Probing nuclear parton densities and parton energy loss processes through photon + heavy-quark jet production in p-A and A-A collisions
PProbing nuclear parton densities and parton energyloss processes through photon + heavy-quark jetproduction in p-A and A-A collisions
Tzvetalina Stavreva , Fran¸cois Arleo and Ingo Schienbein Laboratoire de Physique Subatomique et de Cosmologie, UJF, CNRS/IN2P3,INPG, 53 avenue des Martyrs, 38026 Grenoble, France Laboratoire d’Annecy-le-Vieux de Physique Th´eorique (LAPTH), UMR5108,Universit´e de Savoie, CNRS, BP 110, 74941 Annecy-le-Vieux cedex, FranceE-mail: [email protected] , [email protected] , [email protected] Abstract.
We present a detailed phenomenological study of the associatedproduction of a prompt photon and a heavy-quark jet (charm or bottom) in proton-nucleus (p-A) and nucleus-nucleus (A-A) collisions. The dominant contribution to thecross-section comes from the gluon–heavy-quark (gQ) initiated subprocess, makingthis process very sensitive to the gluon and the heavy quark nuclear parton densities.We show that the future p-A data to be collected at the LHC should allow one todisentangle the various nPDF sets currently available. In heavy-ion collisions, thephoton transverse momentum can be used to gauge the initial energy of the massiveparton which is expected to propagate through the dense QCD medium producedin those collisions. The two-particle final state provides a range of observables (jetasymmetry, photon-jet pair momentum, among others), through the use of which abetter understanding of parton energy loss processes in the massive quark sector canbe achieved, as shown by the present phenomenological analysis carried out in Pb-Pbcollisions at the LHC.
1. Introduction
The production of a prompt photon in association with a heavy-quark jet provides uswith the opportunity to study the structure of the proton and the nucleus as well asthe mechanisms of heavy quark energy loss. The information obtained depends on thecollision type. • For p − ¯ p collisions (at the Tevatron) it was shown in [1] that this process is sensitiveto the charm/bottom PDF, and therefore can provide information and constraintson the presence of intrinsic charm/bottom (IC/IB) in the proton [2]. • In p − A collisions (at RHIC and the LHC) γ + Q production can be used to constrainthe gluon nuclear PDF (nPDF), [3], which presently carries a large error to it, aswill be shown in more detail in Section 2. One should underline that knowing theprecise nPDFs is necessary for obtaining reliable predictions in A − A collisions. • In A − A collisions the study of prompt photons and heavy quarks provides anideal tool for investigating the energy lost by heavy partons in the hot medium(Section 3). As an electromagnetic probe the photon is expected to traverse the a r X i v : . [ h e p - ph ] S e p robing nPDFs and parton energy loss through γ + Q production γ + c and γ + b production providesaccess to the mass hierarchy of parton energy loss.
2. Constraining the gluon nPDF through γ + Q production x R g P b nCTEQEPS09HKN07Nuclear Modifications for g p/Pb (x,Q=50 GeV) Figure 1. a) R P bg ( x, Q = x √ S/ ∼ p T ) for nCTEQ decut3, decut3g3, decut3g9,EPS09 + error band, HKN07 + error band. The box exemplifies the x -region probedat the LHC. b) R P bg ( x, Q = x √ S/ ∼ p T ) for different nCTEQ decut3, decut3g1-decut3g9.
50 100 p T g (GeV) R p P b g + c nCTEQ decut3nCTEQ decut3g3nCTEQ decut3g9EPS09HKN07 p+Pb-> g +c+X / p+p-> g +c+X (cid:214) (cid:190) S = 8800 GeV x R g P b nCTEQ decut3 nCTEQ decut3g3nCTEQ decut3g9EPS09HKN07 Nuclear Modifications for g p/Pb (x, Q = x (cid:214) (cid:190)
S / 2 ~ p T ) Figure 2. a) R γ + cpP b at LHC within ALICE EMCal acceptances, using nCTEQ decut3,decut3g3, decut3g9, EPS09 + error band, HKN07 + error band. b) R P bg ( x, Q = x √ S/ ∼ p T ) in the x region probed at the LHC. Unlike the PDF for a gluon inside a free proton, the nuclear gluon PDF is largelyunconstrained due to the dearth of available data. Currently, only the NMC structurefunction data ( F D ( x, Q ) and F Sn /F C ( x, Q )) impose weak constraints on the gluonnPDF in the x -range 0 . (cid:46) x (cid:46) . ‡ , so that a precise determination is not possible.This large uncertainty in g A ( x, Q ) is presented by the nuclear modification factor to thegluon nPDF, R P bg ( x, Q ) = g p/P b ( x, Q ) /g p ( x, Q ), in Fig.1a) where a comparison betweenthe different nuclear PDF sets currently available (nCTEQ [4, 5, 6], HKN07 [7], EPS09[8]) is shown. Fig.1b) furthermore shows different fits with equally good χ , whose spreadrepresents a lower limit on the uncertainty associated with the nCTEQ set § . The needfor measurements of processes sensitive to the gluon nPDF is evident. Here we pointout that γ + Q production is an excellent probe of g A ( x, Q ), and can serve as one suchprocess, as evidenced by Fig.9 and Fig.10 in Ref. [3]. Fig.9 shows the differential cross-section for both γ + c and γ + b at √ s NN = 8 . p − P b collisions at ALICE EMCalacceptances. The anticipated event rate (before experimental efficiencies) is sufficiently ‡ The EPS09 fit also includes data on π production at RHIC. § These fits are available at http://projects.hepforge.org/ncteq/ . robing nPDFs and parton energy loss through γ + Q production N pP bγ + c = 11900, N pP bγ + b = 2270). In Fig.10 the subprocesscontributions to dσ pP bγ + c /dp T γ are presented, with g − Q and g − g being the dominantones; for more details see Ref. [3]. The sensitivity to the gluon nPDF further shows upin the nuclear modification factor to the cross-section, R γ + cpP b = dσ/dp Tγ ( p Pb → γ + c + X ) dσ/dp Tγ ( pp → γ + c + X ) inFig.2a), when compared to R P bg ( x, Q ) in Fig.2b). It can clearly be seen by juxtaposingFig.2a) and Fig.2b) that R γ + cpP b follows closely R P bg in the region of x probed at the LHCfor each nPDF set. Therefore we can conclude that this process is an excellent candidatefor constraining the gluon nuclear distribution as a measurement of the prompt photon+ heavy-quark jet process with appropriately small error bars will be able to distinguishbetween the three different nPDF sets.
3. Heavy Quark Energy Loss in γ + Q Production
The study of two-particle final states in heavy-ion collisions provides a much moreversatile access to quantifying the energy loss in the Quark Gluon Plasma (QGP), ascompared to the study of a single inclusive process. This is further the case if one ofthe final-state particles is medium insensitive, in particular the study of γ + jet [9] or γ + hadron [10] correlations helps to evaluate the amount of quenching experienced byjets as they traverse the medium while the photon’s energy serves as a gauge of the initialparton energy. Here, the focus on the associated production of γ + heavy-quark jet canhelp clarify the energy loss in the heavy quark sector. Currently, due to the dead coneeffect a definite hierarchy of the energy loss is expected, (cid:15) q > (cid:15) c > (cid:15) b , with the heavierquarks losing less energy [11]. This hierarchy remains to be clarified experimentally,and prompt photon + heavy-quark jet production is a natural and promising processfor this verification.In Fig.3a) we show the effects of the medium on the leading order (LO) differentialcross-section versus p T γ and p T Q . The energy loss of the heavy quark, (cid:15) Q , is computedon an event by event basis, with the use of the quenching weight obtained perturbatively[12]. The following parameters describing the medium have been used ˆ q = 6 .
25 GeV/fm and ω c = 50 GeV. The effects show up in the difference between dσ γ + c ; med dp TQ and dσ γ + c ; vac dp TQ (cid:107) .However, we need not limit ourselves to only one-particle observables as the informationobtained by investigating the correlations of the two final state particles (e.g. photon-jet energy asymmetry, momentum imbalance, photon-jet pair momentum [10]) providesa much better handle on the amount of energy loss. In Fig.3b) we focus in moredetail on the differential cross-section as a function of the photon-jet pair momentum, q ⊥ = | (cid:126)p T γ + (cid:126)p T Q | . At LO accuracy, for the direct contribution one has q ⊥ (cid:39) (cid:15) Q , whereasfor the fragmentation contribution the shift between the q T spectrum in vacuum versusthe one in medium is given by < (cid:15) Q > . Unfortunately when one investigates two-particleobservables for this process at LO, only the fragmentation contributions in medium andin vacuum can be compared, as due to the kinematic constraints the direct componentin vacuum is non-zero only when q T = 0. In Fig.4 the fragmentation contributions inmedium to γ + c and γ + b normalized to the p − p case are shown. Clearly ∆ E c > ∆ E b at (cid:107) The small difference between dσ med p Tγ and dσ vac p Tγ at low p T is due to experimental cuts. robing nPDFs and parton energy loss through γ + Q production q T , while as q T grows the difference disappears, as the quenching weight dependson m/E , which becomes similar for charm and bottom quarks at large q T . However,definite conclusions can only be drawn after a study at NLO accuracy [13].
50 100 150 p T g (p TQ ) [GeV] d s / dp T [ pb / G e V ] p T g no ELp T g ELp TQ no ELp TQ EL g +c at LO (cid:214) (cid:190) S = 5.5 TeV, CTEQ6.6M , no Isolation|y Q, |, |y g |<0.2, p T g , p TQ >12 GeVR = 1000, w c =50 GeV 20 40 60 q T d s / dq T g +c LO no EL g +c LO EL g +c LO EL - direct g +c LO EL - fragm g +b LO no EL g +b LO EL g +b LO EL - direct g +b LO EL - fragm (cid:214) (cid:190) S = 5.5 TeV, CTEQ6.6M , no Isolation|y Q, |, |y g |<0.2, p T g ,p TQ >12 GeVR = 1000, w c =50 GeV g +c g +b (x0.01) Figure 3. a) The LO γ + c differential cross-section versus: p T γ in vacuum (solidline), in medium (dotted line); p T Q in vacuum (dashed line), in medium (dashed-dotted line). b) The LO differential cross-section versus q ⊥ for γ + c and γ + b , showingthe fragmenation and direct contributions in vacuum and in medium.
20 40 60 q T / R AA q T g +b g +c LO Fragmentation Contribution (cid:214) (cid:190)
S = 5.5 TeV, CTEQ6.6M , no Isolation|y Q, |, |y g |<0.2, p T g ,p TQ >12 GeVR = 1000, w c =50 GeV Figure 4. a) The ratio of the LO vacuum fragmentation contribution to the mediumfragmentation contribution for γ + c (solid line) and γ + b (dashed line).
4. Conclusion
Prompt photon + heavy-quark jet production has proven to be an extremely useful andversatile process. It can be employed to constrain the heavy quark PDFs in hadron-hadron collisions, while measurements in p − A collisions can help constrain the gluonnPDF. In heavy-ion collisions it can help estimate the quenching experienced by aheavy-quark jet, while also providing access to the mass hierarchy of parton energy loss. References [1] Stavreva T and Owens J F 2009
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