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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 1 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! 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 2 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! 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 3 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: erad ~ as L2 log(pT/Mq)/pT • String theory drag momentum loss: 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 – 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 4 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) 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 5 LHC c, b RAA pT Dependence WH, M. Gyulassy, nucl-th/0706.2336 – Naïve LHC Prediction Unfortunately, Large Significant suppression expectations rise large inZoo: Rleads born suppression What (pTto )out for flattening a in Mess! pQCD fullpQCD numerical Rad+El similar calculation: to AdS/CFT AA – Let’s Use ofgorealistic through dRAA geometry step (pT)/dp by step > 0 Bjorken => pQCD; expansion dRAA(pTallows )/dpT < saturation 0 => ST below .2 Tand 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 6 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 RcbpQCD(pT) ~ 1 - as n(pT) L2 log(Mb/Mc) ( /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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 7 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) WH, M.times Gyulassy, nucl-th/0706.2336 – AdS/CFT ratio is flat and many smaller than pQCD at only moderate pT 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 8 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 – Ambiguous T for QGP • smallest gcrit for largest T = T(t0, x=y=0): (O) • largest gcrit for smallest T = Tc: (|) 10/26/07 D7 Probe Brane Q Worldsheet boundary Spacelike if g > gcrit x5 Trailing String “Brachistochrone” D3 Black Brane AdS Strings Intersect with Nuclear Beams at Columbia “z” William Horowitz 9 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 10 Measurement at RHIC – Future detector upgrades will allow for identified c and b quark measurements – RHIC production spectrum significantly harder than LHC • • NOT slowly varying y=0 RHIC – No longer expect pQCD dRAA/dpT > 0 • Large n requires corrections to naïve Rcb ~ Mc/Mb 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia LHC William Horowitz 11 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 12 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 13 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? 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 14 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 15 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 16 Backups 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 17 LHC p Predictions WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation 10/26/07 • 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 AWSbased energy loss (next slide) • We wish to understand the origin of this difference AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 18 Asymptopia at the LHC Asymptotic pocket formulae: DErad/E ~ a3 Log(E/m2L)/E DEel/E ~ a2 Log((E T)1/2/mg)/E 10/26/07 WH, S. Wicks, M.with Gyulassy, M. Djordjevic, in preparation AdS Strings Intersect Nuclear Beams at Columbia William Horowitz 19 Langevin Model – Langevin equations (assumes gv ~ 1 to neglect radiative effects): – Relate drag coef. to diffusion coef.: – IIB Calculation: AdS/CFT here • Use of Langevin requires relaxation time be large compared to the inverse temperature: 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 20 But There’s a Catch (II) • Limited experimental pT reach? ALICE Physics Performance Report, Vol. II – 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 21 K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) 10/26/07 A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 22 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 Common to Fourier expand RAA: 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia pT f William Horowitz 23 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 24 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 25 Trouble for wQGP Picture Hydro h/s too small e-2Rtoo too •v wQGP notsmall ruled out, but what if we try AA large strong coupling? A. H. Feng, and J. Jia, C71:034909 (2005) M. Drees, Djorjevic, M. Gyulassy, R.Phys. Vogt,Rev. S. Wicks, Phys. Lett. (first byD.E.Teaney, Shuryak, Phys. Rev. C66:027902 (2002)) Rev. C68, 034913 (2003) B632:81-86 (2006) Phys. 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 26 Qualitative AdS/CFT Successes: -R1~ sMach =(3/4) wave-like s structures , similar • h/s e-strong RAA ~ p, h R ; e )to Lattice ~ 1/4p << weak AA AA(fh/s AdS/CFT pQCD AdS/CFT J. P. Blaizot, S. S. Gubser, E. Iancu, S. S.U. Pufu, Kraemmer, and A. Yarom, A. Rebhan, arXiv:0706.0213 hep-ph/0611393 T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) PHENIX, Phys. Rev. Lett. 98, 172301 (2007) 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 27 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 10/26/07 AdS Strings Intersect with Nuclear Beams at Columbia William Horowitz 28