Gamma-Jet Tomography of Quark-Gluon Plasma in High-Energy Nuclear Collisions
aa r X i v : . [ h e p - ph ] S e p Gamma-Jet Tomography of Quark-Gluon Plasma in High-EnergyNuclear Collisions
Hanzhong Zhang a , b J. F. Owens c Enke Wang a , b and Xin-Nian Wang d a Institute of Particle Physics, Huazhong Normal University, Wuhan 430079, China b Key Laboratory of Quark and Lepton Physics (Huazhong Normal University), Ministry of Education, China c Physics Department, Florida State University, Tallahassee, Florida 32306-4350, USA d Nuclear Science Division, Lawrence Berkeley Laboratory, Berkeley, California 94720, USA
Abstract
Within the next-to-leading order (NLO) perturbative QCD (pQCD) parton model, suppression ofaway-side hadron spectra associated with a high p T photon due to parton energy loss is shownto provide a complete tomographic picture of the dense matter formed in high-energy heavy-ion collisions at RHIC. Dictated by the shape of the γ -triggered jet spectrum in NLO pQCD,hadron spectra at large z T = p hT / p γ T > ∼ γ -triggered jets, whereas small z T hadrons mainly comefrom fragmentation of jets with reduced energy from volume emission. These lead to di ff erentcentrality dependence of the hadron suppression in di ff erent regions of z T .Jet quenching [1] has become a powerful tool for the study of the quark-gluon plasma [2]in high-energy nuclear collisions. Jets are produced in the early stage of heavy-ion collisionsthrough hard parton scattering. When they pass through the dense matter, they will interact withthe medium and lose a significant amount of their energy via gluon radiation induced by multiplescattering.In our previous studies based on a NLO pQCD parton model [3, 4], we checked the tomo-graphic pictures of single jets and di-jets by a simultaneous fit to single hadron and dihadrondata. Single hadrons are dominated by the jet emissions close and perpendicular to the surfaceof the system, while dihadrons are emitted both close and tangential to the surface of the systemalthough there are contributions from punch-through jets from the central region. However, thedominance of surface and tangential emission makes it di ffi cult to extract the space-time profileof the dense medium from single and dihadron spectra.Here we focus on the study of photon-triggered away-side hadron spectra coming from γ -jetevents in central nucleus-nucleus collisions [5]. By selecting γ -hadron pairs with di ff erent valuesof z T = p hT / p γ T which could be larger than 1 due to radiative correction in NLO pQCD, one cane ff ectively control hadron emission from di ff erent regions of the dense medium and thereforeextract the corresponding jet quenching parameters. For the study of photon-hadron correlationin this paper, we focus mainly on photon production with isolation cuts [5, 6]. Therefore, we canneglect those photons that are produced via induced bremsstrahlung [7], jet-photon conversion[8] and thermal production [9, 10] in high-energy heavy-ion collisions.Within the same energy loss formalism as in our previous studies on single and dihadron[4], we calculate the production of the photon-triggered hadron spectrum in central Au + Au col-lisions at √ s =
200 GeV. Shown in Figure 1 are our numerical results for D pp ( z T ) or D AA ( z T ) Preprint submitted to Nuclear Physics A December 17, 2018 .2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.010 -6 -5 -4 -3 -2 -1 D pp z T p+p +h 200GeV |y ,y |<0.35 NLO pQCD =0.5p Trig =0.3, 1.0p
TrigT
TrigT <6GeV 106
TrigT <7GeV 7
TrigT <8GeV 10 -1 TrigT <9GeV 10 -2 TrigT <12GeV 10 -3 TrigT <15GeV 10 -4 PHENIX Pre. -3 -2 -1 D AA ,y |<1.0 z T TrigT <16GeV STAR Pre. NLO pQCD =0.5p
TrigT p+p +h Au+Au +h 0-10% 8
TrigT <16GeV STAR Pre. NLO pQCD =1.2M p+p +h Au+Au +h 0-10%
Figure 1: γ -triggered and hadron-triggered FF’s in p + p and central Au + Au collisions at the RHIC energy. The prelimi-nary data are from [11, 12]. Systematic errors of experimental data are shown as shaded bars when available. [5] compared to data. The left plot is for gamma-hadron spectra in p + p collisions. They fit thePHENIX preliminary data very well for di ff erent values of p trigT . We also show the uncertain-ties (dashed curves) due to the choice of the factorization scale, which mainly comes from thescale dependence of the FF’s. In the right plot we show the gamma-hadron spectra in centralAu + Au collisions (solid curve) as compared to p + p collisions (red dashed curve). The NLOpQCD prediction for the suppression of gamma-hadron spectra agrees well with the STAR pre-liminary data. Such an agreement is extremely nontrivial given the completely di ff erent emissiongeometry as compared to single and dihadron productions as we will see below, and it reinforcesthe success of the parton energy loss picture for the observed jet quenching phenomena. Alsoshown in the right plot are the calculated hadron-triggered FF’s, the dotted curve for p + p colli-sions and the dot-dashed curve for central Au + Au collisions, as compared to the experimentaldata. Hadron-triggered FF’s are larger than photon-triggered FF’s for both p + p and A + A col-lisions mainly because the fraction of hadron-triggered gluon jets is larger than the fraction ofphoton-triggered gluon jets at same p trigT , and the hadron yield of gluon jets is larger than that ofquarks.The nuclear modification factor I AA for the photon-triggered hadrons I AA = D AA / D pp is de-fined to characterize the e ff ect of jet quenching. Shown in the left plot of Figure 2 are thecalculated nuclear modification factors both in LO (dot-dashed) and NLO (solid) calculations ofgamma-triggered FF’s. In the LO pQCD calculation, transverse momentum of the associated jetis balanced exactly by the direct photon in tree 2 → z T = p hT / p γ T ≤ z T > ff ects give rise to NLO I AA very di ff erent from LO results. Therefore, to exactly probe thedense matter from gamma-hadron correlations, one must use NLO pQCD calculations. .Also shown in the left plot of Figure 2 is the dihadron suppression factor, dashed curve.Compared with dihadron I AA , gamma-hadron I AA has a more stronger dependence on z T . Onecan imagine that the gamma-triggered jets contributing to large- z T gamma-hadron are more sus-ceptible to energy loss. Even a small amount energy loss can greatly suppress the large- z T gamma-hadron yield. So large- z T gamma-hadrons are dominated by those gamma-triggered jetsoriginating near and escaping through the surface almost without energy loss. Similar to sin-2 .2 0.4 0.6 0.8 1.0 1.2 1.40.00.20.40.60.8 z T I AA ( z T ) I AA I AA STAR Pre. 8
TrigT <16GeV NLO LO 0-10%+h I CP AA Au+Au 200GeV -1 STAR Pre. 8
10 GeV and the associated hadron with p γ T = , , , ,
10 GeV, respectively (from top to bottom). gle hadron suppression factor, large- z T I AA is mainly determined by the thickness of the coronaof the surface emission. The picture of the surface emission is demonstrated by the left plotof Figure 3. The plot is the spatial transverse distribution of the initial gamma-jet productionvertexes that contribute to the final gamma-hadron pairs with given values of z T . The associ-ated jets are considered along the right direction, and the opposite direction is for the triggeredphotons. The color strength represents the gamma-hadron yield from the fragmentation of thegamma-triggered jets after parton energy loss. The inserted panels are projections of the con-tour plots onto y-axes, solid curve without energy loss, dashed curve with energy loss. As forsmall z T region, it has contributions from energetic jets originated from inside the medium thathave lost a finite amount of energy before fragmenting into hadrons. That’s why these gamma-correlated hadrons come from volume emission, as shown in the right plot of Figure 3. For theintermediate- z T region, gamma-hadrons are determined by the competition of the two emissionmechanisms.The above picture of volume and surface emission for the γ -triggered fragmentation functionin heavy-ion collisions will lead to di ff erent centrality dependence of the nuclear modificationfactor I AA ( z T ) in di ff erent regions of z T . Shown in the right plot of Figure 2 are nuclear modifi-cation factors for γ -triggered hadron spectra as functions of the participant number in Au + Au collisions at the RHIC energy for di ff erent values of z T as compared to the STAR preliminarydata. For small values of z T <
1, the γ -triggered hadron yield is dominated by volume emissionand therefore the centrality dependence of the nuclear modification factor is stronger than that inthe region z T ≥ p T photon-hadron correlations are studied within the NLO pQCD partonmodel with modified parton fragmentation functions due to jet quenching in high energy A + A collisions. We demonstrated that the volume (surface) emission dominates the γ -triggeredhadrons spectra at small z T < z T ≥
1) due to the underlying jet spectra in the NLOpQCD. Therefore, one will be able to extract jet quenching parameters from di ff erent regions ofthe dense medium by measuring the nuclear modification factor of the γ -triggered fragmentation3 /2 p =- j b=5fm – +h g fi < G e V hT < G e V < p g T < p x (f m ) y (fm) fifi -6 -4 -2 0 2 4 60510152025 y (fm) d N / d y No Quench.Quench. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-4-3-2-1012345 /2 p =- j b=5fm – +h g fi < G e V hT < G e V < p g T < p x (f m ) y (fm) fifi -6 -4 -2 0 2 4 60510152025 y (fm) d N / d y No Quench.Quench.
Figure 3: Transverse distributions of the initial γ -jet production vertices that contribute to the final observed γ -hadronpairs along a given direction (arrows) with z T ≈ . z T ≈ . function in the whole kinetic region, including z T ≥
1, achieving a true tomographic study of thedense medium.
Acknowledgements
This work was supported by DOE under contracts DE-AC02-05CH11231 and DEFG02-97IR40122, by NSFC of China under Projects No. 10825523 and No. 10875052 and No.10635020, by MOE of China under Projects No. IRT0624; by MOST of China under ProjectNo. 2008CB317106; and by MOE and SAFEA of China under Project No. PITDU-B08033.
References [1] X. N. Wang and M. Gyulassy, Phys. Rev. Lett. , 1480 (1992).[2] M. Gyulassy, I. Vitev, X. N. Wang and B. W. Zhang, arXiv:nucl-th / / , 212301 (2007).[5] H. Z. Zhang, J. F. Owens, E. Wang and X. N. Wang, Phys. Rev. Lett. , 032302 (2009).[6] H. Baer, J. Ohnemus, and J. F. Owens, Phys. Rev. D , 61 (1990).[7] I. Vitev and B. W. Zhang, Phys. Lett. B , 337 (2008).[8] R. J. Fries, B. Mller and D. K. Srivastava, Phys. Rev. Lett. , 132301 (2003).[9] D. K. Srivastava, J. Phys. G , 104026 (2008).[10] S. Turbide, C. Gale, S. Jeon and G. Moore , Phys. Rev. C. , 014906 (2005).[11] J. Adams et al. , Phys. Rev. Lett. , 162301 (2006); A. M. Hamed, J. Phys. G , 104120 (2008); arXiv:0809.1462.[12] J. Frantz [PHENIX Collaboration], arXiv:0901.1393., 104120 (2008); arXiv:0809.1462.[12] J. Frantz [PHENIX Collaboration], arXiv:0901.1393.