The LHC to Test pQCD vs. AdS/CFT Heavy Quark Energy Loss William Horowitz Columbia University FIAS April 26, 2007 With many thanks to Miklos Gyulassy. 44th RNM Workshop

Good Signs for pQCD at RHIC: (circa 2005) 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 44th RNM Workshop

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)) e- too small M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006) D. Teaney, Phys. Rev. C68, 034913 (2003) Hydro h/s too small 44th RNM Workshop

Strong Coupling The supergravity double conjecture: QCD  SYM  IIB IF super Yang-Mills (SYM) is not too different from QCD, & IF Maldecena conjecture is true Then a tool exists to calculate strongly-coupled QCD in SUGRA 44th RNM Workshop

Ideal Hydro? Hydro merely propagates initial conditions; its results are highly dependent on them pQCD: h/s ~ 1 AdS: universal lower bound for all infinitely coupled systems h/s ~ 1/4p AdS success? Glauber initial state => ideal (ST) hydro CGC initial state => viscous (pQCD) hydro T. Hirano, U. W. Heinz, D. Kharzeev, R. Lacy, Y. Nara, Phys. Lett. B636:299-304 (2006) Must understand initial state better before reaching a conclusion: A. Adil, M. Gyulassy, T. Hirano, Phys. Rev. D73:074006 (2006) 44th RNM Workshop

Simultaneous p, e- Suppression pQCD is not falsified: Elastic loss? Uncertainty in c, b contributions In-medium fragmentation? Resonances? A. Adil and I. Vitev, hep-ph/0611109 Naïve pQCD => large mass, small loss But p, h RAA ~ e- RAA! S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, 034913 (2006) 44th RNM Workshop

Simultaneous RAA, v2 Description Energy loss translates spatial anisotropy of medium to jets RAA and v2 are thus anti-correlated First seen for pions, no nonperturbative model reproduces both RAA and v2 Observed for e-, too No known solution to the puzzle PHENIX, Phys. Rev. Lett. 98, 172301 (2007) WH, Acta Phys. Hung. A27:221-225 44th RNM Workshop

Strings, Jets, and the LHC 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 Considerable debate over its magnitude ST drag calculation Equation for infinitely massive quark moving with constant v through infinitely coupled SYM at uniform T not yet used to calculate observables: let’s do it! 44th RNM Workshop

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); aSYM ~ .05 => D/2pT~3 LHC medium density predictions vary by factor of 2 44th RNM Workshop

Looking for a Robust, Detectable Signal Use large LHC 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: eQCD 0 vs. eAdS indep of pT!! dRAA(pT)/dpT > 0 => pQCD ; dRAA(pT)/dpT < 0 => ST erad ~ a3 L2 log(pT/Mq)/pT eST ~ 1 - Exp(-m L), m = plT2/2Mq S. Gubser, Phys.Rev.D74:126005 (2006) 44th RNM Workshop

Models AdS/CFT Drag “Obvious”: as = aSYM, TSYM = TQCD D/2pT = 3 inspired: as = .05, t0 = 1 Hydro inspired: as = .3, t0 = .6 “Alternative”: l = 5.5, TSYM = TQCD/31/4 WHDG convolved radiative and collisional energy loss as = .3, t0 = .2 WHDG radiative energy loss (similar to ASW) = 40, 100 All use realistic, nonuniform medium with Bjorken expansion 44th RNM Workshop

LHC c, b RAA pT Dependence Full numerical calculation shows ST RAA decreases with pT (as compared to strong increase for pQCD) Saturation, or fragility, occurs at a much smaller RAA due to realistic modeling of the medium 44th RNM Workshop

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 Ratio starts below 1, independent of pT RcAA(pT)/RbAA(pT) ~ 1 - a3 n(pT) L2 log(Mb/Mc) ( /pT) 44th RNM Workshop

LHC RcAA(pT)/RbAA(pT) Prediction Recall the previous plot: Taking the ratio cancels most normalization differences seen previously pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates) ST ratio is flat and many times smaller than pQCD at only moderate pT 44th RNM Workshop

Conclusions PID and large pT reach will give the LHC a unique position to make discoveries in the heavy quark sector 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 will be an important observable Ratio is: flat in ST; asymptotically approaching 1 from below in pQCD While future AdS/CFT calculations could well alter the ST predictions shown here, it is highly unlikely that a pQCD mechanism can be found that allows mass effects to persist out to momenta orders of magnitude larger than Mq A measurement of this ratio NOT going to 1 will be a clear sign of new physics: pQCD predicts ~ 3 times increase in this ratio by 30 GeV—this can be observed in year 1 at the LHC 44th RNM Workshop

Conclusions (cont’d) Additional LHC Goodies: 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 p v2(pT) data) predict flat in pT c, b RAA, with a ratio of 1 Mach cone may be due to radiated gluons: from pQCD the away-side dip should widen with increasing parton mass Moderately suppressed radiative only energy loss shows a dip in the ratio at low pT; convolved loss is monotonic 44th RNM Workshop

Backups: LHC p Predictions 44th RNM Workshop

Suppression of AWS AWS pQCD-based controlling parameter must be nonperturbatively large to fit RHIC data -pQCD gives = c e3/4, where c ~ 2; c ~ 8-20 required for RHIC data -Needed because radiative only energy loss (and > 1? R = (1/2) L3) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) 44th RNM Workshop

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 44th RNM Workshop

Comparison of LHC p Predictions (b) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) Curves of ASW-based energy loss are flat in pT 44th RNM Workshop

Why ASW is Flat Flat in pT curves result from extreme suppression at the LHC When probability leakage P(e > 1) is large, the (renormalized or not) distribution becomes insensitive to the details of energy loss Enormous suppression due to: Already (nonperturbatively) large suppression at RHIC for ASW Extrapolation to LHC assumes 7 times RHIC medium densities (using EKRT) Note: even if LHC is only ~ 2-3 times RHIC, still an immoderate ~ 30-45 As seen on the previous slide, Vitev predicted a similar rise in RAA(pT) as we do Vitev used only radiative loss, Prad(e), but assumed fixed path WHDG similar because elastic and path fluctuations compensate 44th RNM Workshop

Conclusions LHC RAA(pT) data will distinguish between energy loss models GLV Rad+El+Geom predicts significant rise in pT ASW type models predict flat pT dependence 44th RNM Workshop

Backup Slides 44th RNM Workshop

RHIC e- 44th RNM Workshop

RHIC c, b RAA(pT) 44th RNM Workshop

RHIC RcAA(pT)/RbAA(pT) 44th RNM Workshop

n(pT) 44th RNM Workshop

Hydro Initial State Hirano and Nara(’04), Hirano et al.(’06)‏ Kuhlman et al.(’06), Drescher et al.(’06)‏ 44th RNM Workshop

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 gives l ~ 10 Taking aSYM ~ .05 => l ~ 1.8 (keep in mind for later) 44th RNM Workshop

Langevin Scheme 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: ST here 44th RNM Workshop

Plugging in Numbers Langevin pT reach: D/(2pT) = 4/l1/2 from ST: gv(8 GeV e- from c) ~ 11 D/(2pT) = 4/l1/2 from ST: aSYM = aS = .3 => D/(2pT) ~ 1 Oversuppresses RAA aSYM ~ .05 required for D/(2pT) ~ 3 Mass constraint, (for T = 350 MeV) aSYM = .3 this gives ~ .6 GeV aSYM = .05 this gives ~ .25 GeV Both charm and bottom satisfy this condition Not entirely unreasonable 44th RNM Workshop

44th RNM Workshop

44th RNM Workshop

44th RNM Workshop

44th RNM Workshop

Strings, Jet Physics, and the LHC: Looking for a Signal Use large LHC pT reach and identification of c and b to distinguish RAA ~ (1-e(pT))n(pT), pf = (1-e)pi Asymptotic pQCD momentum loss: String theory drag momentum loss: Independent of pT and strongly dependent on m!! T2 dependence makes for a very sensitive probe erad ~ a3 L2 log(pT/Mq)/pT eST ~ 1 - Exp(-m L), m = plT2/2m S. Gubser, Phys.Rev.D74:126005 (2006) 44th RNM Workshop