ATHIC Meeting 2008 10132008 T Gunji Title Heavy

ATHIC Meeting 2008 10/13/2008: T. Gunji Title Heavy Quark and Quarkonia Production at RHIC Taku Gunji Center for Nuclear Study University of Tokyo 1/43

ATHIC Meeting 2008 10/13/2008: T. Gunji Major discovery at RHIC l Evidence of strong coupled QGP l Large energy loss/large opacity (high p. T) l 1000<d. Ng/dy<2000 (GLV), 6<q<24 Ge. V 2/fm (PQM) l Partonic flow/small viscosity (low p. T) l Relativistic hydrodynamics, early thermalization (0. 6 fm/c) l Quark coalescence (mid. p. T) v 2 PHENIX & STAR R. Lacey et al. : PRL 98: 092301, 2007 2

ATHIC Meeting 2008 10/13/2008: T. Gunji Further investigation l Correlation tagged by Jets l Particle correlation in df and dh space l Particle production with respect to reaction plane X-N. Wang, N. Xu, H. Zhang, G-L. Ma, in this conference l Thermal photon measurement l T and d. o. f of the medium Y. Yamaguchi , F-M. Lui in this conference l Heavy quark and Quarknoia measurement l Transport properties of the medium l Deconfinement, Temperature field Y. Kim, T. Gunji, K. Morita, H. Fujii, T. Umeda, Y. Akamatsu, S. Sakai, A. Rothkopf, E. Wang, in this conference l and more …. 3

ATHIC Meeting 2008 10/13/2008: T. Gunji Heavy Quarks 4 B. Mueller, nucl-th/0404015 l m. HQ ≫ T, LQCD l Created only at the beginning of collisions via hard process. l point like p. QCD process and well calibrated in p+p collisions l No chemical equilibrium. Abundance is frozen. l Reveals transport properties of the medium. l Energy loss and flow measurement l Elastic vs. Radiative l Diffusion constant l h/s of the medium G. D. Moore, D Teaney PRC 71, 064904 (2005)

ATHIC Meeting 2008 10/13/2008: T. Gunji Quarkonia 5 Quarkonia l Probe of the Deconfinement l Color screening [T. Matsui and H. Satz (1986)] l Attraction between qqbar pairs is reduced in the medium. l Color force is shorter range and binding is weaker. l When force range/screening radius ( T-1) become less H. Satz (SQM 08) than binding radius, qqbar is never bound. H. Satz (SQM 08) Measurement of Quarkonia suppression Achieved temperature of the medium.

ATHIC Meeting 2008 10/13/2008: T. Gunji Title of Part 1 Heavy Quark Production at RHIC 6

ATHIC Meeting 2008 10/13/2008: T. Gunji Heavy Quark Measurement at RHIC l Single leptons (e, ) via semi-leptonic decay l c-hadron e+ + anything (B. R. : 9. 6%) l D 0 (B. R. : 6. 87%) D (B. R. : 17. 2%) l Cannot separate c/b. l Direct meas. via hadronic decay l Direct measurement (inv. Mass) l D 0 K+p (B. R. : 3. 85%) l Challenging meas. (S/N) l e-h correlation l c/b separation l Df space or mass space. l di-electrons 7

ATHIC Meeting 2008 10/13/2008: T. Gunji PHENIX and STAR l PHENIX l Electrons & hadrons, |y|<0. 35 l p Rejection>103@90% eff. (MB) l Muons, 1. 2<|y|<2. 2 l Cut 98% of hadrons by absorber. l Single leptons, e-h, ee pairs l STAR l Hadrons & electrons, |y|<1 l Larger acceptance for hadrons. l Single electrons, e-h, Direct reconstruction 8

ATHIC Meeting 2008 10/13/2008: T. Gunji Non-photonic electron measurement 9 Non-photonic electron measurement l Electrons from heavy quark decays l Inclusive electrons – photonic electrons l Photonic electrons l Conversion of photons in material l Dalitz decay of light neutral mesons (mainly p 0 and h) l Cocktail subtraction & converter method

ATHIC Meeting 2008 10/13/2008: T. Gunji Spectrum and FONLL calculation 10 Spectrum and FONLL calculation Phys. Rev. Lett 97, 252002 (2006) Heavy flavor electron spectrum compared to FONLL. Data/FONLL = 1. 71 with error Cross section shape for p. T > 1. 6 Ge. V/c agrees with FONLL upper limit

ATHIC Meeting 2008 10/13/2008: T. Gunji b/(c+b) ratio by e-h correlation l ~50% contribution from b for p. Te>3~4 Ge. V 11 S. Sakai

ATHIC Meeting 2008 10/13/2008: T. Gunji Single leptons in d+Au l Shadowing/Cronin effect l Results from 2003 d+Au l Rd. A>1 for south (x 2 is large) l Rd. A<1 for north (x 2 is small) 12 gluons in Pb / gluons in p Shadowing Anti Shadowing l 2008 d+Au data is necessary. x Eskola et al. NPA 696 (2001) 729 Au going d going |y|<1 Raphael (SQM 08)

ATHIC Meeting 2008 10/13/2008: T. Gunji Spectra in Au+Au collisions 13 Spectra in Au+Au collisions PHENIX PRL 98 173301 (2007) Heavy flavor electron spectra Curves: binary scaled p+p Reference (FONLL) Clear high p. T suppression developing towards central collisions MB S/B > 1 for p. T > 2 Ge. V/c according to inside box figure 0%~ ~92% p+p

ATHIC Meeting 2008 10/13/2008: T. Gunji RAA vs. p. T for various centralities 14 RAA vs. p. T for various centralities [p. T<1. 6 Ge. V/c] p+p: data (converter) [p. T>1. 6 Ge. V/c] p+p: scaled FONLL PHENIX PRL 98 173301 (2007) Suppression level is the almost same as p 0 and h in high p. T.

ATHIC Meeting 2008 10/13/2008: T. Gunji Non-photonic electron v 2 15 Non-photonic electron v 2 PHENIX PRL 98 173301 (2007) l. Final result from 2004 Au+Au l. Preliminary result from 2007 Au+Au l. Large v 2 of nonphotonic electrons is observed. Greco et al. , PLB 595 (2004) 202 lp. QCD calculation with and without charm quark flow. l. Clear indication of charm flow in the medium.

ATHIC Meeting 2008 10/13/2008: T. Gunji Model Comparison 16 PHENIX PRL 98 173301 (2007) lp. QCD radiative E-loss with upscaled transport coeff. l. Langevin with elastic p. QCD + resonances + coalescence l. Langevin with upscaled p. QCD elastic lp. QCD elastic scattering l G-1 = ttherm ~ 20 fm/c lp. QCD+resonance+coalescence l G-1 = ttherm ~ 5 fm/c (ttherm for b ~ 15 fm/c)

ATHIC Meeting 2008 10/13/2008: T. Gunji Medium Properties l From diffusion coefficient to h/s strong coupl. h/s ≈ 1/4 p D x (2 p. T) = 1/2 TD weak coupl. h/s ≈ 4/15 n <p> ltr=1/5 TD l Rapp and van Hees [PRC 71: 034907, 2005] l DHQ x 2 p. T ~ 4 -6. l Moore and Teaney [PRC 71: 064901, 2005] l DHQ x 2 p. T ~ 3 -12. l This gives h/s ~ (4/3 -2)/4 p l indicate small value and close to conjectured limit (ħ/4 p) l significantly below h/s of helium (4 ph/s ~ 9) 17

ATHIC Meeting 2008 10/13/2008: T. Gunji Hydro+Heavy Quark Hydro + Heavy Quark Y. Akamatsu et al. ar. Xiv: 0809. 1499 l Relativistic treatment of Brown Motion l Drag force inspired by Ad. S/CFT g = (2. 1 0. 5) from Ad. S/CFT w. c s. c 18 Y. Akamatsu

ATHIC Meeting 2008 10/13/2008: T. Gunji RAAc and RAAb l RAA(e) = r*RAAb+(1 -r)*RAAc, r=b/(c+b) [STAR] p. T>5 Ge. V/c 19 S. Sakai o RAAc& RAAb correlation together with models o Dominant uncertainty is normalization in RAA analysis o. RAAb< 1 ; B meson suppressed o prefer Dissociate and resonance model (large b energy loss) I; Phys. Lett. B 632, 81 (2006) ; d. Ng/dy = 1000 II; Phys. Lett. B 694, 139 (2007) III; Phys. Rev. Lett. 100(2008)192301

ATHIC Meeting 2008 10/13/2008: T. Gunji RAAc/RAAb 20 W. Horowitz SQM 07 l Further constraint of heavy quark transportation l p. QCD rad+el vs. Ad. S/CFT drag momentum loss l High p. T D and B measurement is necessary.

ATHIC Meeting 2008 10/13/2008: T. Gunji Conclusion (1) l Heavy quark measurement has been done by PHENIX and STAR. l Differential cross section can be described by FONLL calculation (within theoretical uncertainty) l Larger than 50% of b contribution for p. Te>3 -4 Ge. V/c l Strong suppression in non-photonic yield was observed in Au+Au collisions. l Compatible to pi 0 and eta suppression. l Large elliptic flow of non-photonic was observed. l From RAA and v 2, l Strongly interacting (coupled) medium even for heavy quarks. l charm quark thermalization ~ 5 fm/c l h/s ~ (4/3 -2)/4 p, close to conjecture limit l Differentiate D/B suppression pattern more helpful 21

ATHIC Meeting 2008 10/13/2008: T. Gunji Title of Part 2 Heavy Quarkonia Production at RHIC 22

ATHIC Meeting 2008 10/13/2008: T. Gunji J/ Mass Spectra at RHIC 2005 p+p 2008 d+Au 2005 Cu+Cu 2004 Au+Au 23

ATHIC Meeting 2008 10/13/2008: T. Gunji J/ Production in p+p collisions PHENIX PRL 98, 232002 (2007) STAR ar. Xiv: 0806. 0353 [nucl-ex] M. J. Leitch RHIC&AGS Meeting 2008 PHENIX PRL 98, 232002 (2007) STAR ar. Xiv: 0806. 0347 [nucl-ex] 24

ATHIC Meeting 2008 10/13/2008: T. Gunji J/ Production in the medium 25 J/ Production in the medium l Initial stage • Gluon shadowing • Gluon saturation (CGC) tccbar~ 0. 06 fm, tform ~ 1 fm/c l Nuclear Matter • Nuclear absorption • Cronin effect Initial + nuclear matter effect = “CNM effect” l Hot and dense medium • Color screening • Dissociation by gluon • Regeneration from heavy qqbar pairs [Bhanot+Peskin ’ 79]

ATHIC Meeting 2008 10/13/2008: T. Gunji Hot and dense medium effects l Color screening Potential Model & lattice simulations S. Digal, F. Karsch and H. Satz TJ/ ~ 1. 2 Tc [A. Mocsy et al, PRL 99(2007)211602, HP’ 08] Tcc ~ 2 Tc [T. Umeda, PRD. 75, 094502 (07)] l Screening and Sequential Melting l Feed down effect l J/ ~ 0. 6 J/ +0. 3 cc+0. 1 ’ l Fraction not clear at RHIC l. Rcc < 42% (90% CL) l. R ’ = 8. 6% 2. 5% 26

ATHIC Meeting 2008 10/13/2008: T. Gunji Hot and dense medium effects l Dissociation by gluons R. Rapp et al. ar. Xiv: 0807. 2470 Eur. Phys. J. C 43: 91 -96, 2005 l Gluo-effect : J/ +g ccbar l Quasifree : J/ +g ccbar+g l Dominance depends on ebind of J/. (Color Screening) l Recombination l l l A. Andronic et al. NPA 789 (2007) 334 From uncorrelated ccbar pairs. Enhance of the yield. Depends on charm production Statistical hadronization (A. Andronic et al. ) Kinetic formation (R. Rapp et al. ) J/ transport (L. Yan, N. Xu, P. Zhuang et al. ) 27

ATHIC Meeting 2008 10/13/2008: T. Gunji J/ Suppression at SPS J/ suppression at SPS F. Karsch et al. , PLB, 637 (2006) 75 Pb-Pb @ 158 Ge. V R. Rapp et al. Phys. Rev. Lett. 92: 212301, 2004. l Sequential Melting l Direct J/ unlikely to melt. cc and ’ are screened. Absence associated feed down to J/. l Dissociation + Recombination la little recombination contribution 28

ATHIC Meeting 2008 10/13/2008: T. Gunji Cold Matter effects 29 l. Initial stage effect l. Gluon shadowing or Gluon Saturation (CGC) l depletion of gluon PDF in heavy nuclei at small x J/ in d+Au @ PHENIX: • -2. 2<y<-1. 2 : x~0. 09 • y~0 : x~0. 02 • 1. 2<y<2. 2 : x~0. 003 l. Nuclear matter effect l Nuclear absorption l. Dissociation of J/ or pre-resonance by spectators. l Cronin effect shadowing antishadowing σabs = 4. 18 ± 0. 35 mb at SPS ar. Xiv: 0802. 0139 Cold Matter effects

ATHIC Meeting 2008 10/13/2008: T. Gunji J/ Production in d+Au collisions PHENIX PRC 77, 024912 (2008) PHENIX revisits systematic error evaluation. l Tendency is well agreement within shadowing predictions. l EKS/NDSG Model (+2 1 process, g+g J/ ) l Break up cross section is 2~4 mb. l Need more statistics to constraint cold matter effects. 30

ATHIC Meeting 2008 10/13/2008: T. Gunji Another shadowing model 31 E. G. Ferreiro et al. ar. Xiv: 0809. 4684[hep-ph] l. Take into accout g+g J/ +g formation process (extrinsic) l Tendency is well agreement with inclusion of extrinsic process. l Less rapidity dep.

ATHIC Meeting 2008 10/13/2008: T. Gunji 2008 d+Au collisions 32 2008 d+Au collisions l PHENIX Run 8 d+Au ~ 30 x Run 3 d+Au 59 nb-1 63 nb-1 4, 369 J/ ee (~6, 000 from all data) 57, 030 J/ (~73, 000 from all data) Precise CNM effects will be studied using high statistic data!

ATHIC Meeting 2008 10/13/2008: T. Gunji J/ Production in A+A collisions |y|<0. 35 PRL. 98, 232301 (2007) PRL 101, 122301 (2008) 1. 2<|y|<2. 2 PRL. 98, 232301 (2007) ar. Xiv: 0801. 0220 RAA (1. 2<|y|<2. 2) < RAA (|y|<0. 35) ~ RAA at SPS (0<y<1) 33

ATHIC Meeting 2008 10/13/2008: T. Gunji CNM effects in A+A 34 CNM effects in A+A l Extrapolation from d+Au collisions PHENIX revisits systematic error evaluation. PHENIX PRC 77, 024912 (2008) E. G. Ferreiro et al. ar. Xiv: 0809. 4684 l. Even though error is large, l CNM effect is similar between both rapidities l Extrinsic treatment (g+g J/ +g) gives stronger CNM at forward. l Stronger suppression than expectations from CNM effect l Need more d+Au data to constraint CNM effects.

ATHIC Meeting 2008 10/13/2008: T. Gunji Gluon Saturation in A+A CGC (cold matter effect) can describe hadron production in A+A collisions at forward rapidity at RHIC. D. Kharzeev et al. ar. Xiv: 0809. 2933 d. N/dy l Normalization factor is from overall fit to data. l can be fixed using high statistic d+Au data. l Rapidity shape can be described by CGC. l Final state effect is roughly rapidity independent. 35

ATHIC Meeting 2008 10/13/2008: T. Gunji Statistical Hadronization Statistical Hadornization A. Andronic et al. NPA 789 (2007) 334, QM 08 l Less recombination at forward rapidity due to smaller cross section of charm at forward rapidity l Need to understand charm production. 36

ATHIC Meeting 2008 10/13/2008: T. Gunji Kinetic formation 37 Kinetic formation X. Zhao, R. Rapp et al. ar. Xiv: 0712. 2407 Total yield with Charm relaxation time Available charm quarks for recombination is controlled by 1 -exp(-t/tc) Total = CNM effects + Dissociation (p-dep) + Coalescence (tc=7 fm/c) l Stronger suppression is supplemented by recombination. l Depends on charm thermalization time (tc ~ 7 fm/c) l Need to understand charm production in Au+Au

ATHIC Meeting 2008 10/13/2008: T. Gunji Sequential Melting (Hydro+J/ ) 38 Sequential Melting (Hydro+J/ ) T. Gunji et al. PRC 76 051901, 2007 TJ/y = 2. 0 Tc Hydro + J/ T. Gunji et al. PRC 76: 051901, 2007 l Embed free-streaming J/ , cc, ’ into the evolution of matter. l 3+1 hydro. Ncol distribution for J/ and p. T from p+p. l complete melting above dissociation temperature. l J/ suppression at RHIC can be described by sequential melting. l direct J/ suppression starts around Npart~160 (T ~ 2 Tc in hydro). l reflect temperature field of the medium. l TJ/ can be determined in a narrow region. (1. 9< TJ/ /Tc < 2. 1)

ATHIC Meeting 2008 10/13/2008: T. Gunji Sequential Dissociation Y. Liu et al. SQM 08 l J/ transport l Loss (dissociation) + gain (recombination) term l. Simplicity : Well agreement with the data TJ/ /Tc = 1. 9 39

ATHIC Meeting 2008 10/13/2008: T. Gunji J/ in high p. T Many effects are here… M. J. Leitch RHIC&AGS 2008 l. Cronin effect l enhance higher p. T l(anti-)Shadowing l enhance p. T l. Recombination l enhance lower p. T l. Screening & dissociation l suppress lower p. T l hot-wind scenario l suppress high p. T l RAA for high p. T J/ = 0. 9 0. 2 l seems less suppression compared to low p. T J/ ( RAA=0. 59 0. 02) but still consistent with RAA = 0. 59 by fitting results. l Need to have more data to disentangle: l Cronin effect (d+Au), leakage effect, recombination, , , 40

ATHIC Meeting 2008 10/13/08: T. Gunji J/ v 2 at RHIC 33 41 J/ v 2 at RHIC D. Krieg et al. ar. Xiv: 0806. 0736 NA 50 HP 08 PRELIMINARY minimum-bias Run-4 Run-7 Rapp & van Hees, PRC 71, 034907 (2005) l First J/ flow measurement by PHENIX. l v 2 = -10% 10 % 2% 3% (mid-rapidity) l J/ ’s from recombination should inherit large charm-quark flow. but difficult to see flow of J/ due to large error bars. l Negative to positive v 2 Just Mass ordering? Charm collectivity. l Need more data and need to understand with charm quark v 2.

ATHIC Meeting 2008 10/13/2008: T. Gunji Conclusion (2) 42 Conclusion (2) l J/ Production has been measured in p+p, d+Au, A+A collisions at RHIC. l J/ Production in d+Au is consistent with shadowing pictures. l Not constrained well due to the large errors. l Wait for 2008 d+Au analysis l J/ Measurement in Au+Au collisions gives many interesting observations. l Similar suppression between at RHIC (y=0) and at SPS l Stronger suppression at forward than at mid-rapidity. l Dissociation+Recombination l Sequential Melting+gluon saturation l Large uncertainty on cold nuclear matter effects prevents a firm conclusion. More d+Au data. This is highest priority! l Other observables (p. T dist. , v 2) with high statistics will be helpful.

ATHIC Meeting 2008 10/13/2008: T. Gunji For the future at RHIC 43 For the future l Detector Upgrade l PHENIX l VTX/FVTX/NCC l STAR l 100, 000 J/ l 13, 000 J/ ee l LHC!! l x 10 charm, x 100 bottom production l ϒ family measurement l J/ complete screening or strong recombination ma l Luminosity advance x l HFT/TOF/DAQ min

ATHIC Meeting 2008 10/13/2008: T. Gunji Backup slides Major discovery at RHIC 2

Major discovery at RHIC ATHIC Meeting 2008 10/13/2008: T. Gunji Non-photonic electron measurement l Inclusive electrons – photonic electrons l Photonic electrons l Conversion of photons in material l Dalitz decay of light neutral mesons (mainly p 0 and h) l Cocktail subtraction & converter method Ne Electron converter yield 0. 8% 0. 4% 1. 7% Dalitz : 0. 8% X 0 equivalent radiation length W/ converter Photonic W/O converter Photonic Non-photonic 0 Material amounts: 0 2

R. Rapp at SQM 08 Q 3. ) Heavy Quarks in the QGP • Brownian Motion: Fokker Planck Eq. [Svetitsky ’ 88, …] scattering rate diffusion constant Microscopic Calculations of Diffusion: q, g • p. QCD elastic scattering: g-1 = ttherm ≥ 20 fm/c slow _ q • D-/B-resonance model: g-1 = ttherm ~ 5 fm/c c [Svetitsky ’ 88, Mustafa et al ’ 98, Molnar et al ’ 04, Zhang et al ’ 04, Hees+RR ’ 04, Teaney+Moore‘ 04 c _ “D” q parameters: m. D , GD c • recent development: l. QCD-potential scattering [van Hees, Mannarelli, Greco+RR ’ 07]

R. Rapp at SQM 08 2. 5 Comparison of Drag Coefficients G • pert. QCD with running coupling ~ Ad. S/CFT • increase with temperature except T-matrix (melting resonances

R. Rapp at SQM 08 2. 1. 3 Thermal Relaxation of Heavy Quarks in QGP Charm: p. QCD vs. Resonances Charm vs. Bottom p. QCD “D” • factor ~3 faster with resonance interactions! • tctherm ≈ t. QGP ≈ 3 -5 fm/c • bottom does not thermalize

ATHIC Meeting 2008 10/13/2008: T. Gunji Major discovery at RHIC Universality of jet quenching l Universal Bound Model l Upper limit of energy, which can escape the medium. 2

Ad. S/CFT vs. p. QCD with Jets • Langevin model – Collisional energy loss for heavy quarks – Restricted to low p. T – p. QCD vs. Ad. S/CFT computation of D, the diffusion coefficient • ASW model – Radiative energy loss model for all parton species – p. QCD vs. Ad. S/CFT computation of – Debate over its predicted magnitude • ST drag calculation – Drag coefficient for a massive quark moving through a strongly coupled SYM plasma at uniform T – not yet used to calculate observables: let’s do it!

Looking for a Robust, Detectable Signal – Use LHC’s large p. T reach and identification of c and b to distinguish • RAA ~ (1 -e(p. T))n(p. T), where pf = (1 -e)pi (i. e. e = 1 -pf/pi) • Asymptotic p. QCD momentum loss: erad ~ as L 2 log(p. T/Mq)/p. T • String theory drag momentum loss: e. ST ~ 1 - Exp(- L), = pl 1/2 T 2/2 Mq S. Gubser, Phys. Rev. D 74: 126005 (2006); C. Herzog et al. JHEP 0607: 013, 2006 – Independent of p. T and strongly dependent on Mq! – T 2 dependence in exponent makes for a very sensitive probe – Expect: ep. QCD 0 vs. e. Ad. S indep of p. T!! • d. RAA(p. T)/dp. T > 0 => p. QCD; d. RAA(p. T)/dp. T < 0 => ST

Langevin Model – Langevin equations (assumes gv ~ 1 to neglect radiative effects): – Relate drag coef. to diffusion coef. : – IIB Calculation: Ad. S/CFT here • Use of Langevin requires relaxation time be large compared to the inverse temperature:

Integrated RAA Submitted to PRL p. T integration, e+/e-: p. T>0. 3 Ge. V/c e+/e-: p. T>3. 0 Ge. V/c Pi 0: p. T>4. 0 Ge. V/c There are large error bars, but we can see clear suppression in p. T>3. 0 Ge. V/c

Charm cross section from STAR – D mesons – Electrons – Muons • Charm cross section is well constrained – 95% of the total cross section – Direct measurement – D-mesons and muons constrain the low-p. T region p Y. Zhang (STAR), Hard Probes 2006 • Use all possible signals

Charm production at RHIC: total cross section • FONLL as baseline – Large uncertainties due to quark masses, factorization and renormalization scale • Phenix about a factor of 2 higher but consistent within errors – Only electrons but less background • STAR data about a factor of 5 higher – More material but it is the only direct measurement of D-mesons • 95% of the total cross section is measured

• Electron RAA from d+Au to central Au+Au Use of non-photonic PHENIX nucl-ex/0611018 STAR nucl-ex/0607012 electron spectra as proxy for energy loss study • RAA show increasing suppression from peripheral to central Au+Au – First evidence of heavy quark EL – Differences between STAR and PHENIX disappear in RAA • Is it smaller than for lightquark hadrons?

X-N. Wang at HP 08 Heavy Quarks Wicks et al’ 06, Djordjevic et al’ 06 DEel for heavy quark is larger than light quarks Langevin Eq. for v<<1 Moore & Teaney’ 05 p. QCD Rcb Ratio Strong coupling SYM Casalderrey-Solana & Teaney’ 06 Gubser’ 06, Herzog et al’ 06 Upbound for escaping energy in strong coupling SYM Kharzeev’ 08 Horowitz & Gyulassy’ 08