO NRQCD spec-trum diverges as pT → 0. Recently, NLO correctionsto the CSM were evaluated as well and were shown toclose the gap between the LO CSM and the PHENIXdata at pT = 1 − 2 GeV. When the NNLO� contribu-tion is included at pT > 5 GeV, the upper limit agreeswith data [40]. We note here that the NLO CSM donot show any divergences at low pT . However, resum-mation of initial state radiation may further improve theagreement with PHENIX data.

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–366

2.2. First LHC results

The first LHC pp run, at 7 TeV, has already producedsuperior quality data after a short time. The CMS [41],ATLAS [42], ALICE [43] and LHCb [44] experimentsreported inclusive J/ψ pT distributions from integratedluminosities of 100 nb−1, 9.5 nb−1, 11.6 nb−1 and 14.2nb−1, respectively. Before ALICE differential cross sec-tions at mid-rapidity are available2, no low pT datawill be available at mid-rapidity, see Fig. 1. ATLASand CMS experiments are equipped with large mag-netic fields, so their single muon pT thresholds are toohigh for reconstruction of low pT J/ψ’s. However, thedata taken at pT > 4 GeV/c are consistent with eachother even though the rapidity ranges differ slightly.The CMS rapidity bin, |y| < 1.4, overlaps the twomidrapidity ranges reported by ATLAS, |y| < 0.75 and0.75 < |y| < 1.5.

[GeV/c]ψJ/

Tp

0 2 4 6 8 10 12 14 16

[n

b / G

eV

/c]

T / d

yd

pσ

d×

) μ

μ →

ψB

R(J

/

-110

1

10

210

= 7 TeVsLHC

Preliminary

ψInclusive J/

|y| < 1.4-1CMS 100 nb

0.75 < |y| < 1.5-1ATLAS 9.5 nb

|y| < 0.75-1ATLAS 9.5 nb

Figure 1: The preliminary mid rapidity inclusive J/ψ pT distributionsmeasured by CMS (|y| < 1.4) and ATLAS (|y| < 0.75 and 0.75 < |y| <1.5). Data compilation courtesy of H. Wohri.

At more forward rapidities, the single muon pT fromJ/ψ decay is high enough for J/ψ reconstruction atpT → 0. A compilation of the forward J/ψ data isshown in Fig. 2. The CMS and ATLAS data, takenin similar rapidity intervals of 1.4 < |y| < 2.4 and1.5 < |y| < 2.25 respectively, agree rather well forpT > 3 GeV/c. They seem to differ somewhat at lowerpT , but the difference is not statistically significant. Themore forward LHCb and ALICE data agree quite well

2 ALICE has released the inclusive differential pT cross sectionsat large-rapidity, but only the invariant yields are available at mid-rapidity at the time of this writeup.

Figure 2: The preliminary forward rapidity inclusive J/ψ pT distribu-tions measured by CMS (1.4 < |y| < 2.4), ATLAS (1.5 < |y| < 2.25),LHCb (2.5 < y < 4.0) and ALICE (2.5 < y < 4.0). Data compilationcourtesy of E. Scomparin and H. Wohri.

with the shape of the somewhat more central rapidityCMS and ATLAS data.

The data shown in Figs. 1 and 2 are for inclusive J/ψproduction which includes feeddown from the χc andψ(2S ) states and semileptonic B meson decays. Thefraction of J/ψ resulting from B meson decays,

B fraction ≡ B → J/ψ Xany inclusive J/ψ

(2)

is compiled in Fig. 3. The preliminary LHC results at√s = 7 TeV are compared with the high statistics CDF

midrapidity data [7] at√

s = 1.96 TeV. The result seemsto be remarkably independent of both center-of-massenergy and rapidity. The lower statistics and lower pT

STAR data also agree with the magnitude of the higherenergy data shown in Fig. 3.

Although the level of the B meson contribution to J/ψproduction seems to be remarkably independent of

√s,

the average p2T of the measured inclusive J/ψ’s has been

seen to increase with√

s. The value of both 〈pT 〉 and〈p2

T 〉 increases approximately linearly with ln√

s from√s ∼ 17 GeV to 200 GeV. The preliminary ALICE mea-

surement reported here [45], seems to follow this trend.The dependence of 〈p2

T 〉 with√

s is shown in Fig. 4.Note that the fixed-target results are centered aroundmidrapidity while two rapidity ranges, |y| < 0.35 and1.2 < |y| < 2.2, measured at RHIC, suggest that the av-erage p2

T is higher at midrapidity than forward rapidity,not a surprising result. The ALICE measurement, usingthe muon spectrometer, is also at forward rapidity.

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 7

[GeV/c]ψJ/

Tp

0 2 4 6 8 10 12 14 16 18

fro

m B

-ha

dro

ns

ψfr

ac

tio

n o

f J

/

0

0.1

0.2

0.3

0.4

0.5

= 7 TeVsLHC

Preliminary

1.4 < |y| < 2.4-1CMS 100 nb

|y| < 1.4-1CMS 100 nb

2.5 < y < 4.0-1LHCb 14.2 nb

|y| < 2.25-1ATLAS 17.5 nb

PRD 71 (2005) 032001

= 1.96 TeV |y| < 0.6sCDF

Figure 3: The preliminary fraction of non-prompt J/ψ as a functionof pT measured by CMS (|y| < 1.4 & 1.4 < |y| < 2.4), ATLAS (|y| <2.25) and LHCb (2.5 < y < 4). Data compilation courtesy of H.Wohri.

Figure 4: The preliminary measurement of 〈p2T 〉 from ALICE com-

pared with lower energy data [45].

We note that comparisons of these data with modelcalculations using standard DGLAP evolution for thegluon distribution with perturbative QCD agree ratherwell (see Fig. 5 for a comparison with the CSM) sug-gesting that, even at rather forward rapidity, in a regionof x and Q2 where the parton densities are not wellmeasured, no alternative factorization schemes involv-ing e.g. saturation effects, are required.

Finally, CMS also reported a preliminary Υ(1S ) mea-surement based on 678 ± 38 events. The Υ(1S ), Υ(2S )

10

100

1000

0 1 2 3 4 5 6

dσ

J/ψ

direct /

dy x

Br

(nb)

y

FJ/ψdirect

= 59±10 %

LO gg CSMPrelim. ALICEPrelim. ATLASPrelim. LHC-b

CMS

Figure 5: Comparison between the LO CSM prediction fordσdirect

J/ψ /dy × Br from gg fusion LO contributions in pp collisionsat√

s = 7 TeV compared to ALICE [46], ATLAS [47], CMS [48]and LHCb [49] results multiplied by the direct fraction (and correct-ing for the non-prompt component, assumed to be 10%, if applicable).Adapted from [29].

and Υ(3S ) peaks are clearly separated in the data.

2.3. What’s next ?

The LHC quarkonium data shown here is just the tipof the iceberg. More data will be forthcoming in thenext runs. Presumably direct J/ψ and Υ(1S ) productionwill also be measurable, i.e. the feeddown contributionswill be distinguished and separated.

On the other hand, after September 2011, the Teva-tron will unfortunately be shut down. There are 8.5 fb−1

of data from Run II on tape with ∼ 10 fb−1 expectedby the end of the run. This should be enough data tomeasure the J/ψ and ψ(2S ) up to pT > 30 GeV/c. Thethree Υ S states will also be measured with relativelyhigh precision. Not only should the final Tevatron mea-surements include the feeddown of χc to J/ψ and χb toΥ, it is expected that the χc and χb P states with largebranching ratios to the S states can be separated fromeach other using photon conversions. Even though RunII will come to an end, the data will continue to be an-alyzed for some time with more exciting results forth-coming.

HERA has already ended its physics run. However,analyses are still in progress. The H1 and ZEUS datahave been combined in these final analyses, increasingthe available statistics. These fits will better improveour understanding of quarkonium photoproduction.

Indeed, utilizing the entire Tevatron and HERA datasets to study the balance between production of color

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–368

singlet and color octet states in hadro- and photopro-duction will provide more insight into the productionmechanisms than fitting to either data set alone. Last butnot least, the B-factory analyses on charmonium pro-duction, not only from B decays, are detailed enoughnowadays to separate out the different inclusive contri-butions, imposing constraints on the production mecha-nisms at B factories, ep colliders and pp colliders. Forinstance, it starts to be rather clear that C = +1 color-octet transitions are much less probable than initiallythought, which suppresses the leading color-octet yieldat pT < 5 GeV in hadroproduction.

In 200 GeV pp collisions, PHENIX has measuredcross sections for production of the (unresolved) Υstates and the ψ(2S ). A χc measurement will be pub-lished soon. All of these measurements involve lowyields and will benefit greatly from improved luminos-ity in the next few years. PHENIX has also measuredthe polarization of the J/ψ in 200 GeV pp collisions andwill also do so with existing 500 GeV data. PHENIXand STAR will also produce unpolarized J/ψ and Υ re-sults at 500 GeV, a new energy midway between the 200GeV data and the Tevatron energy.

RHIC is vigorously pursing a long term plan of de-tector and machine upgrades. The ongoing RHIC lumi-nosity upgrades will be completed by the 2013 run. Theintroduction in 2011 and 2012 of silicon vertex detec-tors into PHENIX at mid and forward rapidity and of theSTAR Heavy Flavor Tracker in 2014, will enable opencharm and open bottom to be measured independentlywith greatly improved precision. The detector upgradeswill also allow improved measurements of quarkoniumstates due to improved mass resolution and backgroundrejection.

The RHIC run plan for the next 5 years or so willbe centered on exploiting the capabilities of the newsilicon vertex detectors and other upgrades, combinedwith the increased RHIC luminosity. There will likelybe long pp runs at 200 GeV, plus shorter runs at 62GeV to explore the energy dependence of open and hid-den heavy flavor production. The luminosity increaseand the PHENIX detector upgrades will enhance thePHENIX heavy quarkonium program with increased pT

reach for the J/ψ and low statistics measurements of thecombined Υ states. The increased luminosity will en-able the large acceptance STAR detector to extend itspT reach to considerably higher values for Υ and J/ψmeasurements than previously possible.

The RHIC program for the period beyond about 5years is still under development. The RHIC experimentsare presently engaged in preparing a decadal plan thatwill lay out their proposed science goals and detector

upgrades for 2011 to 2020.

3. Quarkonium production in pA collisions

The study of charmonium production is an interestingtest of our understanding of strong interaction physics.For pp collisions, various theoretical approaches havebeen proposed, but a satisfactory description of J/ψhadroproduction is still missing [31]. In spite of thissituation, the study of quarkonium production in the ap-parently more difficult proton-nucleus environment hasalso attracted considerable interest. In fact, in pA, theheavy-quark pair is created in the nuclear medium, andthe study of its evolution towards a bound state can addsignificant constraints to the models. For example, thestrength of the interaction of the evolving cc pair withthe target nucleons, that can lead to a break-up of thepair and consequently to a suppression of the J/ψ yield,may depend on its quantum states at the production level(color-octet or color-singlet), and on the kinematic vari-ables of the pair [50, 51]. In addition to final-stateeffects, also initial-state effects may influence the ob-served J/ψ yield in pA. In particular, parton shadowingin the target nucleus [52, 53, 54, 55, 56] may suppress(or enhance, in case of antishadowing) the probability ofproducing a J/ψ, and its effect depends on the kinemat-ics of the cc pair production [57]. Moreover, the energyloss in the nuclear medium of the incident parton [58],prior to cc production, may significantly alter the J/ψcross section and its kinematic distribution. Finally, asuppression of the J/ψ has been proposed a long timeago as a signature of the formation, in ultrarelativisticnucleus-nucleus collisions, of a state where quarks andgluons are deconfined (Quark-Gluon Plasma) [59]. Re-sults from pA collisions, taken in the same kinematicalconditions of AA, and properly extrapolated to nucleus-nucleus collisions, can be helpful to calibrate the contri-bution of the various cold nuclear matter effects to theoverall observed suppression [60, 61].

3.1. Basic phenomena and observables

3.1.1. Hierarchy of time scalesNuclear effects are controlled by the characteristic

time scales of charmonium production. A colorless ccpair created in a hard reaction is not yet a physical char-monium state since it does not have a fixed mass. Ac-cording to the uncertainty relation it takes time to disen-tangle the ground state charmonium from its excitations,

t f =2Ecc

m2ψ′ − m2

J/ψ

. (3)

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 9

This time scale can be also interpreted as formation timeof the charmonium wave function. At charmonium en-ergies Ecc < 25 GeV in the nuclear rest frame this timeis shorter than the mean nucleon spacing in a nucleus,t f < 2fm, so one can treat the formation process asinstantaneous, and the attenuation in nuclear matter iscontrolled by the inelastic charmonium-nucleon crosssection,

S (L) = exp[−σJ/ψN

in L ρA

], (4)

where L is the path length in the medium of density ρA.At much higher energies, Ecc � 100 GeV, the forma-

tion time is long, l f � RA, even for heavy nuclei, theinitial size of the cc dipole is ”frozen” by Lorentz timedilation during propagation through the nucleus, so theattenuation factor gets the simple form,

S (L) =⟨exp

[−σ(rT )L ρA]⟩

rT, (5)

where the exponential is averaged over rT weighted withthe initial and final distribution amplitudes [50]. Thisregime is relevant for J/ψ production at RHIC at themid rapidity, where Ecc = 300 GeV. The J/ψ energyrises with y as ey relative to the target nucleus, but de-creases as e−y relative to the beam nucleus. Therefore,the asymptotic regime is relevant to any positive rapidityin dA collisions, but in AA collisions at forward rapidi-ties nuclear effects turn out to be in different regimes forthe two colliding nuclei.

Another important time scale characterizes the hardprocess of cc pair creation. Although the proper time isshort, t∗ ∼ 1/mc, it is subject to Lorentz time dilation ina frame, where the charm quarks have high energy.

tc =2Ecc

M2cc

(6)

If this time is short, tc < 2 fm, one can consider pro-duction as instantaneous. This regime corresponds tocharmonium energy Ecc < 50 GeV. This estimate is rel-evant for production of χ, but the characteristic energymay be about twice higher for J/ψ, because in the colorsinglet model the invariant mass of cc is 〈M2

cc〉 = 2m2J/ψ.

This time scale is usually short for J/ψ produced atmid rapidity in fixed-target experiments. For instanceat√

s = 40 GeV tc = 1.2 fm if xF = 0.The most difficult for calculations is the intermediate

energy regime, where either tc or/and t f are of the orderof the nuclear size. Theoretical tools for this case, thepath-integral technique, was developed in [50, 62]. Thecc dipole is produced with a separation ∼ 1/mc and endsup with the large size of J/ψ. The time scale for suchan expansion, t f , rises with energy, therefore the effec-tive absorption, or break-up, cross section is expected to

drop with energy [50]. Indeed, this effect was observedin fixed target experiments, as is plotted in Fig. 6. Dataare well explained by color transparency for expandingcc dipoles.

Figure 6: The effective break-up cross section as function of J/ψ en-ergy. The solid curve shows theoretical expectation [62]. The dashedcurves show the estimated theoretical uncertainty.

3.1.2. Higher twist charm quark shadowingIn the regime of long time scale for cc production, of

tc � RA, the process, g → cc, is subject to shadow-ing. This is apparently higher twist, since the mean cctransverse separation is 〈rT 〉 ∼ 1/mc. Same is true forthe break-up cross section of the produced colorless ccpropagating through the nucleus.

The amplitude of cc production at a point with im-pact parameter b and longitudinal coordinate z, aver-aged over the dipole size, reads [63, 64],

Here T−(b, z) =∫ z−∞ dz′ρA(b, z′); T+(b, z) = TA(b) −

T−(b, z), and TA(b) = T−(b,∞). Shadowing for cc pro-duction over the nuclear thickness T−(b, z) occurs withthe shadowing cross section corresponding to a 3-bodydipole, gluon and cc, which for equal momenta of c andc equals to σccg(rT ) = 9

4σcc(rT /2) − 18σcc(rT ).

For tc � RA the weight factor in (7) has the form[63], Wcc(rT ) ∝ K0(mcrT ) r2

T ψJ/ψ(rT ), where one fac-tor rT comes from the amplitude of cc production, and

2σcc(rT )T+(b, z)

].

2σccg(rT )T−(b, z) − 1

S pA(b, z) =∫

d2rT Wcc(rT ) (7)

× exp[−1

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3610

another one either from the amplitude of gluon radia-tion in the case J/ψ production, or from the radial wavefunction of χ2.

With the survival probability amplitude Eq. (7) thenuclear ratio reads,

RpA =1A

∫d2b

∞∫−∞

dz∣∣∣S pA(b, z)

∣∣∣2 . (8)

The results at√

s = 200 GeV are plotted by dashedcurve in Fig. 7 as function of y. [64].

0

0.25

0.5

0.75

1

-1 0 1 2 3

+- 11% Global Scale Uncertainty

y

RpA

Figure 7: Dashed curve presents nuclear suppression of J/ψ as func-tion of rapidity in pA collisions. Solid curve is corrected for gluonshadowing. Data are for dAu collisions at

√s = 200 GeV [65].

3.1.3. Leading twist gluon shadowingIn terms of the Fock state decomposition gluon shad-

owing corresponds to higher Fock components in theprojectile hadron, containing at least one gluon. Mul-tiple interactions of this gluon in the nuclear target arethe source of shadowing.

Theoretical expectations for gluon shadowing arequite diverse. While a weak shadowing was predictedwithin the dipole approach [66] and in some analy-sis [52] of DIS data developed at leading and next-to-leading order – nDS and nDSg parameterizations– a quite strong shadowing and correspondingly anti-shadowing for gluons was evaluated in [67] based onthe hadronic representation [68, 69] and in the EKS98[53, 54], EPS08 [55] and EPS09 [56] parameterizations,the two last including data on proton-nucleus collisions.Note that nDSg and EKS98 parameterizations are com-patible for x < 10−3.

Also, the choice of the adequate partonic productionmechanism – either via a 2 → 1 or a 2 → 2 process –

may affect both the way to compute the nuclear shad-owing and its expected impact on the production [57].

This controversy should be settled after nuclear ef-fects for charmonium production at LHC will be studiedexperimentally.

3.1.4. Non trivial transition from pA to AAThe usual strategy in search for a signal of final state

attenuation of charmonia in the created dense medium,is extrapolation to AA collisions of the cold nuclear mat-ter effects observed in pA. This is how the ”anomalous”suppression of J/ψ was observed in the NA50/60 data[70, 71, 72, 73, 74]: one fits the effective absorptioncross section σabs to describe the nuclear suppressionobserved in pA collisions. Some results of such a pro-cedure are shown in Fig. 6. Then with this cross sectionone predicts the normal cold nuclear matter effects innuclear collisions, and whatever deviates from such anexpectation is called anomalous and is related to the fi-nal state suppression.

However, recent data [75] from the NA60 experimentfor pT broadening of J/ψ depicted in Fig. 8 demonstratethat such an extrapolation may not be straightforward,since the ”cold” nuclear matter in AA collisions turnsout not to be cold at all.

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

0 1 2 3 4 5 6 7 8 9 10

NA50, Pb-Pb 158GeV

NA60, In-In 158GeV

NA60, p-A 158GeV

L (fm)

<p

2 T> (G

eV

/c)2

Figure 8: J/ψ pT broadening measured at SPS as a function of thepath length L in nuclear matter.

Indeed, broadening, Δp2T , is known to be proportional

to the path length in the medium and its density. Thedata show that broadening observed in nucleus-nucleuscollisions is twice as large as in pA for the same totalpath length. This means that the cold nuclear matter istwice as dense in AA compared to pA collisions. Cor-respondingly, the effective absorption cross section σabs

should be taken twice bigger when one makes predic-tions for AA collisions. Such a significant enhancement

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 11

� ��

�

�

Figure 9: Left: A two-dimensional (time - longitudinal coordinate) plot for charmonium production in a collision of nuclei A and B in the c.m.of the colliding nucleons. The solid and dashed lines show the nucleon and gluon trajectories, respectively. Right: Nuclear suppression of J/ψproduction in pA and AB collisions as function of the product A × B. The two curves demonstrate theoretical uncertainty of calculations [76]. Thecircles and squares correspond to pA and AB data, respectively. The data points are from [70, 71, 72].

of absorption effects may explain the observed anoma-lous suppression.

This effect was successfully predicted in [76] as a re-sult of multiple NN collisions and gluon radiation pre-ceding their interaction with the J/ψ (or cc dipole), as isillustrated in the left panel of Fig. 9.

It was also shown that quantitatively this effect is ableto explain the observed anomalous J/ψ suppression, asis depicted in the right panel of Fig. 9. Simultaneously,the same effect of increased medium density leads to asignificant increase of broadening in AA compared topA collisions.

Suppression of J/ψ caused by gluon radiation de-creases as 1/

√s and vanishes at high energies of RHIC

and LHC. However, at the energies of LHC broadeningof J/ψ is expected to be highly enhanced in AA com-pared to pA collisions for another reason.

Notice that observation of an anomalously largebroadening has an important advantage compared toanomalous suppression. While the latter may originatefrom either initial, or final state interactions, which canbe easily mixed up, the former comes entirely from ini-tial state multiple interactions. Indeed, a colorless ccdipole attenuates in a medium, but does not have anyenergy loss and does not change its momentum. Notethat the partonic process may affect this result [77].

3.1.5. Transverse momentum broadeningThe mean transverse momentum squared of heavy

quarkonia increases in pA collisions compared to pp.The magnitude of the effect, Δp2

T = 〈p2T 〉A − 〈p2

T 〉p isusually called broadening. Broadening of a parton prop-agating through a nuclear medium can be calculated

within the dipole approach as [78, 79],

Δp2T = 2 C(E)

L∫0

dz ρA(z), (9)

where the factor C(E) is related to the dipole-protoncross section σqq(rT ) known from phenomenology. Forbroadening of gluons

Cg =98�∇2

rTσqq(rT )

∣∣∣∣∣rT=0

. (10)

Using the dipole cross section in the saturated form fit-ted to DIS data [80, 66] one can predict the factor Cg(E)and broadening Eq. (9). The results depicted in Fig. 10by dashed curves well agree with data for J/ψ and Υ.Inclusion of gluon shadowing corrections reduces theamount of shadowing, but within the error bars.

One should also understand the pT dependence of thecross section and the energy dependence of the meanvalue 〈p2

T 〉, depicted in Fig. 11.Remarkably, data on pp, pA and even AA collisions,

at the energies of fixed target experiments and at RHIC[65], are described well by the simple parametrization,

dσdp2

T

∝⎛⎜⎜⎜⎜⎝1 +

p2T

6〈p2T 〉

⎞⎟⎟⎟⎟⎠−6

. (11)

If one considers that broadening does not alter the shapeof the pT -distribution of produced J/ψ, the simplest wayto calculate the pT -dependence of the pA cross sectionis just making a shift Δp2

T in the mean value 〈p2T 〉 for pA

compared to pp. The resulting A-dependence of the pA

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3612

0

0.1

0.2

0.3

0.4

0.5

10 102

J/ψ

Υ

DY

A

Δ P

2 T (

GeV

2)

DY E772DY E866J/ψΥ

Figure 10: Broadening for J/ψ and Υ [81] is shown by circles andtriangles respectively. The dashed and solid curves correspond to thepredictions based on Eq. (9) without and with the corrections for gluonshadowing respectively.

(GeV) s210

310

2 (

GeV

/c)

⟩2 T

p⟨

2

4

6

8

10

PHENIX p+p (|y|<0.35)PHENIX p+p (1.2<|y|<2.2)NA38/NA51/NA50 p+pE789 p+Au

pCDF p+

)1/2

= -2.4 + 1.2 *ln(s⟩ 2

T p⟨

Figure 11: The J/ψ 〈p2T 〉 in pp collisions as function of energy. Data

are from [10].

over pp ratio, RpA, is presented in Fig. 12 as functionof pT in comparison with data [82] at

√s = 39 GeV.

The A-dependence is parametrized as RpA = Aα−1, andα(pT ) is plotted in Fig. 12.

3.1.6. Feynman xF dependence of nuclear effectsAvailable data on xF-dependence of nuclear effects in

charmonium production demonstrate increasing nuclearsuppression towards large xF , as is shown in Fig. 13, forthe exponent α(xF) characterizing the A-dependence,σ

J/ψpA ∝ Aα.

0.7

0.8

0.9

1

1.1

1.2

1.3

0 1 2 3 4

pT (GeV)

α

E866

Figure 12: The exponent α = 1 + ln(RpA)/ ln(A) as function of pTcalculated with Eq. (11) in comparison with data from [82].

Figure 13: The exponent α(xF ) characterizing the A-dependence,σ

J/ψpA ∝ Aα at

√s = 39 GeV [82] an

√s = 20 GeV [83].

Although several mechanisms contributing to theJ/ψ suppression have been proposed, there is still nocomprehensive description so far of the observed xF-dependence of the nuclear effects. The first mechanismproposed in [84] explored initial state energy loss in-dependent off the collision energy, according to pQCDcalculations, or string model. However, a finite energyloss becomes insignificant at high energies, while datain Fig. 13 demonstrate an approximate xF scaling. Ap-parently, the energy loss must be proportional to the ini-tial energy, in order to provide an xF-scaling. Such anenergy loss was ad hoc introduced in [58], and was crit-icized later in [85], as contradicting perturbative QCDcalculations.

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 13

The observed xF-dependence of nuclear suppressionwas interpreted in [86] in terms of the Fock state decom-position as the energy sharing problem enhanced by thenucleus towards the kinematic limit. This mechanismalso explains a similar suppression observed at large xF

in many other reactions, Drell-Yan process, high andlow pT production of different species of hadrons, etc.

Attempts to explain the observed suppression to glu-ons shadowing, as a dominant mechanism, was not suc-cessful. That would lead to x2 scaling, which is severelybroken in data [81].

3.2. Existing measurements and future perspectives3.2.1. Fixed-target experiments

Since in charmonium production in pA a rather com-plicated interplay of various physical processes occurs,the availability of accurate sets of data, spanning largeintervals in the incident proton energy, and coveringlarge xF and pT regions, is essential for a thorough un-derstanding of the involved mechanisms. At fixed tar-get energies, high-statistics J/ψ samples have been col-lected in recent years by the DESY experiment HERA-B [87], at 920 GeV incident energy, by E866 [88] atFNAL at 800 GeV, by the CERN-SPS experiment NA50at 400 and 450 GeV [89] and by the NA60 experi-ment at 158 and 400 GeV [90]. Usually, nuclear effectshave been parametrized by fitting the A-dependence ofthe production cross section with the simple power lawσ

pAJ/ψ = σ

ppJ/ψ · Aα, and then studying the evolution of

α with xF and pT . Alternatively, nuclear effects havebeen expressed by fitting the data in the framework ofthe Glauber model [91], having as input parameters theinelastic nucleon-nucleon cross section and the densitydistributions for the various nuclei [92]. The modelgives as an output the so-called J/ψ absorption crosssection σabs

J/ψ. Clearly, both α and σabsJ/ψ represent effec-

tive quantities, including the contribution of the varioussources of nuclear effects sketched in the previous sec-tion.

The results for α as a function of xF are summarizedin Fig. 14, and show various remarkable features. Firstof all one can note a steady increase in the strength ofnuclear effects (α decreases) when increasing xF . Morein detail, the decrease of α at large xF has usually beenattributed to energy loss of the projectile partons andindeed various models have tried to explain, at leastqualitatively, such an effect (see e.g. [93] and more re-cently [77]). On the other hand an important constrainton the size of parton energy loss comes from experi-ments studying nuclear effects on Drell-Yan production.At this workshop [94], it has been shown that the initial-state parton energy loss needed to describe the NA3 data

on Drell-Yan production [95] is too small (by a factor 5to 10) to explain at the same time the observed high-xF suppression for J/ψ. Therefore, a quantitative as-sessment of this effect is still lacking. At the other ex-treme of the explored xF region (negative values), oneobserves a slight tendency towards enhancement of theJ/ψ production (α > 1). In this region a model [96] for-mulated in the framework of reggeon phenomenology,indeed predicts an anti-screening effect, which cannotbe reproduced by more conventional approaches basedon the commonly used shadowing parameterizations.

Fx-0.4 -0.2 0 0.2 0.4 0.6 0.8

α

0.8

0.85

0.9

0.95

1

1.05

HERAB 920 GeV

E866 800 GeV

NA50 450 GeV

NA60 400 GeV

NA60 158 GeV

Figure 14: Compilation of experimental results on α vs xF .

At midrapidity, several experiments have studied J/ψproduction. The most remarkable feature is a tendencytowards stronger nuclear effects when

√s of the pA

interaction decreases. In this region, the relevant pro-cesses affecting the production should be the final-statebreakup of the cc pair and the parton shadowing in thenuclear target. Both processes should approximatelyscale with x2, i.e. one would expect nuclear effects tobe the same at a certain x2 independently of the initialproton energy. However, recent results by NA60 [97],comparing α as a function of x2 for J/ψ production at158 and 400 GeV, show that such a scaling does nothold, and that therefore other mechanisms should be in-voked to explain the

√s-dependence of nuclear effects

at midrapidity.To summarize, in spite of the rather extended set of

measurements, which clearly define a trend for nucleareffects on J/ψ production, the interpretation of fixed-

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3614

2x0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

αΔ

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Figure 15: Δα=α400GeV −α158GeV vs x2, as measured by NA60 in pAcollisions at 158 and 400 GeV.

target observations still remains unsatisfactory. For thefuture, further results obtained at lower energies, at theSPS or at the future FAIR facility, may help producea better characterization of the evolution of nuclear ef-fects vs

√s. First ideas for fixed-target measurements at

higher√

s [98], using proton beams extracted from theLHC, are also under consideration.

3.2.2. Collider experiments

The study of J/ψ production and propagation in coldnuclear matter has also been carried out at RHIC en-ergies, through dAu collisions. The conclusions fromthe first round of measurements from the PHENIX ex-periment were not so sharp [65], because of the limitedavailable statistics, but this problem has been recentlyovercome, with the availability of a first set of resultscorresponding to a much larger data sample (Run-6).One of the key features of the PHENIX results is thelarge rapidity coverage, including positive and negativerapidities, corresponding to a large range of relative mo-menta between the cc pair and the medium.

More in detail, PHENIX has recently released dAuRCP data for J/ψ production [14] in nine rapidity binsover |y| < 2.4. Systematic uncertainties associated withthe beam luminosity, detector acceptance, trigger effi-ciency, and tracking efficiency cancel when RCP, theratio of central to peripheral events, normalized to thenumber of NN collisions, is formed. There is a remain-ing systematic uncertainty due to the centrality depen-dence of the tracking and particle identification efficien-cies.

0

2

4

6

8

10

12

14

16

18

-2 -1 0 1 2y

sig

ma ab

s(m

b)

0

2

4

6

8

10

12

14

16

18

-2 -1 0 1 2y

sig

ma ab

s(m

b)

0

2

4

6

8

10

12

14

16

18

-2 -1 0 1 2y

sig

ma ab

s(m

b)

Figure 16: The effective absorption cross section as a functionof rapidity extracted from PHENIX dAu RCP data in the extrinsic2 → 2 scheme [102] (in red closed circle) compared to the 2 → 1scheme [99] (in blue open circle) using a) EKS98, b) EPS08 and c)nDSg. From [102].

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 15

More importantly, there are significant systematic un-certainties in the centrality dependence of RCP due to theuse of a Glauber model to calculate the average numberof nucleon-nucleon collisions as a means of estimatingthe relative normalization between different centralitybins. The systematic uncertainty due to the Glauber cal-culation is independent of rapidity.

The PHENIX dAu RCP data have been independentlyfitted at each of the nine rapidities [99] employing amodel including shadowing and J/ψ absorption. Themodel calculations [100] use the EKS98 and nDSgshadowing parameterizations with 0 ≤ σabs

J/ψ ≤ 15 mb.The best fit absorption cross section was determined ateach rapidity, along with the ±1σ uncertainties asso-ciated with a) rapidity-dependent systematic uncertain-ties and b) rapidity-independent systematic uncertain-ties. The most notable feature is the stronger effectiveabsorption cross section at forward rapidity, similar tothe behavior observed at lower energies [88]. In fact, itis striking that the extracted cross sections at forwardrapidity are very similar for PHENIX (√sNN = 200GeV) and for the E866 collaboration (√sNN = 38.8GeV) [101], despite the large difference in center-of-mass energy. One should note the large global system-atic uncertainty in σabs extracted from the PHENIX RCP

data, dominated by the uncertainty in the Glauber esti-mate of the average number of collisions at each central-ity. Although it does not affect the shape of the rapid-ity dependence of σabs

J/ψ, it results in considerable uncer-tainty in the magnitude of the effective absorption crosssection.

It was recently suggested [57, 102] that the large in-crease in effective absorption cross section at forwardrapidity obtained from a LO CEM calculation [99], maybe significantly moderated if a more accurate 2 → 2kinematics is used. Figure 16 shows the results fromthe 2 → 1 kinematics [99], compared to the ones from a2 → 2 kinematics [102] using the s-channel cut [103] aspartonic model. The difference emphasizes the impor-tance of understanding the underlying production mech-anisms.

PHENIX has very recently released [104] final RdAuand RCP data from the 2008 dAu RHIC run (where RdAuis the J/ψ yield in dAu collisions normalized to the ppyield times the number of NN collisions). The final RCP

data are in very good agreement with the preliminaryresults described above. A comparison of the RdAu datawith the RCP data shows that a simultaneous descriptionof the two observables will require a stronger than lineardependence of the J/ψ suppression on the nuclear thick-ness function at forward rapidity. The dependence of thesuppression on nuclear thickness is at least quadratic,

and is likely higher. This result may have importantimplications for the understanding of forward-rapiditydAu physics, as well as for the estimate of cold nuclearmatter effects in AuAu collisions.

3.2.3. Cold nuclear matter effects at LHC energyThe new energy regime recently opened up by the ad-

vent of the LHC offers new possibilities for the studyof quarkonium in cold nuclear matter. However, al-though the study of pA collisions is foreseen in the LHCphysics program, the details of the acceleration schemeand the choice of the nuclear beam still have to be final-ized. Consequently, the study of the physics observablesaccessible to the experiments is still at a rather prelim-inary level. Clearly, pA data at the LHC are essentialto investigate various physics effects, and “in primis”nuclear shadowing in a still unexplored x-range. Thefinal-state interaction of charmonia with cold nuclearmatter is another attractive topic. Due to the expectedvery short overlap time of the heavy-quark pair with nu-clear matter, one could expect its influence on the stillalmost point-like cc to be very small. However, theseconsiderations are very qualitative and deeper theoreti-cal studies are clearly necessary.

At this workshop, preliminary studies carried out inthe frame of the ALICE experiment have been dis-cussed [105]. In particular, the availability of a forwardmuon spectrometer (rapidity coverage 2.5 < y < 4)gives the opportunity for studying effects connectedwith gluon saturation via the measurement of RpPb forthe J/ψ. A model for heavy-quark production in aColor-Glass Condensate environment [106] has beenused to make predictions for RpPb as a function of y andpT in the acceptance of the ALICE muon spectrometer.Such predictions quantitatively differ from the expec-tations related to a pure shadowing scenario, makingsuch a measurement an interesting tool to investigatesaturation-related effects.

4. Polarisation and feed-down in quarkonium pro-

duction

Until recently, the numerous puzzles in the predic-tion of quarkonium-production rates at hadron collid-ers were attributed to non-perturbative effects associ-ated with channels in which the heavy quark and an-tiquark are produced in a colour-octet (CO) state [107,108, 109, 110]. It is now widely accepted that α4

s andα5

s corrections to the CSM [3] are fundamental for un-derstanding the pT spectrum of J/ψ and Υ produced inhigh-energy hadron collisions [24, 23, 25, 26, 18, 32].

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3616

The effect of QCD corrections is also manifest in thepolarisation predictions. While the J/ψ and Υ producedinclusively or in association with a photon are predictedto be transversally polarised at LO via a color singlet(CS), it has been recently emphasised that their polari-sation at NLO is increasingly longitudinal when pT getslarger [25, 18, 127, 128].

On the other hand, the LO NRQCD calculation (forwhich CO transitions dominante) predicts a sizabletransverse polarisation rate for large pT J/ψ [111, 112,113, 114, 115] whereas the Tevatron CDF measurementat Fermilab [8] displays a slight longitudinal polarisa-tion at large pT for J/ψ and Υ and a stronger one forψ(2S ).

To clarify the situation, more efforts on both exper-imental and theoretical aspects are expected from theforthcoming LHC. In the following, we review impor-tant aspects of quarkonium polarisation both from atheoretical and experimental perspective with particu-lar emphasis on the J = 1 states such as the J/ψ, ψ(2S )and Υ(nS ) .

4.1. Frames and polarizationsThe polarisation of the J = 1 quarkonia is defined

from their dilepton decay. In general, the angular distri-bution of the dilepton is

W(ϑ, ϕ) ∝ 1(3 + λϑ)

(1 + λϑ cos2 ϑ + λϕ sin2 ϑ cos 2ϕ

+λϑϕ sin 2ϑ cosϕ),(12)

where ϑ and ϕ are the (polar and azimuthal) angles ofthe positive lepton with, respectively, the polarisationaxis z and the production plane xz (containing the col-liding particles and the decaying meson). Several polar-isation frames have been used in the past. In the helicityframe the polar axis coincides with the flight directionof the meson in the centre-of-mass frame of the collid-ing hadrons. In the Collins-Soper frame, the polar axisreflects, on average, the direction of the relative velocityof the colliding partons.

To clarify this puzzling situation, improved measure-ments are needed. So far, most experiments have pre-sented results based on a fraction of the physical in-formation derivable from the data: only one polarisa-tion frame is used and only the polar projection of thedecay angular distribution is studied. These incom-plete results prevent model-independent physical con-clusions. Moreover, such partial descriptions of the ob-served physical processes reduce the chances of detect-ing possible biases induced by insufficiently controlled

systematic effects. In the forthcoming LHC measure-ments, it is important to approach the polarisation mea-surement as a multidimensional problem, determiningthe full angular distribution in more than one frame.

In a series of recent works [116, 117, 118, 119], aframe-invariant formalism was proposed to minimizethe dependence of the measured result on the experi-mental acceptance. It provides a much better controlof the systematic effects due to detector limitations andanalysis biases. The overall idea is to study both exper-imentally and theoretically the quantity

λ =λϑ + 3λϕ1 − λϕ , (13)

instead of λϑ and λϕ.

4.2. Charmonium polarizationThe NLO QCD corrections to J/ψ polarisation in the

CSM at Tevatron and LHC have been calculated forthe first time in [25]. At order α4

S , one should alsotake into account the contribution for gg → J/ψ +cc [23]. These are dominant at large pT . The resultsshowed that the J/ψ polarisation changes drasticallyfrom strongly transverse at LO into strongly longitu-dinal at NLO. While, this does not completely agreewith the CDF data, the trend is rather encouraging es-pecially since feed-down from P-waves can alter theprompt yield polarisation. The same trend is observedfor the ψ(2S ) [32], for which polarization measurementsare not affected by the P-waves. This is illustrated byFig. 17.

Figure 17: Polarisation of ψ(2S ) directly produced as function of itstransverse momentum pT at the Tevatron as predicted by the CSM atLO, NLO+ (including gg → J/ψcc) and at NNLO� compared to theCDF measurement at

√s = 1.96 TeV.

The first NLO QCD corrections of the J/ψ produc-tion via CO states

[1S (8)0 ,

3S (8)1

]at the Tevatron and LHC

were studied in [27]. Contrary to the CS case, thesecorrections only slightly change the J/ψ pT distribu-tions and the polarisation compared to the LO NRQCDcalculations. This result implies that the perturbative

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 17

Figure 18: Direct-J/ψ yield polarisation α based on the work [27]and the NRQCD matrix elements are from the recent work [34]. Theexperimental data is from the CDF measurement at the Tevatron [8]for the prompt J/ψ.

QCD expansion quickly converges for J/ψ productionvia the S -wave CO state, in contrast to the CSM, wherethe NLO contributions open new channel which show aleading pT behaviour with a different J/ψ polarisation.

As shown in Fig. 4.2, an obvious gap between thetheoretical results for J/ψ polarisation calculated up toNLO including CO transition [27] and the experimentalmeasurements at Tevatron is observed for increasing pT .There still remains only a narrow window which mightfill the gap if one follows the a priori rigourous theo-retical framework of NRQCD, namely the NLO correc-tions to J/ψ production via P-wave CO states and J/ψproduction by feed down from χcJ . It is worth notinghowever that the latter possible solution does not applyfor ψ(2S ) where a similar gap is observed –with a largemagnitude even–, while the former one would be at oddswith the suppression of C = +1 CO transition expectedfrom e+e− studies.

The results given by two recent works [34, 35, 120]show that the pT distribution of the P-wave CO contri-bution at QCD NLO can be decomposed into the linearcombination of the two S -wave COs. In Ref. [34], theχc feed down to prompt J/ψ hadroproduction is takeninto account, contributing at the level of 20 − 40%. Inthis case, the NRQCD matrix elements 〈OH

n 〉 are deter-mined to be 〈Oψ

8 (3S 1)〉 = 0.0005 GeV3 and 〈Oψ8 (1S 0)〉 =

0.076 GeV3. It should be noted that some experimentaldata have been omitted since the fit of the pT distribu-tion starts at 7 GeV. The theoretical prediction for thepolarisation of the direct J/ψ hadroproduction is plottedin Fig. 18, based on the calculation of Ref. [27]. We alsonote that such a value for 〈Oψ

8 (1S 0)〉 does comply withthe constraint of Eq. (1). This either hints at an overesti-mation of this transition in these studies or at a breakingof NRQCD matrix-element universality for charmonia.In such a case, NRQCD would become nearly unpredic-tive as far as charmonium production is concerned.

Two aspects should be emphasized when comparing

the theoretical prediction and the existing experimen-tal measurements. It is impossible to give the polarisa-tion of the prompt J/ψ hadroproduction without a cal-culation of the polarisation for the χc feed-down con-tribution if it really contributes 20 − 40% to the pT

distribution. In addition, the polarisation prediction inFig. 18 for direct J/ψ production assumes that the CO3P[8]

J (J/ψ) NRQCD matrix element can be neglected. Ifnot, its contribution to J/ψ polarisation must calculatedat NLO accuracy. At LO, the χc and the P-wave COcontributions were both taken into account in the firstNRQCD-based predictions [113].

4.3. Bottomonium polarization

As regards the polarisation of Υ produced in pp col-lisions, the NLO CSM correction was first presentedin [26], and followed by an analysis including the real-emissions at NNLO [18] which we discuss later on. Thepolarization is quite similar to that of J/ψ, i.e. the polar-isation changes drastically from strongly transverse atLO into strongly longitudinal at NLO. The NLO resultsare also rather similar to those obtained in the kT fac-torisation approach at LO [121, 122].

Figure 19: Transverse momentum distribution of polarization param-eter α for direct Υ production at the Tevatron.

The NLO QCD corrections of the Υ production viaCO

[1S (8)0 ,

3S (8)1

]at the Tevatron and the LHC were stud-

ied for the first time in [33]. The Υ polarization param-eter, α, from CO

[3S (8)1

]as function of pT is shown in

Fig. 19. Slight changes can be observed when the NLOcorrections are taken into account. For any pT , the di-rect Υ yield from CO is transversally polarized, withα > 0.5 as soon as pT > 10 GeV. The predictions forthe polarization of Υ production when the CSM NLOyield is added are also presented in the figure as a “to-tal” result.

In Fig. 20, the polarization of inclusive (i.e. prompt)Υ production at the Tevatron is shown. As the polariza-tion of Υ from the feed-down of χb(nP) is not availableyet, a huge band is obtained only by imposing that the

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3618

Figure 20: Extrapolated prompt Υ(1S ) polarization as a function of its transverse momentum at the Tevatron as predicted by NRQCD (includingCO transitions) [33], CSM at NLO [18] and CSM at NNLO� [18], compared to the D0 [22] and CDF [123] data.

polarization of this part is between -1 to 1. The experi-mental data from D0 and CDF is also shown in the samefigure. Since both data sets clearly disagree, it is diffi-cult to draw any strong conclusion from such a compar-ison. Yet, if one follows the CDF analysis based on ahigher integrated luminosity and where the 3 Υ statesare clearly separated out, one observes the same gapopening with pT as for the ψ’s, even with such a largetheoretical uncertainty. For the sake of completeness,one should underline that the direct yield from CO tran-sitions is always predicted to be transverse. The COyield can only become slightly longitudinal thanks tothe (unknown) feed-down. This is a clear motivationfor the CDF and D0 to measure the polarisation of di-rect Υ(1S ) or that of Υ(3S ), the latter being de factodirect.

In addition to the evaluation of the NLO CSM con-tributions to Υ production, a subset of the NNLO con-tributions were evaluated in [18], these are the real-emission contribution at order α5

S believed to providethe leading contribution at large pT . It was indeedfound that these contributions, included in the NNLO�

yield, could be large and bring an agreement betweena CSM-based evaluation and the CDF data. It also oc-cured that the NNLO� yield showed the same polarisa-tion than the NLO yield, excepted for the –important–fact that the yield was correctly described. The polar-ization of directly-produced Υ predicted likewise doesnot agree with the experimental data since it is strongly

longitudinally polarized. Nevertheless, as we havediscussed above, the experimental data includes con-tributions from P-wave decays, up to roughly 40 %,and these can decay into transversally polarised Υ(1S ).Even if the feed-down yield is unpolarized, the promptpolarization would only be 0.6 times the direct polar-ization. Clearly when this is taken into account, theCSM NNLO� and the NLO agree with the CDF data,as depicted by the gray (labeled NLO) and red (labeledNNLO�) band of Fig. 20.

In this partial QCD NNLO calculation, some infrareddivergences are not automatically regulated since theloop corrections at α5

s are missing. This imposed theintroduction of an infrared cut-off, whose effect is be-lieved to decrease as pT increases, provided that thereal-emissions dominates at large pT . This may notbe exactly realised if double t-channel gluon exchangeshave an important impact. In this case, the result couldbe overestimated. However, the agreement with the kT

factorisation results gives us the hope that the infrareddivergences are for a large part under control.

This partial QCD NNLO calculation was also appliedto the J/ψ and the ψ(2S ) case [32] and the contributionwas also found to be important. Yet, contrary to the Υcase, there is still a small gap opening at large pT . Atthe leading order in v, the prediction for the J/ψ and theψ(2S ) are identical. The ψ(2S ) polarisation as functionof pT is depicted by the red band (labeled NNLO�) bandof Fig. 17. It is similar to that of NLO.

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 19

4.4. Polarization in photoproduction and at RHICThe J/ψ polarization in photoproduction at HERA

was also studied up to NLO in [124, 125]. The resultsshowed that the transverse momentum, pT , and energyfraction, z, distributions of J/ψ production do not agreewell with the observations. The theoretical uncertain-ties on the z distributions of the J/ψ polarization pa-rameters in the target frame for various choices of therenormalization and factorization scales are too large toprovide a definite prediction relative to the experimentaldata [126]. It is quite easy to understand that the uncer-tainty in the QCD effects could be rather large since thepT of the J/ψ is quite small at HERA, 1 < pT < 5 GeV.Thus the theoretical prediction is not expected to agreewell with the measurements.

The NLO CSM polarisation of the J/ψ produced inproton-proton collisions at RHIC at

√s = 200 GeV has

been studied [40]. The results show that the polarisationpattern at NLO in the helicity frame is in good agree-ment with the PHENIX data both in the central [15] andthe forward [12] regions when extra contribution fromcg fusion and a data-driven range for the χc contribu-tion to the J/ψ polarisation are considered. For the timebeing, nothing is known about P-wave feed downs atRHIC especially at large pT where xT starts to be large.This prevents any strong conclusion based on the com-parison with the data regarding the status of the CO con-tributions and a possible overestimation by the partialNNLO contribution.

4.5. Perspectives on polarization studiesTo clarify the J/ψ polarisation puzzle, other observ-

ables such as the measurements of J/ψ (Υ) hadropro-duction in association with a photon at the LHC canbe considered. The NLO CS contribution was stud-ied [127] and the results show that the J/ψ polariza-tion changes from transverse at leading-order to longi-tudinal at NLO. It is known that the CO contribution tothe inclusive J/ψ hadroproduction may be one order ofmagnitude larger than the CS contribution, and the po-larization distribution may be dominated by the CO atNLO. In contrast, the CS contribution for J/ψ + γ pro-duction is at least of the same order as the CO contribu-tion. The polarization should then arise from both theCS and CO. Therefore, measurements of J/ψ produc-tion associated with a direct photon at hadron colliderscould be an important test of the theoretical treatmentof heavy-quarkonium production. The partial NNLOresult [128], NNLO�, is about one order of magnitudelarger than the NLO J/ψ pT distribution. The predictedpolarization are almost the same. Therefore, it will bereality check on the partial NNLO treatment.

Moreover, to compare the polarisation measurementsin different frames, we need theoretical predictionsbased on different polarisation frames such as the helic-ity frame (HX) and Collins-Soper frame. Along theselines, we would like to mention a recent pioner work onthe polarization studies of Υ + γ in the kT factorizationapproach using different polarization frames [129].

Theoretical predictions of the new, proposed, frame-independent polarisation parameter λ are needed. Ofcourse, all the prediction should at NLO accuracy. Fur-thermore, the comparison between experimental dataand theory must consider the experimental acceptanceand efficiency. Experiments measure the net polarisa-tion of the specific cocktail of quarkonium events ac-cepted by the detector, trigger and analysis cuts. It willbe very useful to have an event generator where thequarkonium decay into lepton pairs for inclusive pro-duction at NLO which could be embedded into MonteCarlo simulations.

5. Open heavy-flavor production in pp and pA colli-

sions

Open heavy-flavor production in pp and pA colli-sions is tightly connected to the process of quarkonium(hidden flavor) production. Nevertheless, it is in it-self one of the most interesting processes to study fromtheoretical and experimental points of view (see, e.g.,Refs. [130, 131] for a review on recent results). Infact, the production of heavy quarks allows us to testfundamental concepts, such as perturbative QCD, fac-torization and non perturbative power corrections. Italso represents a mandatory benchmark for quarkoniumproduction and parameters derived in open heavy-flavorproduction serve as the basis for calculations of quarko-nium production.

Thanks to the massiveness of heavy quarks, the pro-duction cross section can be calculated analyticallyin perturbative QCD down to pT = 0 at the par-tonic level [132]. However, differential distributionsand event shapes exhibit large logarithmic contribu-tions, typically corresponding to soft or collinear par-ton radiation, which need to be resummed to all or-ders [133, 134, 135]. Furthermore, dead-cone effectssuppress gluon radiation around the heavy-quark direc-tion, which has relevant phenomenological implicationson both parton- and hadron-level spectra. As far asheavy-hadron production is concerned, one can modelnon perturbative effects by means of a fragmentationfunction, depending on a few tunable parameters, orby including power corrections in a ‘frozen’ or ‘effec-tive’ strong coupling constant [136, 137, 138]. Reliable

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3620

hadronization models should also be capable of distin-guishing the spin of the produced hadrons, e.g. sepa-rating the D∗ from the D, and describing both baryonsand mesons and the multiplicity ratios Λc/D or Λb/B.Typically, hadronization models, such as the cluster[139] or string [140] models, are implemented withinthe framework of Monte Carlo generators, such as HER-WIG [141], PYTHIA [142] or MC@NLO [143] and aretuned to heavy-hadron data from e+e− experiments, e.g.LEP and SLD data (see, for example, [144] for a tuningto b-quark fragmentation). Multi-purpose generatorshave been available for several years for lepton/hadroncollisions in the vacuum and have been lately modifiedto include the effects of dense matter [145, 146] (seealso [147, 148, 149, 150, 151] for generators specificfor heavy-ion collisions).

A profound knowledge of open heavy-quark produc-tion is crucial for the understanding of quarkonium phe-nomenology. The production, e.g., of the J/ψ in Nonrelativistic QCD (NRQCD) is described as the convolu-tion of the perturbative cc cross section and a non pertur-bative operator, possibly depending on the color of thecc state, according to the color-singlet and color-octetmechanisms (see e.g. [152]).

In order to promote the formalism used to describeopen heavy flavors to pA and ultimately AA collisions,one has to introduce medium-modification effects, tak-ing into account the existing differences between lightand heavy quarks (hadrons) [153]. In particular, one ofthe most striking observations of heavy-ion collisions isthe jet-quenching phenomenon, namely the suppressionof hadron multiplicity at large transverse momentum(pT ) with respect to pp processes [154, 155, 156, 157].

In the case of heavy hadrons, the measured suppres-sion is expected to be lower than that of light-flavormesons, due to the dead-cone effect discussed above.This effect becomes less important in the high-pT limitwhere pT � mQ. So far, suppression of heavy-flavoredmesons in pA or AA collisions has only been mea-sured through leptons, i.e., the non-photonic electronsand muons from semi leptonic decays of heavy-flavoredmesons [158, 159, 160]. Despite being a rather com-plex study, non-photonic electrons and muons have var-ious experimental advantages, the most important onebeing the possibility to deploy the fast triggers, in sucha way to allow the experiments to collect large data sam-ples. On the other hand, they originate from both charmand bottom mesons with only few indirect experimentalhandles available to disentangle the two contributions.

Suprisingly, the energy loss observed through non-photonic electrons is substantial already at moderate pT

of ∼3 GeV/c. Figure 21 shows this suppression via the

[GeV/c]T

p

0 1 2 3 4 5 6 7 8 9

AA

R

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

: 0-10 % CentralAAR

= 200 GeVNNsAu+Au @

Figure 21: Nuclear modification factor (RAA) for non-photonic elec-trons originating from semileptonic decays of heavy-flavored mesonsin the 0-10% most central AuAu collisions at RHIC measured byPHENIX [158]. This corresponds to the ratio of the invariant yieldsin AuAu and pp collisions normalized by the number of binary nu-cleon collisions. This measurement indicates a strong suppression ofheavy-flavored mesons in central heavy-ion collisions.

nuclear modification factor RAA defined as the ratio ofinvariant yields in AuAu over that in pp collisions timesthe number of binary nucleon collisions in the AuAusystem at a given centrality. In the absence of any nu-clear or dense matter effects RAA is unity. Several mech-anisms to describe heavy-flavor energy loss in the densemedium have been so far proposed. Most prominentare collisional and radiative energy loss, typically calcu-lated in the weak-coupling regime. However, the mag-nitude of the observed suppression at RHIC is hard toaccommodate in these models. Recent attempts, assum-ing strong coupling between the heavy-flavor mesonsand the dense medium, and based on the AdS/CFT cor-respondence, lead to higher suppression factors, but fur-ther studies and experimental data are needed beforeany conclusions can be drawn.

It is still an open question to what extent the energy-loss mechanisms, observed in open heavy-flavor pro-duction, affect the quarkonium yields in AA collisions.After including quark-antiquark recombination effects,the quenching of open heavy-flavored hadrons will alsoserve as a benchmark for quarkonia in heavy-ion colli-sions.

Another crucial issue in heavy-flavor phenomenol-ogy concerns heavy-quark parton distributions in pro-tons and nuclei. In fact, processes with the produc-tion of heavy quarks are fundamental to constrain thePDFs. Higher-order corrections to the production ofheavy quarks, with the implementation of soft/collinearresummation to improve the differential distributions,

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 21

will also be helpful to acquire information on heavyquark densities. The possible inclusion of medium ef-fects in the hard-scattering cross section, along with nu-clear parton distribution functions, will eventually leadto a prediction taking fully into account the modifica-tions induced by the dense matter. However, unlike col-lisions in the vacuum, there is no guarantee that factor-ization should also work in a medium.

In the following, we shall review the main results dis-cussed within the Open Heavy-Flavor Working Groupin the Quarkonium 2010 workshop. We shall discusshigher-order calculations of heavy-flavor productionspectra at RHIC, taking particular care about the roleplayed by the resummation on transverse-momentumdistributions. We shall then present a few selected top-ics on specific features of heavy quarks and dead-coneeffects, as well as novel developments on the modellingof energy loss from heavy quarks in dense matter andits possible relation with the jet-quenching observation.Later on, recent results on the production of photonplus heavy quarks, along with its relevance to constraincharm/bottom PDFs in proton and heavy ions, will beinvestigated.

5.1. Open heavy-flavor production at RHIC andFONLL calculations

As our understanding of heavy-ion collisions be-comes more mature, it becomes increasingly clear thatheavy-flavor studies are a mandatory tool to furtherour understanding of the quark-gluon-plasma formed inhigh energy nuclear collisions at RHIC and now at LHC.Having reliable measurements of all aspects of heavy-flavor production is compelling.

Experimentally, the total charm cross section is notwell constrained. Measurements of charm meson pro-duction at the Tevatron could be conducted only at largetransverse momenta (pT > 5 GeV/c) while measure-ments at lower energies exhibit rather large uncertain-ties. At RHIC, measurements of D mesons in con-junction with low-pT non-photonic electrons and muonsin dAu collisions [161] (STAR) indicate a rather largetotal charm cross section of ∼1.3 mb. On the otherhand, the non-photonic lepton measurements in pp col-lisions [158] (PHENIX) suggest a considerably smallercross section of ∼ 0.6 mb. In all cases assumptionsabout rapidity distributions and contributions from un-measured charm mesons and baryons (e.g. Λc) haveto be made, adding further contributions to the alreadylarge statistical and systematic uncertainties. Upgradesto the existing RHIC detectors (for an overview see[162]) will help to overcome these shortcomings. A

√s (GeV)10 210 310

μb)

(N

N ccσ

1

10

210

310

410

510 STAR d+Au; PRL 94, 062301STAR Au+Au (preliminary)PHENIX p+p; PRL 97, 252002PHENIX Au+Au; PRL 94, 082301PHENIX Au+Au; PRL 88, 192303

UA2 pMUON cosmic rays; NPB 122, 353PAMIR cosmic rays; NPB 122, 353NA32 p+A; PR 433, 127E769 p+A; PR 433, 127NA16 p+A; PR 433, 127NA27 p+A; PR 433, 127E743 p+A; PR 433, 127E653 p+A; PR 433, 127HERA-B p+A; PR 433, 127NA50 p+A; PR 433, 127NA60 In+In (preliminary)

; PLB 236, 488p

NLO with CTEQ6M NLO Uncertainty Bound

(from R. Vogt, arXiv:0709.2531)

Figure 22: Comparison of total charm cross section measurements.The STAR and PHENIX results are given as cross section per binarycollisions. Vertical lines reflect the statistical errors, horizontal barsindicate the systematic uncertainties (where available). From [162].

summary of current total charm cross sections (σcc) ispresented in Fig. 22.

On the theory side, the state of the art for charm-quark production is NLO with the inclusion of n f = 3active flavors [132]. A few ingredients of the NNLOcorrections are available [163, 164], but the full NNLOcalculation has not been completed yet. Another possi-ble approach to compute the cross section is to integratethe transverse momentum distribution computed in theso-called FONLL approximation, i.e. soft/collinearresummation to next-to-leading logarithmic accuracy(NLL), matched to the NLO result. The total cross sec-tion is still NLO, but the charm quark is treated as anactive flavor, and therefore n f = 4 in the calculation,which leads to a difference in the result [135].

The FONLL calculation can of course be employedto predict differential distributions, in particular thetransverse momentum one, wherein contributions ∼αk

S lnk−2(pT /mQ) (LL) and ∼ αkS lnk−3(pT /mQ) (NLL),

large for pT � mQ, are summed up to all orders. Thespectra of c-flavored hadrons are then obtained by con-voluting the charm distribution with the appropriate nonperturbative fragmentation function, fitted, e.g., to LEPdata. When doing the fit, the calculation of heavy-quarkproduction in e+e− annihilation must be carried out inthe same perturbative approximation, i.e. NLO+NLL,and the scales are to be consistently set [165, 166].

The main sources of uncertainty on such predictions

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3622

are the renormalization and factorization scales, thequark masses, entering in the perturbative calculation,parton distribution functions, such as the gluon densityabout the charm/bottom mass scale. As for the quarkmass, it is also unclear whether in the calculation oneshould use the pole, the MS or even the hadron mass.For the purpose of the PDFs, the gluon distribution ex-hibits large uncertainties at small x, especially a strongdependence on the factorization scale.

)3

c-2

(m

b G

eV

3/d

pσ

3E

d

-1010

-910

-810

-710

-610

-510

-410

-310

-210

-110

(a)=200 GeVs)/2 + X at -

+ e+

(e→ p+p

PHENIX data

FONLL(total)

e)→FONLL(c

e)→FONLL(b

e)→ c →FONLL(b

(GeV/c)T

p0 1 2 3 4 5 6 7 8 9 10

0.5

1

1.5

2

2.5

3

DA

TA

/FO

NL

L (b)

Figure 23: Non-photonic electron measurements at RHIC (PHENIX)in pp collisions at

√s = 200 GeV. (a) Invariant differential cross

section of single electrons as a function of pT . (b) The ratio ofFONLL/Data as a function of pT . The upper (lower) curve showsthe theoretical upper (lower) limit of the FONLL calculation. From[158].

From the D- and B-hadron distribution one can de-rive the non-photonic electron spectrum at FONLL andcompare it with RHIC data. Both the new PHENIX(shown in Fig. 23) and STAR pp data are compatiblewith the FONLL computation, within the theoreticaland experimental uncertainties. However, the data fa-vors large cross sections, about 1.5 times the nominalFONLL calculation, just on the upper edge of the un-certainty band (Fig. 23b). Non-photonic electron spec-tra at low pT are notoriously difficult to analyze due tothe increased photonic backgrounds, which increase theuncertainties for pT < 2 GeV/c considerably and makethe evaluation of σcc from electrons alone problematic.

Furthermore, much work has been carried out to-wards the separation of charm from bottom contribu-tions to the lepton spectra in pp and pA collisions. Ex-perimental progress has been made using e-h and e-Dcorrelations [167, 168] shown in Fig. 24. Again, results

(GeV/c)Telectron p0 1 2 3 4 5 6 7 8 9

)Be

+N

De/(

NBe

N

0

0.2

0.4

0.6

0.8

1PHENIX e-h correlation

STAR e-D correlation

FONLLFONLL uncertainty

p+p, √s=200GeVSTAR e-h correlation

90% C.L.

90% C.L.

Figure 24: Transverse momentum dependence of the relative contri-bution from B mesons to the non-photonic electron yields as mea-sured by PHENIX [167] and STAR [168]. Error bars are statisticaland brackets/boxes are systematic uncertainties. The solid line is aFONLL prediction and the dotted lines represent the uncertainty onthis FONLL prediction.

are consistent with the FONLL calculation, although ex-perimental errors are currently still too large to allow anaccurate separation of bottom and charm production inpp processes.

The final answer has to come from direct measure-ments of charm through D mesons (if able to subtractthe B → D contribution looking e.g. at the impact pa-rameter distribution) and that of bottom through B →J/ψ + X and/or b-tagged jets or leptonic decays. Thesemeasurements will require high precision vertexing thatwill become available for both RHIC experiments in thenear future [162].

5.2. Properties of gluon radiation off heavy quarks

A heavy quark Q is characterized by the fact thatits mass is much larger than the typical hadronizationscale, say mQ � ΛQCD, e.g., in the MS renormalizationscheme. The fact that the quark mass acts as a regulatorof the collinear singularity and that the strong couplingconstant is evaluated at relatively large scales, depend-ing on the observable one is looking at, makes perturba-tive QCD applicable.

When dealing with multiple emissions from heavyquarks, an essential difference with respect to lightquarks is that gluon radiation is suppressed inside theforward angular cone with an opening angle mQ/E, theso-called dead cone, with E being the heavy-quark en-ergy [169]. The dead cone implies the decrease of theoverall energy loss and thus to the leading-particle ef-fect, i.e. heavy-hadron energy distributions are peakedat large x, with x being the energy fraction in the centre-of-mass frame [136]. In other words, after multi-parton

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 23

radiation and hadronization, a heavy hadron still car-ries a significant fraction of the parent-quark energy.Also, for x � 1 −ΛQCD/mQ, one starts to be sensitive tonon perturbative effects which can be included, e.g., bymeans of a fragmentation function or a frozen/effectivecoupling constant. Another relevant result, which canbe related to the dead cone is that, unlike the naiveparton-model expectation, the multiplicity differencebetween heavy and light hadrons is roughly independentof the centre-of-mass energy [170].

More generally, soft radiation obeys the Low–Barnett–Kroll (LBK) theorem [171, 172], according towhich soft gluons are classical and therefore incapableof modifying the quantum numbers, such as the color,of a given system. Also, due to its classical nature, soft-parton emission is independent of the underlying hard-scattering process and of the quantum properties of theemitter. This implies that, if a process is forbidden by agiven symmetry, such a veto cannot be relaxed by emit-ting extra soft photons/gluons.

This property of soft radiation can be connected tothe longstanding puzzle of J/ψ production, whose mea-sured rate at large pT at the Tevatron was about 50 timeslarger than the theoretical prediction. In fact, the color-octet mechanism was formulated in order to explainsuch a discrepancy. In other words, such a model pre-dicts, at one loop in gluon-gluon fusion, the productionof a J/ψ and a gluon, with the J/ψ being in a color-octetstate.

However, as discussed above, in order to change theJ/ψ color, the emitted gluon cannot be soft: accordingto the LBK theorem, the price to pay for the emission ofa hard gluon is ∼ (ΛQCD/mc)2.

Therefore, it is probably worthwhile investigat-ing alternative mechanisms which, besides the color-evaporation model and the color-octet model, can in-crease the yield of large-pT J/ψ production in hadroncollisions and hence recover the agreement with theTevatron data. In fact, the production of quarkonia atlarge transverse momentum has a very small cross sec-tion and therefore it is a rare configuration, wherein fluc-tuations are expected to play a role [173].

5.3. Heavy quarks and energy loss in dense matterA crucial issue in heavy-quark phenomenology is the

description of energy loss in a dense medium and its re-lation to the quarkonium spectrum in matter. It is com-monly assumed that partons at large transverse momen-tum traversing the medium lose energy through incoher-ent radiation of gluons as well as collisional energy loss.The approach presented in [174] assumes that a fast par-ton in a medium undergoes multiple collisions, charac-

terized by a moderate momentum transfer and large val-ues of the strong coupling constant. As for the coupling,non perturbative effects are taken into account by usinga frozen coupling constant [136, 137]. Indeed, such amodel manages to reproduce quite well the RAA ratiomeasured by the PHENIX collaboration, for AuAu col-lisions at 200 GeV over the full transverse-momentumrange, up to a normalization K-factor of about 2.

As for the radiative energy loss, for light quarksone usually relies on the Baier–Dokshitzer–Mueller–Peigne–Schiff (BDMPS) approximation [175] whichassumes static scattering centres, independent soft emis-sions and hadronization outside the medium. For heavyquarks one can rely to the Gunion–Bertsch approach[176]: the medium-induced gluon-radiation spectrum iscorrected by means of terms depending on the heavy-quark mass and on the fictitious gluon thermal mass.Moreover, gluons radiated by massive quarks are re-solved in a smaller time with respect to light quarks,which implies a milder dependence on coherence effectsand evolution variables for multiple radiation. There-fore, as a first approximation, one can even think ofneglecting coherence effects when dealing with emis-sions from heavy quarks. The result is that if one addsboth collisional and radiative energy loss contributions,a scaling factor of 0.6 is enough to reproduce the RAA

data at RHIC. Future data from the LHC will possiblyshed light on the issue of the energy loss; to this goal, itwill be very useful having more exclusive probes, suchas azimuthal correlations or tagged c- or b-flavored jets.Another open issue concerns the gluon thermal massand whether it can be theoretically predicted or it shouldrather be fitted to experimental data, like a non pertur-bative parameter.

5.4. Heavy quark plus photon production as a probe ofthe heavy quark PDF

The production of a direct photon accompanying aheavy quark at hadron colliders is an important process,also relevant to constrain the heavy-quark density. Asit escapes confinement, a photon can be exploited totag the hard scattering; also, its transverse momentumdistribution gives meaningful information on the heavy-quark production process and PDF.

At leading order, i.e. O(ααS ), there is only one hardscattering process, namely gQ → Qγ. At NLO in thestrong coupling constant, i.e. O(αα2

S ), several subpro-cesses contribute to Qγ production, with gluons, heavyand light quarks in the initial state [177]. Considering,e.g., charm production, such processes will help to shedlight on the charm distribution and whether it is radia-tively generated by means of gluon emissions, in which

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3624

case c(x,Q2) � g(x,Q2), or there is an intrinsic charmcontribution to the proton. In fact, there exist light conemodels, wherein intrinsic charm is relevant at large x[178], and sea-like models, with c(x) � u(x) + d(x).As for the comparison between the photon spectra pro-duced in association with charm and bottom quarks,there are remarkable differences both at LO and at NLO.At large transverse momenta, the discrepancy betweenLO and NLO gets larger [177].

The NLO calculation has been compared with D0data [179] on the photon transverse momentum in Qγevents: the agreement is pretty good in the case ofbγ production, whereas discrepancies are present forcharm production, with the NLO computation yieldinga lower cross section for moderate and large values ofpT . Such disagreement can be traced back to the possi-ble existence of intrinsic charm in the proton. Using theBrodsky–Hoyer–Peterson–Sakai (BHPS) PDF set [178]slightly improves the comparison, although meaningfuldifferences are still present at very large pT . The dis-crepancy is instead milder when comparing the ratioof charm and bottom cross sections. At the LHC, onecan still investigate the presence of the intrinsic charm.However, since the probed values of x are on averagesmaller than at the Tevatron, one is basically sensitiveto the sea-like model. Also, the forward-rapidity regionwill be particularly suitable to discriminate between ra-diative and intrinsic contributions to the charm PDF.

The LO/NLO calculations for b/c+ γ production canbe extended to pA collisions, e.g. proton-lead processesat the LHC. A first approximation consists in using thesame amplitudes as in the vacuum and convoluting themwith nuclear parton densities, such as the EPS [55],HKN [180] and nCTEQ [181] sets. Unlike the pro-ton case, the gluon distribution in a nucleus is poorlyknown, and it is one of the main differences among thenuclear PDF sets. In fact, possible measurements at theLHC of γ + c/b final states will help to investigate bothgluon and charm/bottom distributions in dense matter.

Likewise, similar studies can be carried out fordeuterium-gold collisions at RHIC. Since the Bjorken-x regions probed at RHIC and LHC are complementary,these measurements will help to discriminate among thenuclear parton distribution sets. As for the hard scat-tering, how to implement medium modifications, forboth light and heavy quark production, is still an openissue; moreover, collinear factorization is an assump-tion that has not yet been proved. The BDMPS andGunion–Bertsch approximations discussed above workwell only for soft/collinear emissions. Indeed, thereare prescriptions for hard/large-angle radiation, but athorough implementation and phenomenological analy-

sis on medium-modified hard scatterings is still missing.Convoluting possible medium-induced hard matrix ele-ments with nuclear parton densities will ultimately leadto cross sections fully including dense-matter effects.

6. Quarkonia as a Tool

6.1. Proton-Proton Collision Studies

Since the start of LHC operation, new experimentaldata on quarkonium production has revived the interestin understanding the production mechanisms of variousquarkonium states in hadronic collisions. All the mod-els describing various sources of onia in hadronic colli-sions share the common basis: the factorisation betweenthe hard collison subprocess and the parton-parton col-lision luminosity, calculated as a convolution of the par-ton distribution functions (PDFs).

Clearly, the range of accessible x1,2 depends on therapidity interval covered by the experiments. For char-monium at the Tevatron, with a partonic center-of-massenergy

√s � 3.5 GeV,

√s � 2 TeV, the CDF range is :

y � 0 ⇒ x1,2 � 1.8 × 10−3

while for D0:

− 1.6 � y � 1.6 ⇒ x1,2 � (0.36 − 8.9) × 10−3

Their values of x1,2 lie within the range where the PDFsare well-established. Hence the uncertainties on the par-ton luminosities at the Tevatron are fairly small.

At the LHC, not only is the energy higher by a factorof 3.5, but the rapidity coverage of the various experi-ments is also significantly wider, especially if one com-bines the results from ATLAS and CMS with those ofLHCb and ALICE. One get for ATLAS and CMS:

− 2.4 � y � 2.4 ⇒ x1 � (0.04 − 6.0) × 10−3

x2 � (6.0 − 0.04) × 10−3

while for LHCb:

2 � y � 5 ⇒ x1 � (4 − 80) · 10−3

x2 � (0.07 − 0.003) × 10−3

ALICE has complementary coverages (|y| < 1 & 2.5. <y < 4.0). For the kinematics of LHC experiments,the accessible x range of charmonium production mea-surements is up to three orders of magnitude below the“safe” value of 10−3. Processes usually used for de-termining gluon PDFs, such as jets, prompt photons oropen charm pairs, are for various reasons unlikely to beuseful at these extremely low x, leaving charmonium as

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 25

the only source of information on gluon PDFs in thisarea.

The smallest√

s value for bottomonium is about10 GeV, three times larger than for charmonium. Thisrestricts the “reach” of Υ studies to x1,2 values threetimes larger than those contributing to J/ψ. However,this is still significantly smaller than the currently acces-sible range, and thus should be useful as a consistencycheck and maybe also to test the Q2 evolution (provid-ing data with a higher Q2 for similar xB, which may behelpful to differentiate between a BFKL- and DGLAP-like evolution).

The main experimental difficulties include a reducedacceptance for J/ψ when both pT and |y| are small,and the necessity of suppressing non-prompt charmo-nia (which come from larger s). Theoretical complica-tions include proper and consistent treatment of intrinsicparton pT , initial-state radiation, and higher-order per-turbative effects, as well as the possibility of gluon re-combination at high densities. So concerted efforts fromtheorists and experimentalists will be needed to extendour measurements of the PDFs to much smaller x thanprior to the LHC. This is necessary for understandingthe dynamics of quarkonium hadronic production.

6.2. Nuclear Collision StudiesFrom statistical QCD we know that strongly inter-

acting matter undergoes a deconfinement transition toa new state, the quark-gluon plasma (QGP). The objec-tive of high energy nuclear collisions is to produce andstudy the QGP under controlled conditions in the lab-oratory. How then can we probe the QGP - what phe-nomena provide us with information about its thermo-dynamic state? Here the ultimate aim must be to carryout ab initio calculations of the in-medium behaviourof the probe in finite temperature QCD. Quarkonia maywell provide the best tool for this presently known, butin nuclear collisions other phenomena will also lead tomodified quarkonium production. As a consequence,parton distribution changes, parton energy loss and coldnuclear matter effects (absorption) on quarkonium pro-duction must be accounted for before any QGP studiesbecome meaningful. For the sake of definiteness, in thissection we shall refer to the non-QGP effects as normal,in contrast to the anomalous suppression (or enhance-ment) we want to look for.

Any modifications observed when comparingJ/ψ production in AA collisions to that in pp inter-actions thus have two distinct origins. Of primaryinterest is obviously the effect of the secondary mediumproduced in the collision - this is the candidate forthe QGP we want to study. In addition, however, the

presence of the “normal” initial and final state effectswill presumably also affect the production process andthe measured rates. This ambiguity in the origin of anyobserved J/ψ suppression will thus have to be resolved.

A second empirical feature to be noted is that theobserved J/ψ production consists of directly produced1S states as well as of decay products from χc(1P) andψ′(2S) production. The presence of a hot QGP affectsthe higher excited quarkonium states much sooner (atlower temperatures) than the ground states. This resultsin another ambiguity in observed J/ψ production - areonly the higher excited states affected, or do all statessuffer?

An ideal solution of these problems would be to mea-sure separately J/ψ, χc and ψ′ production first inpA (ordA) collisions, to determine the effects of cold nuclearmatter, and then measure, again separately, the produc-tion of the different states in AA collisions as functionof centrality at different collision energies.

Until such studies become available, we resort to amore operational approach, whose basic features are:• We assume that the J/ψ feed-down rates in pA and

AA are the same as in pp, i.e., 60 % direct J/ψ , 30% decay of χ(1P), and 10 % decay of ψ′(2S ).

• We specify the effects due to cold nuclear matterby a Glauber analysis of pA or dA experiments interms of σi

abs for i =J/ψ, χc, ψ′. This σiabs is not

meant to be a real cross section for charmoniumabsorption by nucleons in a nucleus; it is ratherused to parametrize all initial and final state nucleareffects, including shadowing/antishadowing, par-ton energy loss and pre-resonance/resonance ab-sorption.

• In the analysis of AA collisions, we then use σiabs

in a Glauber analysis to obtain the predicted formof normal J/ψ suppression. This allows us to iden-tify anomalous J/ψ suppression as the differencebetween the observed production distribution andthat expected from only normal suppression. Weparametrize the anomalous suppression throughthe survival probability

S i =(dNi/dy)exp

(dNi/dy)Glauber(14)

for each quarkonium state i.

With the effects of cold nuclear matter thus accountedfor, what form do we expect for anomalous J/ψ sup-pression? If AA collisions indeed produce a fully equi-librated QGP, we should observe a sequential suppres-sion pattern for J/ψ and Υ, with thresholds predicted

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3626

(quantitatively in temperature or energy density) by fi-nite temperature QCD [183, 184, 185, 186]. The result-ing pattern for the J/ψ is illustrated in Fig. 25.

1

ψJ/

S

urv

ival

Pro

bab

ilit

y

ε(2S) ε(1P)

(2S)(1P) (1S)

(1S)ε

Energy Density

Figure 25: Illustration of sequential J/ψ suppression.

Its consequences are quite clear. If, as present sta-tistical QCD studies indicate, the direct J/ψ survivesup to about 2 Tc and hence to ε ≥ 25 GeV/fm3, then allanomalous suppression observed at SPS and RHIC mustbe due to the dissociation of the higher excited statesχc and ψ′. The suppression onset for these is predictedto lie around ε � 1 GeV/fm3, and once they are gone,only the unaffected J/ψ production remains. Hence theJ/ψ survival probability for central AuAu collisions atRHIC should be the same as for central PbPb collisionsat the SPS.

A further check to verify that the observed J/ψ pro-duction in central collisions is indeed due to the un-modified survival of the directly produced 1S state isprovided by its transverse momentum behaviour. Initialstate parton scattering causes a broadening of the pT dis-tributions of charmonia [187, 188, 189]: the gluon fromthe proton projectile in pA collisions can scatter a num-ber of times in the target nucleus before fusing with atarget gluon to produce a cc. Assuming the gluon fromthe proton to undergo a random walk through the targetleads to

〈p2T 〉pA = 〈p2

T 〉pp + NAc δ0 (15)

for the average squared transverse momentum of the ob-served J/ψ. Here NA

c specifies the number of collisionsof the gluon before the parton fusion to cc, and δ0 thekick it receives at each collision. The collision numberNA

c can be calculated in the Glauber formalism; hereσabs has to be included to take the presence of cold nu-clear matter into account, which through a reduction ofJ/ψ production shifts the effective fusion point further“down-stream” [190].

In AA collisions, initial state parton scattering occursin both target and projectile and the corresponding ran-

dom walk form becomes

〈p2T 〉AA = 〈p2

T 〉pp + NAAc δ0, (16)

where now NAAc denotes the sum of the number of col-

lisions in the target and the projectile prior to parton fu-sion. It can again be calculated in the Glauber schemeincluding σabs. The crucial point now is that if the ob-served J/ψ’s in central AA collisions are due to undis-turbed 1S production, then the centrality dependence ofthe pT broadening is fully predicted by such initial stateparton scattering [186]. In contrast, any onset of anoma-lous suppression of the J/ψ would lead to a modifica-tion of the random walk form [190].

In Fig. 26 we summarize the predictions for J/ψ sur-vival and transverse momentum behaviour in AA col-lisions at SPS and RHIC, as they emerge from ourpresent state of knowledge of statistical QCD. Includedare some preliminary and some final data; for a discus-sion of the data analysis and selection, see Ref. [ 186].

0.25

0.50

0.75

1.00

1 2 3 4 5

In−In, SPS

Au−Au, RHIC, |y| < 0.35

Pb−Pb, SPS

Au−Au, RHIC, |y|=[1.2,2.2]

ψS(J/ )

ε (GeV/fm )3

10 10102 3

Ncoll

In−In, SPS

Au−Au, RHIC

Pb−Pb, SPS

5

10

[ <p > − <p > ] / T2

T2

δAA pp 0

Glauber (preliminary)

Figure 26: J/ψ survival and transverse momentum at SPS and RHIC.

We conclude that the present experimental results arecompatible with the present information from statisticalQCD. This was not the case previously, and such a con-clusion can be drawn today because of several changesin our theoretical and experimental understanding.

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 27

• Finite T lattice QCD suggests direct J/ψ suppres-sion at energy densities beyond the RHIC range;previous onset values were much lower (see, e.g.,Ref. [182]).

• SPS InIn data suggest an onset of anomalous sup-pression at ε � 1 GeV/fm3; previous onset valuesfrom PbPb and SU interactions were considerablyhigher, with ε � 2 − 2.5 GeV/fm3 (see, e.g., Ref.[191]).

• Within statistics, there is no further drop of theJ/ψ survival rate below 50 - 60 %, neither at RHICnor at the SPS; a second drop in very central SPSPbPb data (see, e.g., Ref. [191]) is no longer con-sidered viable.

6.2.1. J/ψ Enhancement by RegenerationIn this section we want to consider an alternative ap-

proach which can so far also account for the availabledata. The basic idea here is that the medium producedin nuclear collisions is not a QGP in full equilibrium butrather one which is oversaturated in its charm content.

A crucial aspect in the QGP argumentation of theprevious sections was that charmonia, once dissociated,cannot be recreated at the hadronization stage since theabundance of charm quarks in an equilibrium QGP isfar too low to allow this. The thermal charm quark pro-duction rate, relative to that of light quarks, is

ccqq

� exp{−mc/Tc} � 6 × 10−4, (17)

with mc = 1.3 GeV for the charm quark mass andTc = 0.175 GeV for the transition temperature. Theinitial charm production in high energy nuclear inter-actions, however, is a hard non-thermal process, andthe resulting c/c production rates grow with the number(Ncoll) of nucleon-nucleon collisions. In contrast, thelight quark production rate grows (at least in the presentenergy regime) essentially as the number (Npart) of par-ticipant nucleons, i.e., much slower. The initial charmabundance in AA collisions is thus much higher than thethermal value; we illustrate this in Fig. 27 for A = 200as function of the collision energy

√s. What happens

to this excess in the course of the collision evolution?The basic assumption of the regeneration approach

[192, 193, 194] is that the initial charm excess is main-tained throughout the subsequent evolution, i.e., that theinitial chemical non equilibrium will persist up to thehadronization point. If that is the case, a c from a givennucleon-nucleon collision can, at hadronization, com-bine with a c from a different collision (“off-diagonal”pairs) to recreate a J/ψ. This pairing provides a new sec-ondary statistical charmonium production mechanism,

10

10

10

10

10

10 10 102 3

s

thermal, T=175 MeV

−2

0

−4

−6

−8

SPS

RHICLHC

hard pQCD

−cc/qq−

Figure 27: Thermal vs. hard charm production.

in which the c and the c in a charmonium state havedifferent parents, in contrast to the primary dynamicalproduction in a pp collision. At sufficiently high energy,this mechanism will lead to enhanced J/ψ productionin AA collisions in comparison to the scaled pp rates.When should this enhancement set in?

In recent work [192, 193, 194], it is generally as-sumed that the direct J/ψ production is strongly sup-pressed for ε ≥ 3 GeV/fm3. This is evidently in contrastto the statistical QCD results discussed in the previoussections; however, we recall the caveat that the tempera-ture dependence of the charmonium widths is so far notknown. Moreover, it is of course always possible thatthe medium produced in nuclear collisions is quite dif-ferent from the quark-gluon plasma of statistical QCD.

Next, it is assumed that the regeneration rate is de-termined by statistical combination in a QGP in kineticequilibrium, with or without wave function corrections.In other words, if a c and a c meet under the right kine-matic conditions, they are taken to form a J/ψ. An evo-lution towards a QGP in chemical equilibrium wouldalso allow annihilation at this point.

To account for the J/ψ production rates observed atRHIC, it is then assumed that the new statistical produc-tion just compensates the proposed decrease of the di-rect primary 1S production, as illustrated in Fig. 28. Atthe LHC, with much higher energy densities, one shouldthen observe a J/ψ enhancement relative to the rates ex-pected from scaled pp results.

We thus have to find ways of distinguishing betweenthe two scenarios discussed here: the sequential sup-pression predicted by an equilibrium QGP or a strongerdirect suppression followed by a J/ψ regeneration in amedium with excess charm. Fortunately the basic pro-duction patterns in the two cases are very different, so

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–3628

J/

P

rod

uct

ion

Pro

bab

ilit

yψ

1

Energy Density

thermal dissociation

statistical regeneration

Figure 28: Illustration of regeneration of J/ψ production.

that one may hope for an eventual resolution.The overall J/ψ survival probability in the two cases

is illustrated in Fig. 29. Sequential suppression providesa step-wise reduction: first the higher excited charmo-nium states are dissociated and thus their feed-downcontribution disappears; at much higher temperature,the J/ψ itself is suppressed. Both onsets are in principlepredicted by lattice QCD calculations. In the regenera-tion scenario, the thermal dissociation of all “diagonal”J/ψ production is obtained by extrapolating SPS data tohigher energy densities. The main prediction of the ap-proach is therefore the increase of J/ψ production withincreasing energy density. Ideally, the predictions forthe LHC are opposite extremes, providing of course thathere the feed-down from B-decay is properly accountedfor.

J/

P

rod

uct

ion

Pro

bab

ilit

yψ

1

Energy Density

statistical regeneration

sequential suppression

Figure 29: J/ψ survival: sequential suppression vs. regeneration.

The expected transverse momentum behaviour in thetwo cases is also quite different. In the region of fullJ/ψ survival, sequential suppression predicts the nor-mal random walk pattern specified through pA stud-ies; the eventual dissociation of direct J/ψ states thenleads to an anomalous suppression also in the aver-age p2

T [190]. Regeneration alone basically removesthe centrality dependence since the different partners

come from different collisions. It is possible to intro-duce some small centrality dependence [195], but therandom walk increase is essentially removed. The re-sulting behaviour is schematically illustrated in Fig. 30.More generally, the quarkonium momentum distribu-tions, whether transverse or longitudinal, should in theregeneration scenario be simply a convolution of thecorresponding open charm distributions; this providesa further check [195].

[ <p > − <p > ] / T2

T2

δAA pp 0

5

10

Centrality

sequential suppression

statistical regeneration

Figure 30: pT -behaviour: sequential suppression vs. regeneration.

6.2.2. Conclusions

• In statistical QCD, the spectral analysis of quarko-nia provides a well-defined way to determine tem-perature and energy density of the QGP.

• If nuclear collisions produce a quark-gluon plasmain equilibrium, the study of quarkonium produc-tion can provide a direct way to connect experi-ment and statistical QCD.

• For a QGP with surviving charm excess, off-diagonal quarkonium formation by statistical com-bination may destroy this connection and insteadresult in enhanced J/ψ production.

7. New observables in quarkonium production

In order to better understand the mechanisms respon-sible for heavy quarkonium production, it is now essen-tial to introduce new observables. The theoretical un-certainties on the predicted yields are too large to drawany strong conclusions on production models. More-over, polarization studies are known to be experimen-tally challenging and not always possible over the fullphase-space region even if the yield is otherwise mea-sured. The LHC will certainly provide new informationon the yields and polarizations. In addition, the LHCis well positioned to make unique new measurements

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 29

previously unavailable due to unsufficient luminosity,center-of-mass energy, detector resolution or even man-power.

7.1. Hadronic activity around quarkoniumThe first observable that we discuss, hadronic activ-

ity around quarkonium [196], is, in fact, not completelynew. Indeed, UA1 compared their charged-track dis-tributions with Monte Carlo simulations of a J/ψ com-ing from a B decay and a J/ψ coming from a χc de-cay [197, 198]. In the early nineties –before the Teva-tron results– χc feed-down was still expected to be themajor source of prompt J/ψ production. However, ifwe assume either that production proceeds through COtransitions or through CS transitions at higher-orders,we now expect more complex distributions, even for theprompt yield. It is therefore not clear how accuratelysuch methods – recently revived by STAR in [13] – candetermine the B-feeddown to J/ψ, other than with mea-surements of displaced vertices typical of B decays. In-stead, the hadronic activity around quarkonium couldbe a good discriminant between CO and CS contribu-tions to quarkonium production since gluon emissionduring CO transitions would increase the hadronic ac-tivity. This study is, however, difficult to carry out inpractice [196].

7.2. Associated productionWe therefore urgently need more observables easier

to predict that test the many production models avail-able [107, 109]. We argue that the study of associatedproduction channels, ψ + cc and Υ + bb, first in ppcollisions, then in pA and AA, fills both these require-ments. These reactions are potentially very interestingsince the LO description already shows leading pT be-haviour. We expect that higher-QCD corrections willbe less important and the cross section will thus be lesssensitive to the renormalisation scale, allowing for moreprecise predictions.

Further motivation for such studies is the amazinglylarge fraction of J/ψ produced in association with an-other cc pair at B-factories. For instance, the Belle col-laboration first found [199]

σ (e+e− → J/ψ + cc)σ (e+e− → J/ψ + X)

= 0.59−0.13+0.15 ± 0.12. (18)

More recently, the Belle collaboration reported newmeasurements [37]:

σ (J/ψ + X) = 1.17 ± 0.02 ± 0.07 pb ,

σ (J/ψ + cc) = 0.74 ± 0.08+0.09−0.08 pb ,

σ (J/ψ + Xnon cc) = 0.43 ± 0.09 ± 0.09) pb,

(19)

which confirm that associated J/ψ+cc production is thedominant production mechanism at B factories.

Until now, it is unknown whether such a high associ-ated fraction also holds for hadroproduction. Analysesat the Tevatron (CDF and D0) and at RHIC (PHENIXand STAR) are feasible, in addition to the LHC. Thepredicted Tevatron Run II integrated cross sections at√

s = 1.96 TeV are significant [23] :

σ(J/ψ + cc) × Br(�+�−) � 1 nb,σ(Υ + bb) × Br(�+�−) � 1 pb.

(20)

Neglecting the likely reduction of the CO matrix ele-ments needed to comply with the e+e− results and in-duced by higher-order QCD corrections to the color-singlet contributions (see section 2), the integratedcross sections for associated J/ψ + cc production werefound [200] to be dominated by the CS part. This is alsothe case for the pT distribution up to at least 5 GeV forψ and 10 GeV for Υ. This clearly means that such ob-servables directly probe the CS mechanism. For most ofthe other observables, it is not as clear whether the COcontribution dominante over the CS one and they cannotbe regarderd as a clean probe of CS constributions dueto the inherent uncertainty from the CO yield.

If the effect of CO transitions is indeed negligiblefor inclusive Υ production, Υ’s produced in associationwith a bb pair would be unpolarised at the LHC, inde-pendent of pT .

Besides discriminating between the CO and the CStransitions, the ψ yield in association with a cc shouldshow an a priori completely different sensitivity to theχc feed-down than the inclusive yield. The same holdstrue for Υ+bb relative to χb feed-down. The CS P-stateyield is expected to be smaller than the S -state one sincethey are suppressed by powers of the relative velocity v.Contrary to the inclusive case, no additional gluon isneeded to attach to the heavy quark loop to produce theψ (or Υ) compared to P-states.

For the CO transitions, associated production of χc +

cc can occur via gg → gg where both final-state gluonssplit into cc pairs. One of them then hadronizes intoa χc via a CO transitions. This contribution is certainlysuppressed up to pT � 20 GeV. At larger pT , a dedicatedcalculation is needed. However, this mechanism couldbe easily disentangled from the CS contributions sinceboth c quarks are necessarily emitted back to back fromthe χc and thus to the J/ψ.

The non-prompt signal would originate as usual fromgg → bb, where one b quark decays into a ψ + X. Usu-ally, hadronisation of the b produces the ψ with light

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quarks only. This means that we have a single c quarkin the event, produced from the decay of the recoiling bquark and therefore back to back from the ψ. The non-prompt signal could then be simply suppressed downby searching for a D meson near the ψ. It is possiblethat hadronisation of the b produces both the ψ and aD meson. In this case, kinematic cuts would not helpsuppress the non-prompt yield. Fortunately, this finalstate is a priori suppressed compared to the first caseand even further suppressed relative to the direct yield.Indeed, there is no gain in the pT dependence since boththe gg → bb and gg → ψ + cc cross sections scale likep−4

T . A cross check sizing up the non-prompt yield witha displaced vertex measurement would be instructive.

Associated production has also been studied in directγγ collisions in ultraperipheral collisions (UPC) [201].At least for direct γγ collisions, associated production isthe dominant contribution to the inclusive rate for pT ≥2 GeV/c.

To conclude, studies can be carried on by detectingeither the “near” or “away” heavy-quark with respectto the quarkonia. There are, of course, different waysto detect the D, B, or b-jet, ranging from a displacedvertices to detection of semileptonic decays to e or μ.

As mentionned in section 4, associated production ofJ/ψ or Υ with a prompt photon may also be investigatedat the LHC. Interestingly, contrary to the inclusive case,the C = +1 CO should impact the large pT region, whileC = −1 CO the small and mid pT region. The NLO CScontribution was recently studied [127] and, contrary tothe inclusive case, it was shown that for this process theCO and CS induced yield should be similar, even withthe largest possible CO matrix elements. At NNLO, theCS yield is expected to be further enhanced [128] andto dominate over the CO yield. The measurements ofJ/ψ and Υ production associated with a direct photon athadron colliders could thus be an important test of thetheoretical treatment of heavy-quarkonium production.

The background to these processes should also betaken into account. The Quarkonium event genera-tor Madonia [202], imbedded in Madgraph [203], willsurely be of a great help in achieving this. In any case,we hope that such measurements would provide clearinformation on the mechanisms at work in quarkoniumproduction.

8. Conclusion

Quarkonium production measurements in pp colli-sions have motivated many theoretical investigations.However, despite advances, there is still no clear pictureof the quarkonium hadroproduction mechanism. Such

a mechanism should be able to explain both the crosssection and the polarization measurements at the Teva-tron and RHIC, as well as comparable measurements atB factories and lepton-hadron colliders. Presently, wehave several different approaches at our disposal, suchas the Color Singlet Model (CSM), in which the QQis produced color neutral at short distances, and Non-Relativistic QCD (NRQCD), where quarkonium pro-duction can also proceed via creation of color-octet QQpairs, via the Color Octet Mechanism (COM). These ap-proaches have both advantages and disadvantages.

NRQCD has successfully explained the excess incharmonium production reported by the CDF Collab-oration, orders of magnitude larger than the LO CSM.However so far it fails to provide a consistent descrip-tion of production and polarization in pp collisions andthe rates at B factories.

Higher order corrections in αs have only recentlybeen calculated. The CS corrections at high pT are verylarge given that the corrections open new productionchannels which are relevant at high pT . On the contrary,CO calculations show that the cross sections do not in-crease much when these corrections are taken into ac-count since NLO CO contributions do not open any newchannels. The contributions of the NLO CS correctionsreduce the discrepancy between the CSM cross sectionsand the CDF data, but still fall too steeply at high pT todescribe this region successfully. The NNLO� contribu-tion may be able to fill the gap between calculations andhigh pT data. At RHIC, the high pT STAR data seemsto favor the COM over the CSM, while at low pT thePHENIX data are well reproduced by both approaches.It is, however, worth noting that little is known aboutfeed down contributions at RHIC, while there does notexist any NLO theoretical predictions for the χc yield,in either approach.

In addition, the LO NRQCD calculation predicts asizable transverse polarization rate for large pT J/ψwhereas the Tevatron CDF measurement at Fermilabdisplays a slight longitudinal polarization at large pT

for the prompt yield. This problem is still presentin calculations at NLO, since these corrections onlyslightly change the pT dependence of J/ψ produc-tion rate and polarization with respect to the LOcalculations. However, the CSM results drasticallychange from transverse-polarization dominance at LOto longitudinal-polarization dominance at NLO, nearlyin agreement with the data on J/ψ polarization producedin pp collisions both at the Tevatron and RHIC, if thepolarization of the J/ψ from χc feed down is assumed.

In order to solve this puzzle, improved measurementsare needed. So far, most experiments have presented

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results based on a fraction of the physical informationderivable from the data: only one polarization frameis used and only the polar projection of the decay an-gular distribution is studied. These incomplete resultsprevent model-independent physical conclusions. In theforthcoming LHC measurements, it is important to ap-proach the polarization measurement as a multidimen-sional problem, determining the full angular distributionin more than one frame.

The feed downs from more massive states, such ashigher-mass quarkonium states, cannot yet be taken intoaccount in most of the calculations. While there areCDF measurements of direct production, the χc feeddown can significantly influence the polarization of theprompt J/ψ yield. A better way to avoid the feed-downproblem is to study ψ′ and Υ(3S ) where no importantfeed down from higher excited states exist.

The behavior of quarkonium production in pA col-lisions due to Cold Nuclear Matter (CNM) effects isnot yet understood. Puzzling features in proton-nucleusdata put forward new aspects of charmonium physics innuclear reactions, namely the role of cold nuclear mattereffects (CNM). Two CNM effects are considered to beof particular importance: the modification of the initialparton distributions (PDFs) due to the nuclear environ-ment, an initial-state effect known as shadowing; andthe breakup of cc pairs after multiple scatterings withthe remnants of target nucleus, referred to as the nuclearabsorption.

Parton shadowing in the target nucleus may suppress(or enhance, in case of antishadowing) the probabilityof producing a J/ψ. Its effect depends on the kinemat-ics of the cc pair production. The theoretical expecta-tions for gluon shadowing are quite diverse. A weakshadowing effect was predicted by the dipole approachand in some analysis of DIS data such as the one de-veloped by deFlorian and Sassot at leading and next-to-leading order – the nDS and nDSg parameterizations–. However, strong gluon shadowing and antishadowingwas obtained in the EKS98, EPS08, and EPS09 param-eterizations by Eskola and collaborators. We note thatsome pA data were included in the EPS08 and EPS09analyses. The nDSg and EKS98 parameterizations arecompatible for x < 10−3.

Secondly, there is the effect of the nuclear absorp-tion. The strength of the interaction of the evolving ccpair with the target nucleons can break up the pair andconsequently suppress the J/ψ yield. The intensity ofthis effect may also depend on the quantum states of thecc pair at the production level (color octet or color sin-glet), and on the kinematic variables of the pair. Indeed,a colorless cc pair created in a hard reaction is not yet

charmonium since it does not have a fixed mass. It takestime to disentangle ground state charmonium from itsexcitations, t f ∼ 1/(m2

ψ′ − m2J/ψ). This time scale is in-

terpreted as the formation time of the charmonium wavefunction. At low energies, this time is shorter than themean nucleon spacing in a nucleus so that the forma-tion process can be treated as instantaneous. At muchhigher energies, the formation time is long and the ini-tial size of the cc dipole is ”frozen” by Lorentz timedilation while propagating through the nucleus.

According to the above arguments, at high energy,the heavy state in the projectile should undergo coherentscattering off the nucleons of the target nucleus, in con-trast to the incoherent, longitudinally ordered scatteringthat takes place at low energies. This should lead to adecrease of σabs

J/ψ with increasing energy√

sNN . Compi-lation and systematic study of many experimental dataindicate that σabs

J/ψ appears either constant or decreasingwith energy, following the most recent theoretical ex-pectations.

The energy regime recently opened up by the adventof the LHC offers new possibilities. Clearly pA dataat the LHC are essential to investigate various physicseffects, in particular nuclear shadowing in a still unex-plored x-range. The final-state interaction of quarkoniawith CNM is another attractive topic. Due to the ex-pected very short overlap time of the heavy-quark pairwith nuclear matter, one could expect its influence onthe still almost point-like cc to be rather limited. How-ever, these considerations are still very qualitative anddeeper theoretical studies are clearly necessary.

The study of open heavy flavour production in ppand pA collisions is tightly connected to the process ofquarkonia (hidden flavor) production. It offers a goodbasis to establish fundamental parameters for quarko-nium calculations, together with an outstanding frame-work to test fundamental concepts, such as perturbativeQCD, factorization and non-perturbative power correc-tions. Because heavy quarks are massive, the produc-tion cross section can be calculated in perturbative QCDdown to pT = 0 at the parton level.

However, differential distributions and event shapesexhibit large logarithmic contributions, typically cor-responding to soft or collinear parton radiation, whichneed to be resummed to all orders. Furthermore,dead-cone effects suppress gluon radiation around theheavy-quark direction, which has relevant phenomeno-logical implications on both parton- and hadron-levelspectra. As far as heavy-hadron production is con-cerned, one can model non perturbative effects bymeans of hadronization models such as the Lund-basedstring models, which are implemented within the frame-

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work of Monte Carlo generators HERWIG, PYTHIA,MC@NLO, etc. Multi-purpose generators have beenavailable for several years for lepton/hadron collisionsin the vacuum and some have been lately modified toinclude the effects of dense matter.

In order to promote the formalism used to describeopen heavy flavors to pA and ultimately AA collisions,one has to introduce medium-modification effects. Inparticular, one of the most striking observations ofheavy-ion collisions is the jet-quenching phenomenon,namely the suppression of hadron multiplicity at largetransverse momentum with respect to pp processes. Inthe case of heavy hadrons, the measured suppression isexpected to be lower than that of light-flavor mesons,due to the dead-cone effect. So far, suppression ofheavy-flavored mesons in pA or AA collisions has onlybeen measured through leptons (non-photonic electronsand single muons), i.e., the leptons from semi leptonicdecays of heavy-flavored hadrons. Surprisingly, the en-ergy loss observed through heavy-flavor leptons is sub-stantial already at moderate pT of ∼3 GeV/c. Severalmechanisms to describe heavy-flavor energy loss in thedense medium have been proposed. Most prominentare collisional and radiative energy loss, typically calcu-lated in the weak-coupling regime. However, the mag-nitude of the observed suppression at RHIC is hard toaccommodate in these models. Recent attempts, assum-ing strong coupling between the heavy-flavor mesonsand the dense medium and based on AdS/CFT corre-spondence lead to higher suppression factors. Furtherstudies as well as experimental data are needed beforeany conclusions can be drawn. Future data from theLHC will possibly shed light on the issue of the energyloss. It will be very useful to have more exclusive probessuch as azimuthal correlations or tagged c- or b-flavoredjets.

Another crucial issue in heavy-flavor phenomenol-ogy concerns heavy-quark parton distributions in pro-tons and nuclei. In fact, processes with the productionof heavy quarks are fundamental to constrain the PDFs.In particular, the production of a direct photon accom-panying a heavy quark at hadron colliders is an impor-tant process, also relevant to constrain the heavy-quarkdensity. As it escapes confinement, a photon can be ex-ploited to tag the hard scattering; also, its transverse mo-mentum distribution gives meaningful information onthe heavy-quark production process and PDF.

The LO/NLO calculations for γ+ c/b production canbe extended to pA collisions, e.g. proton-lead processesat the LHC. To a first approximation, the process can becalculated by convoluting the vacuum matrix elementswith nuclear PDFs. While the gluon distribution in the

proton is rather well constrained, it is poorly knownin the nucleus, hence large discrepancy between gluonshadowing parametrizations. In fact, possible measure-ments at the LHC of γ + c/b final states will help toinvestigate both gluon and charm/bottom distributionsin dense matter. Since the Bjorken-x regions probedat RHIC and LHC are complementary, these measure-ments will help to discriminate among the nuclear par-ton distribution sets.

Lattice QCD calculations predict that, at sufficientlylarge energy densities, hadronic matter undergoes aphase transition to a plasma of deconfined quarks andgluons (QGP). Considerable efforts have been investedin the study of high-energy heavy-ion collisions to re-veal the existence of this phase transition and to studythe properties of strongly interacting matter in the newphase, in view of e.g. improving our understanding ofconfinement, a crucial feature of QCD. The study ofquarkonium production and suppression is among themost interesting investigations in this field. Calcula-tions indicate that the QCD with binding potential isscreened in the QGP phase, the screening level increas-ing with energy density. Given the existence of severalquarkonium states of different binding energies, it is ex-pected that they will be consecutively dissolved (intoopen charm or bottom mesons) above certain energydensity thresholds.

One of the objectives of high energy nuclear colli-sions is to produce and study the QGP under controlledconditions in the laboratory. How then can we probethe QGP - what phenomena provide us with informa-tion about its thermodynamic state? Here the ultimateaim must be to carry out ab initio calculations of thein-medium behaviour of the probe in finite tempera-ture QCD. Quarkonia may well provide the best toolpresently known for this. However, quarkonium pro-duction will also be modified in nuclear collisions byother phenomena. Parton distribution modifications,parton energy loss and cold nuclear matter effects onquarkonium production must be accounted for beforeany QGP studies become meaningful.

Any modifications observed when comparingJ/ψ production in AA collisions to that in pp interac-tions thus have two distinct origins. Of primary interestis obviously the effect of the medium produced in thecollision - this is the candidate for the QGP we wantto study. In addition, however, the presence of the“normal” initial and final state effects will presumablyalso affect the production process and the measuredrates. This ambiguity in the origin of any observedJ/ψ suppression will thus have to be resolved.

A second empirical feature to be noted is that the

Z. Conesa del Valle et al. / Nuclear Physics B (Proc. Suppl.) 214 (2011) 3–36 33

observed J/ψ production consists of directly produced1S states as well as of decay products from χc(1P) andψ′(2S) production. The presence of a hot QGP affectsthe higher excited quarkonium states much sooner (atlower temperatures) than the ground states. This resultsin another ambiguity in observed J/ψ production - areonly the higher excited states affected, or do all statessuffer?

Ideally, one would measure J/ψ, χc and ψ′ produc-tion separately first in pA (or dA) collisions, to deter-mine the effects of cold nuclear matter, and then, againseparately, in AA collisions as a function of collisioncentrality at different center-of-mass energies.

To deepen our understanding of heavy-quarkoniumproduction mechanisms in pp and pA, we must now be-gin to study new observables such as associated produc-tion. As we have discussed above, theoretical uncertain-ties on the yields are too large to draw any strong con-clusions in favour or disfavour of one model or the other.In addition, polarization studies are in practice chal-lenging and not always possible in the complete phase-space region where one can measure the yield. Much isexpected from the LHC on the latter two observables.Nonetheless, one should also use the LHC for exper-imental investigations of new measurements, not pos-sible previously. These observables can test the manyproduction models available, in particular the CSM, theCOM, the CEM and the kT factorization. The study ofassociated production, ψ+ cc, Υ+ bb, ψ+ γ, . . . , first inpp collisions, then in pA and AA, should be very fruit-ful.

Acknowledgments

The authors appreciate and acknowledge support for thisworkshop and for the work on this document provided, in partor in whole, by

• the French IN2P3/CNRS;

• the ReteQuarkonii Networking of the EU I3 HadronPhysics 2 program;

• Xunta de Galicia under contract (2008/012);

• the Spanish Ministerio de Ciencia under contractFPA2008-03961-E;

• the U.S. Department of Energy under the contracts DE-AC52-07NA27344 (R. V.), DE-AC02-07CH11359 (V.P.);

• the U.S. National Science Foundation under grant NSFPHY-0555660 (R. V.);

• the German Research Foundation (DFG) under grantPI182/3-1 (B. K.);

• the Fondecyt (Chile) under grant 1090291;

• the Conicyt-DFG under grant No. 084-2009;

• the Georgian National Science Foundation grantGNSF/ST08/4-421.

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