Falsifying AdS/CFT Drag or pQCD Heavy Quark Energy Loss with A+A at RHIC and LHC William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) November 30, 2007 arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions) With many thanks to Miklos Gyulassy, and Simon Wicks Nuclear Theory Seminar, Texas A&M

QCD Calculations Previously only two tools: Lattice QCD pQCD All momenta Euclidean correlators Any quantity Small coupling Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M 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 Nuclear Theory Seminar, Texas A&M

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) Q.M. SSYM => C.M. SNG Nuclear Theory Seminar, Texas A&M

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 Nuclear Theory Seminar, Texas A&M

Connection to Experiment a.k.a. the Reality Check for Theory Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M pQCD Success 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 Nuclear Theory Seminar, Texas A&M

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) Nuclear Theory Seminar, Texas A&M

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) S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213 T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) Nuclear Theory Seminar, Texas A&M

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! Nuclear Theory Seminar, Texas A&M

Energy Loss Dependence t x Q, m v D7 Probe Brane D3 Black Brane (horizon) 3+1D Brane Boundary Black Hole z = 0 zh = pT zm = 2pm / l1/2 AdS/CFT Drag: dpT/dt ~ -(T2/Mq) pT Compare to Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT Compare to LPM dpT/dt ~ -LT3 log(pT/Mq) Nuclear Theory Seminar, Texas A&M

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 Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M 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) Nuclear Theory Seminar, Texas A&M

LHC c, b RAA pT Dependence WH, M. Gyulassy, arXiv: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 Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M 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) Nuclear Theory Seminar, Texas A&M

LHC RcAA(pT)/RbAA(pT) Prediction Recall the Zoo: WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] 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, arXiv:0706.2336 [nucl-th] Nuclear Theory Seminar, Texas A&M

But There’s a Catch 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 Similar to BH LPM gcrit ~ Mq/(lT) Ambiguous T for QGP smallest gcrit for largest T = T(t0, x=y=0): “(” largest gcrit for smallest T = Tc: “]” D7 Probe Brane Q “z” x5 Worldsheet boundary Spacelike if g > gcrit Trailing String “Brachistochrone” D3 Black Brane Nuclear Theory Seminar, Texas A&M

LHC RcAA(pT)/RbAA(pT) Prediction (with speed limits) WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] T(t0): (O), corrections unlikely for smaller momenta Tc: (|), corrections likely for higher momenta Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M 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 Nuclear Theory Seminar, Texas A&M

RHIC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M RHIC Rcb Ratio pQCD pQCD AdS/CFT AdS/CFT WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] Wider distribution of AdS/CFT curves due to large n: increased sensitivity to input parameters Advantage of RHIC: lower T => higher AdS speed limits Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M 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 Nuclear Theory Seminar, Texas A&M

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 Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M Conclusions (cont’d) Additional 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 Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M Backups Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M 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 Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M 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 Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M 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 Nuclear Theory Seminar, Texas A&M

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 Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M 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) Nuclear Theory Seminar, Texas A&M

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: Nuclear Theory Seminar, Texas A&M

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 Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M Pion RAA Is it a good measurement for tomography? Yes: small experimental error Claim: we should not be so immediately dis-missive of the pion RAA as a tomographic tool Maybe not: some models appear “fragile” Nuclear Theory Seminar, Texas A&M

Fragility: A Poor Descriptor All energy loss models with a formation time saturate at some RminAA > 0 The questions asked should be quantitative : Where is RdataAA compared to RminAA? How much can one change a model’s controlling parameter so that it still agrees with a measurement within error? Define sensitivity, s = min. param/max. param that is consistent with data within error Nuclear Theory Seminar, Texas A&M

Different Models have Different Sensitivities to the Pion RAA GLV: s < 2 Higher Twist: DGLV+El+Geom: AWS: s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007) WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M A Closer Look at ASW The lack of sensitivity needs to be more closely examined because (a) unrealistic geometry (hard cylinders) and no expansion and (b) no expansion shown against older data (whose error bars have subsequently shrunk (a) (b) 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) Nuclear Theory Seminar, Texas A&M

Surface Bias vs. Surface Emission Surface Emission: one phrase explanation of fragility All models become surface emitting with infinite E loss Surface Bias occurs in all energy loss models Expansion + Realistic geometry => model probes a large portion of medium A. Majumder, HP2006 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 Nuclear Theory Seminar, Texas A&M

Nuclear Theory Seminar, Texas A&M A Closer Look at ASW Difficult to draw conclusions on inherent surface bias in AWS from this for three reasons: No Bjorken expansion Glue and light quark contributions not disentangled Plotted against Linput (complicated mapping from Linput to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) Nuclear Theory Seminar, Texas A&M