Probing AdS/CFT with Heavy Quarks William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) October 26, 2007 arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions) With many thanks to Miklos Gyulassy, Simon Wicks, and Ivan Vitev AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia Introduction AdS/CFT looks promising, pQCD also has its successes Desire a robust probe that can cleanly falsify one or both formalisms: Try Heavy Quarks! AdS Strings Intersect with Nuclear Beams at Columbia

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! AdS Strings Intersect with Nuclear Beams at Columbia

Looking for a Robust, Detectable Signal Use future detectors’ 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 AdS Strings Intersect with Nuclear Beams at Columbia

Model Inputs for LHC Predictions 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) AdS Strings Intersect with Nuclear Beams at Columbia

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 AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia 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) AdS Strings Intersect with Nuclear Beams at Columbia

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 AdS Strings Intersect with Nuclear Beams at Columbia

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 Worldsheet boundary Spacelike if g > gcrit Trailing String “Brachistochrone” D3 Black Brane AdS Strings Intersect with Nuclear Beams at Columbia

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 AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia 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 AdS Strings Intersect with Nuclear Beams at Columbia

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 AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia 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 AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia 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? AdS Strings Intersect with Nuclear Beams at Columbia

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 AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia 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 AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia Backups AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia 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 AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia Asymptopia at the LHC Asymptotic pocket formulae: DErad/E ~ a3 Log(E/m2L)/E DEel/E ~ a2 Log((E T)1/2/mg)/E AdS Strings Intersect with Nuclear Beams at Columbia WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

AdS Strings Intersect with Nuclear Beams at Columbia 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 AdS Strings Intersect with Nuclear Beams at Columbia

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 AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia 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) AdS Strings Intersect with Nuclear Beams at Columbia

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: AdS Strings Intersect with Nuclear Beams at Columbia

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 AdS Strings Intersect with Nuclear Beams at Columbia

AdS Strings Intersect with Nuclear Beams at Columbia pQCD Success at RHIC: (circa 2005) Y. Akiba for the PHENIX collaboration, nucl-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 AdS Strings Intersect with Nuclear Beams at Columbia

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) AdS Strings Intersect with Nuclear Beams at Columbia

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) AdS Strings Intersect with Nuclear Beams at Columbia

h/s Sensitive to Initial Conditions Diffuse BGK IC => Ideal Hydro, h/s ~ 1/4p Sharp CGC IC => Viscous Hydro Currently no exp. constraint on IC T. Hirano, U. Heinz, D. Kharzeev, R. Lacey, Y. Nara, Phys. Lett. B636:299-304,2006 AdS Strings Intersect with Nuclear Beams at Columbia