Possible String Theoretic Deviations from pQCD in Heavy Quark Energy Loss at LHC William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) June 1, 2007 With many thanks to Miklos Gyulassy, Simon Wicks, Ivan Vitev, Jorge Casalderrey-Solana. CERN Heavy Ion Forum

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 CERN Heavy Ion Forum

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) CERN Heavy Ion Forum

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 CERN Heavy Ion Forum

Qualitative AdS/CFT Successes: Mach wave-like structures sstrong=(3/4) sweak, similar to Lattice e- RAA ~ p, h RAA; e- RAA(f) h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD 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) CERN Heavy Ion Forum

Give up on pQCD? Old and Busted: pQCD New Hotness: AdS/CFT CERN Heavy Ion Forum

If You Ask Me… Use the LHC to Test the Two! Let’s look at Heavy Quark Jet Suppression CERN Heavy Ion Forum

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 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! CERN Heavy Ion Forum

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: 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) CERN Heavy Ion Forum

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 CERN Heavy Ion Forum

Model Inputs AdS/CFT Drag “Obvious”: as = aSYM, TSYM = TQCD D/2pT = 3 inspired: as = .05 pQCD/Hydro inspired: as = .3 (D/2pT ~ 1) “Alternative”: l = 5.5, TSYM = TQCD/31/4 WHDG convolved radiative and collisional energy loss as = .3 WHDG radiative energy loss (similar to ASW) = 40, 100 All use realistic, nonuniform medium with Bjorken expansion Two medium densities for LHC: PHOBOS (dNg/dy = 1750); CGC (dNg/dy = 2900) CERN Heavy Ion Forum

LHC c, b RAA pT Dependence 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 Significant rise in RAA(pT) for pQCD Rad+El Large suppression leads to flattening Use of realistic geometry and Bjorken expansion allows saturation below .2 CERN Heavy Ion Forum

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 - as n(pT) L2 log(Mb/Mc) ( /pT) CERN Heavy Ion Forum

LHC RcAA(pT)/RbAA(pT) Prediction Recall the Zoo: 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 CERN Heavy Ion Forum

But There’s a Catch (I) 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: (|) CERN Heavy Ion Forum

LHC RcAA(pT)/RbAA(pT) Prediction (with speed limits) O: corrections unlikely for smaller momenta |: corrections likely for higher momenta CERN Heavy Ion Forum

But There’s a Catch (II) Limited experimental pT reach? ALICE Physics Performance Report, Vol. II CERN Heavy Ion Forum

Zoom In Factor ~2-3 increase in ratio for pQCD Possible distinction for Rad only vs. Rad+El at low-pT CERN Heavy Ion Forum

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 ~ 2-3 times increase in this ratio by 30 GeV—this can be observed in year 1 at the LHC CERN Heavy Ion Forum

Conclusions (cont’d) Additional LHC c, b PID 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 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 CERN Heavy Ion Forum

AdS/CFT CERN Heavy Ion Forum J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 AdS/CFT CERN Heavy Ion Forum

Backups CERN Heavy Ion Forum

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 CERN Heavy Ion Forum

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 CERN Heavy Ion Forum

RHIC e- CERN Heavy Ion Forum

RHIC c, b RAA(pT) CERN Heavy Ion Forum

RHIC RcAA(pT)/RbAA(pT) CERN Heavy Ion Forum

n(pT) CERN Heavy Ion Forum

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 CERN Heavy Ion Forum

Drag Picture The Heavy Quark Brachistochrone: CERN Heavy Ion Forum J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007 CERN Heavy Ion Forum