Identified Charm and Bottom Jets to Test pQCD vs. AdS/CFT Energy Loss William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) August 22, 2007 arXiv:0706.2336 (LHC predictions) With many thanks to Miklos Gyulassy, Simon Wicks, Jorge Casalderrey-Solana, and Urs Wiedemann. Los Alamos P-25 Seminar

QCD Calculations No real debate on the QCD Lagrangian, but how to calculate observables using this beast? Los Alamos P-25 Seminar

Previously only two tools: QCD Calculations Previously only two tools: Lattice QCD pQCD All momenta Euclidean correlators Any quantity Small coupling Los Alamos P-25 Seminar

Maldacena Conjecture Large Nc limit of d-dimensional conformal field theory dual to string theory on the product of d+1-dimensional Anti-de Sitter space with a compact manifold 3+1 SYM z = 0 Los Alamos P-25 Seminar

Regime of Applicability 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) D7 Probe Brane t x v Q, m 3+1D Brane Boundary zm = 2pm / l1/2 Q.M. SSYM => C.M. SNG D3 Black Brane (horizon) zh = pT Black Hole z = 0 Los Alamos P-25 Seminar

Strong Coupling Calculation 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 Los Alamos P-25 Seminar

Connection to Experiment a.k.a. the Reality Check for Theory Los Alamos P-25 Seminar

Introduction to Jargon Naïvely: if medium has no effect, then RAA = 1 Common variables used are transverse momentum, pT, and angle with respect to the reaction plane, f pT f Common to Fourier expand RAA: Los Alamos P-25 Seminar

Geometry of a HI Collision Medium density and jet production are wide, smooth distributions Use of unrealistic geometries strongly bias results S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007 1D Hubble flow => r(t) ~ 1/t => T(t) ~ 1/t1/3 M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005 Los Alamos P-25 Seminar

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 Los Alamos P-25 Seminar

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 strong coupling? e- RAA too small M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006) Los Alamos P-25 Seminar

Qualitative AdS/CFT Successes: h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD e- RAA ~ p, h RAA; e- RAA(f) sstrong=(3/4) sweak, similar to Lattice Mach wave-like structures 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) Los Alamos P-25 Seminar

Quantitative AdS/CFT 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! Los Alamos P-25 Seminar

Looking for a Robust, Detectable Signal Use LHC’s large pT reach and identification of c and b to distinguish between pQCD, AdS/CFT 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 Los Alamos P-25 Seminar

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) Los Alamos P-25 Seminar

LHC c, b RAA pT Dependence WH, M. Gyulassy, nucl-th/0706.2336 Naïve expectations born out in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST LHC Prediction Zoo: What a Mess! Let’s go through step by step Significant rise in RAA(pT) for pQCD Rad+El Unfortunately, large suppression pQCD similar to AdS/CFT Large suppression leads to flattening Use of realistic geometry and Bjorken expansion allows saturation below .2 Los Alamos P-25 Seminar

An Enhanced 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) Los Alamos P-25 Seminar

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 Los Alamos P-25 Seminar

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” D3 Black Brane Los Alamos P-25 Seminar

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 Los Alamos P-25 Seminar

Measurement at RHIC Future detector upgrades will allow for identified c and b quark measurements RHIC production spectrum significantly harder than LHC y=0 RHIC LHC NOT slowly varying No longer expect pQCD dRAA/dpT > 0 Large n requires corrections to naïve Rcb ~ Mc/Mb Los Alamos P-25 Seminar

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 Los Alamos P-25 Seminar

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 Los Alamos P-25 Seminar

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 Universality of pQCD and AdS/CFT Dependencies? Los Alamos P-25 Seminar

Additional Discerning Power Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1 Does not include partonic energy loss, which will be nonnegligable as ratio goes to unity Los Alamos P-25 Seminar

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 Los Alamos P-25 Seminar

Backups Los Alamos P-25 Seminar

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 Los Alamos P-25 Seminar

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 Los Alamos P-25 Seminar

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 Los Alamos P-25 Seminar

But There’s a Catch (II) Limited experimental pT reach? ATLAS and CMS do not seem to be limited in this way (claims of year 1 pT reach of ~100 GeV) but systematic studies have not yet been performed ALICE Physics Performance Report, Vol. II Los Alamos P-25 Seminar

K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) 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) Los Alamos P-25 Seminar