pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) June 26, 2007 arXiv:0706.2336 (LHC predictions) With many thanks to Miklos Gyulassy, Simon Wicks, Jorge Casalderrey-Solana, and Urs Wiedemann. SQM 2007

pQCD Success at RHIC: (circa 2005) Consistency: RAA(h)~RAA(p) Y. Akiba for the PHENIX collaboration, hep-ex/0510008 Consistency: RAA(h)~RAA(p) Null Control: RAA(g)~1 GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy SQM 2007

Trouble for wQGP Picture v2 too large A. Drees, H. Feng, and J. Jia, Phys. Rev. C71:034909 (2005) (first by E. Shuryak, Phys. Rev. C66:027902 (2002)) D. Teaney, Phys. Rev. C68, 034913 (2003) Hydro h/s too small wQGP not ruled out, but what if we try… e- RAA too small M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006) SQM 2007

Strong Coupling The supergravity double conjecture: QCD  SYM  IIB IF super Yang-Mills (SYM) is not too different from QCD, & IF Maldacena conjecture is true Then a tool exists to calculate strongly-coupled QCD in SUGRA SQM 2007

Qualitative AdS/CFT Successes: e- RAA ~ p, h RAA; e- RAA(f) Mach wave-like structures h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD sstrong=(3/4) sweak, similar to Lattice J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 AdS/CFT PHENIX, Phys. Rev. Lett. 98, 172301 (2007) J. J. Friess, S. S. Gubser, G. Michalogiorgakis, S. S. Pufu, Phys. Rev. D75:106003 (2007) T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) SQM 2007

AdS/CFT vs. pQCD with Jets Langevin model Collisional energy loss for heavy quarks Restricted to low pT pQCD vs. AdS/CFT computation of D, the diffusion coefficient ASW model Radiative energy loss model for all parton species pQCD vs. AdS/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! SQM 2007

Looking for a Robust, Detectable Signal Use LHC’s large pT reach and identification of c and b to distinguish RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. e = 1-pf/pi) Asymptotic pQCD momentum loss: String theory drag momentum loss: Independent of pT and strongly dependent on Mq! T2 dependence in exponent makes for a very sensitive probe Expect: epQCD 0 vs. eAdS indep of pT!! dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST erad ~ as L2 log(pT/Mq)/pT eST ~ 1 - Exp(-m L), m = pl1/2 T2/2Mq S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006 SQM 2007

Model Inputs AdS/CFT Drag: nontrivial mapping of QCD to SYM “Obvious”: as = aSYM = const., TSYM = TQCD D/2pT = 3 inspired: as = .05 pQCD/Hydro inspired: as = .3 (D/2pT ~ 1) “Alternative”: l = 5.5, TSYM = TQCD/31/4 Start loss at thermalization time t0; end loss at Tc WHDG convolved radiative and elastic energy loss as = .3 WHDG radiative energy loss (similar to ASW) = 40, 100 Use realistic, diffuse medium with Bjorken expansion PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900) SQM 2007

LHC c, b RAA pT Dependence WH, M. Gyulassy, nucl-th/0706.2336 LHC Prediction Zoo: What a Mess! Let’s go through step by step Naïve expectations born out in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST Large suppression leads to flattening Use of realistic geometry and Bjorken expansion allows saturation below .2 Significant rise in RAA(pT) for pQCD Rad+El SQM 2007

A Cleaner Signal But what about the interplay between mass and momentum? Take ratio of c to b RAA(pT) pQCD: Mass effects die out with increasing pT Ratio starts below 1, asymptotically approaches 1. Approach is slower for higher quenching ST: drag independent of pT, inversely proportional to mass. Simple analytic approx. of uniform medium gives RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27 Ratio starts below 1; independent of pT RcbpQCD(pT) ~ 1 - as n(pT) L2 log(Mb/Mc) ( /pT) SQM 2007

LHC RcAA(pT)/RbAA(pT) Prediction Recall the Zoo: WH, M. Gyulassy, nucl-th/0706.2336 Taking the ratio cancels most normalization differences seen previously pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates) AdS/CFT ratio is flat and many times smaller than pQCD at only moderate pT WH, M. Gyulassy, nucl-th/0706.2336 SQM 2007

But There’s a Catch Speed limit estimate for applicability of AdS/CFT D7 Probe Brane Speed limit estimate for applicability of AdS/CFT drag computation g < gcrit = (1 + 2Mq/l1/2 T)2 ~ 4Mq2/(l T2) Limited by Mcharm ~ 1.2 GeV Ambiguous T for QGP smallest gcrit for largest T = T(t0, x=y=0): (O) largest gcrit for smallest T = Tc: (|) Q “z” x5 Induced horizon Appears if g > gcrit Trailing String “Brachistochrone” Black D3 Brane SQM 2007

LHC RcAA(pT)/RbAA(pT) Prediction (with speed limits) WH, M. Gyulassy, nucl-th/0706.2336 T(t0): (O), corrections unlikely for smaller momenta Tc: (|), corrections likely for higher momenta SQM 2007

Identified c and b at RHIC Index of power law production spectrum: y=0 RHIC LHC NOT slowly varying No longer expect pQCD dRAA/dpT > 0 Large n requires corrections to naïve Rcb ~ Mc/Mb SQM 2007

RHIC c, b RAA pT Dependence WH, M. Gyulassy, to be published Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well SQM 2007

RHIC Rcb Ratio pQCD pQCD AdS/CFT AdS/CFT WH, M. Gyulassy, to be published Wider distribution of AdS/CFT curves due to large n: increased sensitivity to input parameters Advantage of RHIC: lower T => higher AdS speed limits SQM 2007

Conclusions Year 1 of LHC could show qualitative differences between energy loss mechanisms: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST Ratio of charm to bottom RAA, Rcb, will be an important observable Ratio is: flat in ST; approaches 1 from below in pQCD partonic E-loss A measurement of this ratio NOT going to 1 will be a clear sign of new physics: pQCD predicts ~ 2-3 times increase in Rcb by 30 GeV—this can be observed in year 1 at LHC Measurement at RHIC will be possible AdS/CFT calculations applicable to higher momenta than at LHC due to lower medium temperature SQM 2007

Conclusions (cont’d) Additional c, b PID Goodies: Need for p+A control Adil Vitev in-medium fragmentation results in a much more rapid rise to 1 for RcAA/RbAA with the possibility of breaching 1 and asymptotically approaching 1 from above Surface emission models (although already unlikely as per v2(pT) data) predict flat in pT c, b RAA, with a ratio of 1 Moderately suppressed radiative only energy loss shows a dip in the ratio at low pT; convolved loss is monotonic. Caution: in this regime, approximations are violated Mach cone may be due to radiated gluons: from pQCD the away-side dip should widen with increasing parton mass Need for p+A control SQM 2007

Backups SQM 2007

LHC p Predictions Our predictions show a significant increase in RAA as a function of pT This rise is robust over the range of predicted dNg/dy for the LHC that we used This should be compared to the flat in pT curves of AWS-based energy loss (next slide) We wish to understand the origin of this difference WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation SQM 2007

Asymptopia at the LHC Asymptotic pocket formulae: DErad/E ~ a3 Log(E/m2L)/E DEel/E ~ a2 Log((E T)1/2/mg)/E WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation SQM 2007

n(pT) SQM 2007

Langevin Model Langevin equations (assumes gv ~ 1 to neglect radiative effects): Relate drag coef. to diffusion coef.: IIB Calculation: Use of Langevin requires relaxation time be large compared to the inverse temperature: AdS/CFT here SQM 2007

But There’s a Catch (II) Limited experimental pT reach? ALICE Physics Performance Report, Vol. II SQM 2007

Zoom In Factor ~2-3 increase in ratio for pQCD Possible distinction for Rad only vs. Rad+El at low-pT SQM 2007

Regimes of Applicability String Regime Large Nc, constant ‘t Hooft coupling ( ) Small quantum corrections Large ‘t Hooft coupling Small string vibration corrections Only tractable case is both limits at once Classical supergravity (SUGRA) RHIC/LHC Regime Mapping QCD Nc to SYM is easy, but coupling is hard aS runs whereas aSYM does not: aSYM is something of an unknown constant Taking aSYM = aS = .3 (D/2pT ~ 1); D/2pT ~ 3 => aSYM ~ .05 SQM 2007