arXiv:1101.0290v2 [nucl-th] 29 Jun 2011 and ahlnt “ and/or colli- spectra length ion parton heavy path underlying a different in with processes but loss sion, energy same the probe aso ftesprsinrltv oterato plane reaction the to relative (RP) suppression the of pansion nhayincliin swl nw [ known mechanism well loss is energy collisions ion possible heavy the in constrain to ables adriptsetu n ieetsto ah com- paths of set different to a pared and spectrum input harder n hsc r igehdo suppression single are physics ing aftececeto h cos(2 the of coefficient the half ferent ieetpt egh;o h te hand, other the on lengths; path different ‡ † ∗ the examined which publication previous one than other deriva- principles first on that built model tions loss energy firmly an been [ find has RHIC phenomenon, at interac- experimental established partonic an state as final via tions, quenching effort, long ns twr ntesG se .. [ e.g., (see, sQGP mech- the loss in de- energy work a dominant, at is even there anism or and exact, the exists, over model bate such no Currently ables. itosadeprmna esrmnso high- of measurements experimental and dictions sG)cetdi uA olsosa h Relativistic [ the (RHIC) at Collider collisions Ion Heavy Au+Au in plasma created the (sQGP) determining strongly-interacting for the basis of properties unique a provides observables lcrncaddress: Electronic address: Electronic orsodto Correspond orosralso neeti edn atcequench- particle leading in interest of observables Four Introduction: v 2 I R AA φ AA s hs bevbe r neetn eas they because interesting are observables These . R a dnia nu atnsetabtexplores but spectra parton input identical has td ftecreain ewe e unhn observabl quenching jet between correlations the of study A ( AA simultaneously φ 3 eateto hsc,Uiest fCp on rvt Bag Private Town, Cape of University Physics, of Department v atclrw n htaqaiaieeeg osmdlgives model loss energy m qualitative loss a energy that the find we into particular insight valuable provide observables hnw ae∆ take we when hssm ∆ same This aaadmksnvlpeitosfrtecnrlt depende centrality the for predictions novel makes and data urn aasget,abi iheteeylreuncerta large extremely with albeit suggests, data Current ewrs eaiitchayincliin,Quark-gluo collisions, heavy-ion Relativistic 25.75.-q Keywords: 24.85.+p, 12.38.Mh, models. numbers: loss PACS energy current in reproduce to difficult is s h motneo sn utpeobserv- multiple using of importance The . 2 l I [email protected] eednis o example For dependencies. ” = AA ouigo ortpso orlto plots, correlation of types four on Focusing edmntaehwtecnrlt eedneof dependence centrality the how demonstrate we , φ [email protected] [email protected] − 1 h obnto ftertclpre- theoretical of combination The eateto hmsr,SoyBokUiest,SoyBro Stony University, Brook Stony Chemistry, of Department 2 Ψ hsc eatet rohvnNtoa aoaoy Upto Laboratory, National Brookhaven Department, Physics 3 RP .Tecalnefrter sto is theory for challenge The ]. E ) ihdo suppression di-hadron )), E ecie h nw observ- known the describes ∼ inyn Jia, Jiangyong 1 ∼ l – φ 3 3 s l oe loqaiaieydsrbstetrigger the describes qualitatively also model 3 .Atrnal decade a nearly After ]. emi h ore ex- Fourier the in term ) n eimgoer eeae yamdlo h oo ls C Glass Color the of model a by generated geometry medium a and 3 6 – – 5 10 ,2, 1, ]). R I AA .However, ]. AA R ∗ AA Dtd uut2,2018) 27, August (Dated: , rbsa probes .A Horowitz, A. W. v tdif- at 2 p T I (one AA jet , R AA lsa e unhn,JtTomography Jet quenching, Jet plasma, n ing where 0GeV/ 10 ieaduulya ucinof a function at a observable as one usually made and was time data and theory between etaiydpnec of dependence centrality R o7GeV/ 7 to rlcliin for collisions tral I nalmost an rlt eedneo h orlto rvdsnvlin- novel high- provides cen- the the correlation into studying the sights and of other dependence each trality against directly ables selection. mnal tRI n h LHC: the exper- and studied be RHIC can at that imentally correlations of types four pose are u ytePEI xeietusing experiment PHENIX the by out carried high- comparisons: ical spectra. parton and geometry collision the from [ eue odsnagete“ can the correlations disentangle these to how We used of be shape. discussion spectra a parton sen- with and their conclude geometry exploring the the by on demonstrate correlations sitivities we these experimental model, of absorption the importance jet from a revealed Using features correlations main data. the four explore the then of We each RHIC. of measurements at experimental observable the of overview brief 12 vs. AA dφ nti okw ru htcreaigteeobserv- these correlating that argue we work this In vriwo xeietlrslsadtheoret- and results experimental of Overview , correlations , pp v s 13 3, p I 2 R T , AA lk)cliin tipc parameter impact at collisions -like) † ,reaching ], ny that inty, N AA caimi ur-lo lsa In plasma. quark-gluon a in echanism R n ifn Liao Jinfeng and oddsrpinof description good a igehdo upeso n nstoywere anisotropy and suppression hadron single c bin c o this for nce AA R vs. ( p c for φ AA h u ean oiiea higher at positive remains but , 3 odbsh70,SuhAfrica South 7701, Rondebosch X3, T ( b s vs. idpnetfco f5sprsini cen- in suppression 5 of factor -independent stenme fbnr hr scatter- (hard binary of number the is ) v cos(2 ) v ( 2 p I 2 ewe utpejtquenching jet multiple between p AA T . I v T AA 2 I ,N 19,USA 11796, NY n, φ , R eedneof dependence k Y174 USA 11794, NY ok, p AA p and T T AA , φ p R s h otpeiemaueet of measurements precise most The I ≫ s T b , > ∼ AA AA ) sdfie as defined is / v nryls ehns.W pro- We mechanism. loss energy ) v GeV/ 4 2 0GeV/ 20 R 2 R ≡ vs. vs. orlto that correlation a , 2, vs. dφ AA ‡ l N eedneo nryloss energy of dependence ” v R I s AA v bin 2 I vs AA R AA d sa RHIC at es 2 I 2 dN AA R c AA ( p The . v correlation. c AA b T vs. ondensate. and 2 esalfis iea give first shall We . AA ) ( ( R p for p φ dN [ T T 11 → vs. AA d v s φ , 2 2 .The ). v h pp p o n centrality one for ,tecomparison the ], R + 2 T s only v I → X vs. b , AA ( AA vs. 2 p h ) T + rp rm3 from drops ) X p b v n beyond and and , T R 2 , π , Current . AA 0 R mesons AA shows v 2 (1) vs. ≡ 2 jet quenching models based on the pQCD framework, when tuned to RAA data, significantly under-predict the v2 [13]. In contrast, non-perturbative approaches, for example those based on AdS/CFT gauge gravity dual- ity [14], seem to work well. The data seem to prefer the ∆E ∼ l3 path length dependence, a result based on AdS/CFT [7], as opposed to the quadratic depen- dence ∆E ∼ l2 predicted radiative energy loss predicted by pQCD [15]. Alternatively, a simultaneous descrip- tion of RAA and v2 may also be achieved via a late-stage non-perturbative effect near the QCD confinement tran- sition [11, 16]. The suppression of the away-side jet is quantified by IAA, the ratio of the per-trigger yield (away-side jet mul- tiplicity normalized by number of triggers) in Au+Au collisions to that in p+p collisions. Pure geometrical considerations would imply IAA < RAA, due to a longer path length traversed by the away-side jet. But recent PHENIX [17] and STAR [18] measurements show that a 0 IAA is constant for associated hadron pT > 3 GeV/c, FIG. 1: (Color online) (Top panels) PHENIX π − h corre- t a within the current experimental uncertainties, and this lation results with 7 < pT < 12 GeV/c and 0.5 < pT < 7 constant level is above the RAA for the trigger , GeV/c [17]. (Bottom panel) the STAR jet-h correlation results with reconstructed trigger jet momentum in 10 < i.e. IAA > RAA (see Fig. 1). Furthermore, the constant jet t pT,rec < 40 GeV/c [18]. Both are for the 0-20% Au+Au level of IAA increases for higher trigger pT . This result can be qualitatively explained by the bias of the away- centrality bin. side jet energy by the trigger pT : as we show with a PYTHIA simulation in Fig. 2, the initial away-side jet PYTHIA 6.19 TuneA p+p at s=200 GeV spectra becomes harder as higher pT triggers are re- h-h correlation dN 1 10-1 Away-side yield fit with ∝ quired. As we discuss in more detail below, the harder dp p n-1 T T the input spectrum, the larger the fractional energy loss T is required for the same IAA value. The ACHNS model 10-2

[19] results, constrained by the RAA data, are incom- dN/dp patible with the IAA values shown in Fig. 1; while the trig

1/N -3 ZOWW model [20] seems to describe the IAA data alone 10 t 4

t 2 3 l2 v / ∈ l3 v / ∈ (b) (pT ∈ [4 − 5] GeV/c), κaway = κ/3 in Fig. 4 (c) l Glauber l Glauber 2 Glauber 2 Glauber t 2 3 (p ∈ [7 − 9] GeV/c), and κaway = κ/4 in Fig. 4 (d) l CGC l CGC l2 v / ∈ l3 v / ∈ T 1 1 2 CGC 2 CGC t π0 (p ∈ [9 − 12]). The toy model improves its agreement v2 0-50% T in 10% steps ∈ Data v / Glauber with the PHENIX data when both the path length and p ∈[6-9] GeV/c 2 T Data v /∈ 2 CGC spectral dependencies are included. In particular the l3 AdS/CFT-like energy loss model AA

R that described the RAA vs. v2 data so well appears to de- 0.5 0.5 scribe the RAA vs. IAA data to within about 2-3 standard deviations. One also again sees that the CGC medium yields results whose centrality dependence is in slightly better agreement with the data than the results from 3 (a) (b) the Glauber medium. However it is clear that the l 0 0 0 0.05 0.1 0.15 0 0.2 0.4 models systematically under-predict the IAA data. On the other hand the l2 models tend to disagree more on v2 v =v /∈ 2,r 2 the level of 1 standard deviation. That the l2 models tend to describe the normalization and correlation–but l 3 Glauber 0.6 not anisotropy–of R and I might suggest the im- 3 AA AA l CGC portance of or flow-coupling effects that

AA Zoom in view of panel (a) are neglected in our model [11, 16, 30]. R 0.4 In general the toy model predicts significantly differ- ent RAA vs. IAA curves as a function of centrality as a (c) function of trigger momentum: the larger pt (or, equiva- 0.2 T lently, smaller κaway), the more concave the RAA vs. IAA 0.05 0.1 v2 curve becomes. The concavity of the correlation is also in general larger for a CGC medium than for a Glauber

FIG. 3: (Color online) (a) Centrality dependence of RAA vs. medium. It would be interesting to see these predictions v2 from the jet absorption model in 5% centrality steps and compared with future measurements performed over the data (solid circles); only statistical errors are shown. (b) The full centrality range in small centrality bins. same data and calculations, except v2 is divided by the ec- The strong suppression of the away-side jet should also centricity. (c) The same as in (a) but zoomed in and with lead to an anisotropy of the IAA relative to the RP. Fig. 5 centrality binning explicitly shown for the theoretical results. (a) shows the predicted correlation between IAA and IAA 1 v2 , assuming κaway = 2 κ. The corresponding correla- tion between I and reduced anisotropy vIAA = vIAA /ǫ geometry is smaller relative to the Glauber geometry), AA 2,r 2 is shown in Fig. 5 (b). The results for κ = 1 κ are and normalizing with respect to eccentricity has empha- away 4 sized this mismatch in the centrality-binned results for shown in Fig. 5 (c)-(d). theory and data. Thus RAA versus v2/ǫ can better illus- Several interesting features can be identified from the IAA 2 3 trate the relation between jet quenching and azimuthal figure. First, v2 increases dramatically from l to l 3 anisotropy, indicating here that our model only describes dependence, but even the l model under-predicts the the RAA vs. v2 data for AdS/CFT-like energy loss in a PHENIX data [22] by about one standard deviation, CGC medium. where the uncertainty is currently very large. Second, IAA calculated v values are very sensitive to κaway: they Fig. 4 shows the correlation between RAA and IAA 2 are larger than the inclusive hadron v2 of Fig. 3 for from the jet absorption model, calculated over the full 1 1 centrality range. The model results are compared with κaway = 2 κ, but are less for κaway = 4 κ. It will there- IAA STAR and PHENIX data from Fig. 1 (0-20% central- fore be very useful to see experimental results for v2 a as a function of trigger momentum. Finally, we also see ity bin) with their IAA values integrated over pT > 3 IAA GeV/c (where IAA is flat). In Fig. 4 (a), the data points a strong anti-correlation between v2 /ǫ and IAA, quite have roughly the same RAA value, but are spread out similar to that between v2/ǫ and RAA. Such similar- t ity may not be surprising if the physics of jet quench- in IAA for different trigger momenta, pT . The reason, as explained in the discussion of Fig. 1 & Fig. 2, is that ing for the trigger and away jets were identical (as in IAA depends not only on the path length but also on the present model calculation). A precision measurement the shape of the input spectra, and the larger the trig- of these two correlations, therefore, could either confirm t such similarity or suggest new physics in the away-side ger momentum pT the harder the away-side spectrum. Fig. 4 (a) also shows that IAA < RAA when only the jet quenching. IAA path length effect is included (i.e. we take κaway = κ). The correlation between IAA and v2 is also quite We then attempt to model the effect of the trigger bias sensitive to the choice of the collision geometry: switch- on the hardening of the away-side spectrum (see Fig. 2) ing from Glauber geometry to CGC geometry leads to IAA IAA by using Eq. (4), which yields κaway = κ/2 in Fig. 4 about a 20% reduction of v2 and v2 /ǫ at fixed IAA 5

1 2 3 I 3 I 2 l Glauber l Glauber 2 AA ∈ AA ∈ PHENIX π0-h 0-20% l Glauber l v2 / Glauber l v2 / Glauber 2 2 3 l CGC l CGC l CGC 2 I AA 3 I AA t 1 1 l v / ∈ l v / ∈ p ∈[4-5],[7-9],[9-12] GeV/c 3 2 CGC 2 CGC T l Glauber π0-h PHENIX 1010.1521 0.8 l3 CGC 1 κ = 1κ κ = κ κ κ κ 1κ away 2 away 2 away= away=

2 AA I 0.6 0.5 0.5 AA R 0.4 (a) (b) 0 0 3 I 3 I 0.2 l2 Glauber l Glauber 2 AA ∈ AA ∈ l v / Glauber l v / Glauber 2 3 2 2 Increasing trigger p 0 l CGC l CGC 2 I 3 I T PHENIX π -h 0-20% 1 1 AA ∈ AA ∈ t l v2 / CGC l v2 / CGC p ∈[4-5] GeV/c π0-h PHENIX 1010.1521 (a) (b) T 0 1 1 κ = 1κ κ = κ away 4 away 4 AA I 0.8 0.5 0.5

κ =1κ κ =1κ 0.6 away 3 away 4 (c) (d) AA 0 0 R 0 0.1 0.2 0.3 0 0.5 1 IAA I I 0.4 v AA AA ∈ 2 v2,r=v2 /

0.2 FIG. 5: (Color online) (a) Centrality dependence of IAA vs. PHENIX π0-h 0-20% PHENIX π0-h 0-20% IAA pt ∈[7-9] GeV/c pt ∈[9-12] GeV/c v2 from jet absorption model in 5% centrality steps and (c) T (d) T 0 data (solid circles). (b) The same data and calculations, ex- 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 cepts their vIAA have been divided by the eccentricities. (c), I 2 AA IAA 1 (d) are same as (a), (b) but are calculated for κaway = 4 κ.

FIG. 4: (Color online) Centrality dependence of RAA vs. IAA from the jet absorption model, compared with PHENIX 1 1 for κaway = κ) . data [17] in the 0-20% centrality bin. The calculations were 4 done assuming κ for away-side jet is (a) the same, (b) 1/2, Before closing this section, we want to discuss all corre- (c) 1/3, or (d) 1/4 of that for inclusive jets. We compare the lations together. In general, jet quenching models predict model curves in (b) to the left-most ([4-5] GeV/c trigger), (c) an anti-correlation between suppression and anisotropy IAA to the central ([7-9] GeV/c trigger), and (d) to the right-most (RAA vs. v2, and IAA vs. v2 ), while they predict a ([9-12] GeV/c trigger) PHENIX data point. The dotted di- correlation between the suppressions (RAA vs. IAA) and agonal line indicates IAA = RAA. The explicit predictions for IAA between the anisotropies (v2 vs. v2 ). Thus it is rather 0-20% centrality are shown as diamond and cross symbols. surprising to see from the data that IAA has a larger IAA anisotropy than that for RAA (v2 > v2), yet it is less suppressed. This feature is very difficult to reproduce in 1 1 for κaway = 2 κ (significantly smaller for κaway = 4 κ). our simple model (see Fig. 4 (d) and Fig. 5 (c)), and, in Thus a precise measurement of this correlation may help general, is a challenge for jet quenching theory [21]. in distinguishing between different initial geometries. Summary: IAA The simultaneous description of multiple Fig. 6 shows the correlation between v2 and v2 for 1 1 observables tightly constrains jet quenching models. In κaway = 2 κ and κaway = 4 κ. Since both observables first this paper we identified four correlations among single increase then decrease from peripheral to central colli- hadron and di-hadron observables as useful for constrain- sions, the correlation plot shows a rather sharp turn at ing jet quenching models: RAA vs. v2, RAA vs. IAA, IAA around 20-30% centrality (Npart ∼ 150). This provides IAA IAA vs. v2 and v2 vs. v2 . Using a jet absorption model, a rather precise way of identifying the centrality range we showed that these correlations are sensitive to various at which the anisotropy reaches a maximum. The right ingredients in the jet quenching calculations, such as the panel shows the correlation of reduced anisotropies. We path length dependence, collision geometry, and input see that all four scenarios fall approximately on a univer- 1 spectra shape. Specifically, RAA vs. v2 is most sensitive sal curve, especially for κaway = κ, but with different 2 to l dependence, RAA vs. IAA is sensitive to both spectra reaches along the curve. Apparently, the reach is larger IAA shape and path length dependence, and IAA vs. v2 is for Glauber geometry and higher order l dependence. sensitive to all three ingredients. This implies that the efficiency with which jet quench- We found that only our energy loss model with ∆E ∼ ing converts the eccentricity into anisotropy depends on l3 AdS/CFT-like energy loss and a CGC medium de- collision geometry and l dependence. This curve also has 1 an interesting shape: At small v2,r (. 0.2 for κaway = 2 κ 1 and . 0.3 for κaway = 4 κ), which corresponds to more IAA peripheral collisions, v2 is larger than v ; but then 1 l2 v > vIAA 2 However for and CGC geometry, 2 2 in all centrality IAA 1 bins v2 > v2 at large v2,r (> 0.2 for κaway = 2 κ or > 0.3 6

0.4 important physics such as hadronization or flow-coupling Peripheral Peripheral effects missing from our calculation. (Note that the for- 0.1 0.3 Central mer is unlikely given the very large v2 values seen at very ∈ / 2 large pT ∼ 10 GeV/c.) More dynamical calculations of 2 v =v 0.2 these correlations should provide more quantitative and 0.05 2 2,r l Glauber v l 2 CGC detailed information, and it is to this end that the pro- l 3 Glauber 0.1 3 Central l CGC posed correlations should be useful. κ = 1κ κ = 1κ (a) away 2 (b) away 2 We also identified a number of interesting experimen- 0 0 0.4 tal measurements that—once analyzed—will help further constrain energy loss calculations. Our absorption model 0.1 0.3 showed a nontrivial change in the centrality dependence ∈ /

2 of the RAA vs. IAA correlation as a function of the mo- 2 v =v 0.2 mentum of the trigger particle, due to the hardening of 0.05 2 2,r l Glauber v l 2 CGC the away-side spectrum; currently there is only a single l 3 Glauber 0.1 l 3 CGC data point for this correlation for any particular trigger κ = 1κ κ = 1κ (c) away 4 (d) away 4 pT . Interestingly, the absorption model predicts a uni- 0 0 IAA 0 0.1 0.2 0 0.2 0.4 0.6 0.8 versal eccentricity-scaled correlation between v2 and v I I I 2 v AA v AA=v AA/∈ 2 3 2 2,r 2 for both l and l path length dependencies irrespective of the medium geometry; it would be very interesting to see if this universal relationship is observed in data. Most IAA IAA FIG. 6: (Color online) (a) v2 vs. v2 and (b) v2,r vs. v2,r fascinating is the new correlation measurement between 1 IAA for 5% centrality steps and four cases for κaway = 2 κ. (c), I and v . For the given di-hadron suppression, the 1 AA 2 (d) are same as (a), (b) but are calculated for κaway = 4 κ. very large magnitude of the anisotropy of this suppres- The scaling seen in (b) and (d) is broken in more central sion cannot be described by either l2- or l3-type energy collisions as the fluctuations in eccentricity ǫ dominate the loss models. Future measurements that reduce the exper- 2 mean, hǫi≪ (ǫ −hǫi) . IAA q imental uncertainty on v2 may be extremely difficult to reconcile with current notions of high-pT energy loss physics. scribes the RAA vs. v2 data well as a function of central- ity and is also qualitatively (within two to three standard deviations) consistent with the RAA vs. IAA data as a 2 Acknowledgements function of the trigger pT . While the l , pQCD-like en- ergy loss model is completely inconsistent with the RAA 2 vs. v2 correlation, the l model describes the RAA vs. IAA This research is supported by the NSF under award correlations better than the l3 model, possibly indicating number PHY-1019387.

[1] M. Gyulassy and L. McLerran, Nucl. Phys. A750, 30 [12] A. Adare et al. (PHENIX), Phys. Rev. Lett. 101, 232301 (2005), arXiv:nucl-th/0405013. (2008), arXiv:0801.4020. [2] U. A. Wiedemann (2009), arXiv:0908.2306. [13] A. Adare et al. (PHENIX), Phys. Rev. Lett. 105, 142301 [3] A. Majumder and M. Van Leeuwen (2010), (2010), arXiv:1006.3740. arXiv:1002.2206. [14] C. Marquet and T. Renk, Phys. Lett. B685, 270 (2010), [4] W. A. Horowitz (2010), arXiv:1011.5965. arXiv:0908.0880. [5] J. Jia (PHENIX), Nucl. Phys. A855, 92 (2011), [15] M. Gyulassy and X.-n. Wang, Nucl. Phys. B420, 583 arXiv:1012.0858. (1994), arXiv:nucl-th/9306003. [6] H. Zhang, J. Owens, E. Wang, and X.- [16] J. Liao and E. Shuryak, Phys. Rev. Lett. 102, 202302 N. Wang, Phys.Rev.Lett. 98, 212301 (2007), (2009), arXiv:0810.4116. arXiv:nucl-th/0701045. [17] A. Adare et al. (The PHENIX), Phys. Rev. Lett. 104, [7] F. Dominguez, C. Marquet, A. H. Mueller, B. Wu, 252301 (2010), arXiv:1002.1077. and B.-W. Xiao, Nucl. Phys. A811, 197 (2008), [18] J. Putschke, talk given at Hard Probes 2010. arXiv:0803.3234. [19] N. Armesto, M. Cacciari, T. Hirano, J. L. Nagle, [8] S. A. Bass, C. Gale, A. Majumder, C. Nonaka, G.-Y. Qin, and C. A. Salgado, J.Phys.G G37, 025104 (2010), et al., Phys.Rev. C79, 024901 (2009), arXiv:0808.0908. arXiv:0907.0667. [9] T. Renk, Phys.Rev. C78, 034904 (2008), [20] H. Zhang, J. F. Owens, E. Wang, and X.-N. Wang, Phys. arXiv:0803.0218. Rev. Lett. 103, 032302 (2009), arXiv:0902.4000. [10] T. Renk and K. Eskola (2011), arXiv:1106.1740. [21] J. L. Nagle, Nucl. Phys. A830, 147c (2009), [11] W. A. Horowitz, Acta Phys. Hung. A27, 221 (2006), arXiv:0907.2707. arXiv:nucl-th/0511052. [22] A. Adare et al. (PHENIX) (2010), arXiv:1010.1521. 7

[23] A. Drees, H. Feng, and J. Jia, Phys. Rev. C71, 034909 and Y. Nara, Phys. Rev. C74, 044905 (2006), (2005), arXiv:nucl-th/0310044. arXiv:nucl-th/0605012. [24] J. Jia and R. Wei, Phys. Rev. C82, 024902 (2010), [28] B. Alver et al., Phys. Rev. C77, 014906 (2008), arXiv:1005.0645. arXiv:0711.3724. [25] K. Adcox et al. (PHENIX), Nucl. Phys. A757, 184 [29] A. Adare et al. (PHENIX), Phys. Rev. Lett. 105, 062301 (2005), arXiv:nucl-ex/0410003. (2010), arXiv:1003.5586. [26] W. A. Horowitz (2010), arXiv:1011.4316. [30] W. A. Horowitz and J. Jia, in preparation. [27] H.-J. Drescher, A. Dumitru, A. Hayashigaki,