2/7/09 William Horowitz High-p T Physics at LHC1 Testing AdS/CFT at LHC William Horowitz The Ohio State University February 6, 2009 With many thanks to Yuri Kovchegov and Ulrich Heinz

2/7/09 William Horowitz High-p T Physics at LHC2 First, a Perturbative Detour

2/7/09 William Horowitz High-p T Physics at LHC3 pQCD Success in High-p T at RHIC: –Consistency: R AA (  )~R AA (  ) –Null Control: R AA (  )~1 –GLV Calculation: Theory~Data for reasonable fixed L~5 fm and dN g /dy~dN  /dy Assuming pQCD E-loss, let’s clear up some myths Y. Akiba for the PHENIX collaboration, hep-ex/ (circa 2005)

2/7/09 William Horowitz High-p T Physics at LHC4 Surface Emission: Red Herring? If you believe in pQCD E-loss, observed jets come from deep in the medium T. Renk and K. J. Eskola, PoS LHC07, 032 (2007) S. Wicks, et al., Nucl. Phys. A784, 426 (2007) HT, AMY, ASWWHDGBDMPS + Hydro S. A. Bass, et al., arXiv: [nucl-th].

2/7/09 William Horowitz High-p T Physics at LHC5 Fragility is Fragile Linear-linear plot of R AA (qhat) is the incorrect way to think about the problem PHENIX, Phys. Rev. C77, (2008) K. J. Eskola, et al., Nucl. Phys. A747, 511 (2005)

2/7/09 William Horowitz High-p T Physics at LHC6 Fragility is Fragile (cont’d) If you believe in pQCD E-loss, R AA is NOT a fragile probe of the medium –Linear on a log-log plot –Double => halve R AA –Similar results for WHDG, GLV, AMY, ZOWW, etc. PHENIX, Phys. Rev. C77, (2008)

2/7/09 William Horowitz High-p T Physics at LHC7 Quantitative Extraction Model params to within ~20% – Experimental error only!! Sys. theor. err. could be quite large –Running coupling uncertainties »Smaller at LHC? –Multi-gluon correlations? »Larger at LHC? –Handling of geometry –…–… See also TECHQM wiki: S. Wicks, et al., Nucl. Phys. A783, 493 (2007) PHENIX, PRC77, (2008)

2/7/09 William Horowitz High-p T Physics at LHC8 Trouble for High-p T wQGP Picture –v 2 too small –NPE supp. too large STAR, Phys. Rev. Lett. 98, (2007)  0 v 2 M Tannenbaum, High-p T Physics at LHC ‘09 PHENIX, Phys. Rev. Lett. 98, (2007) NPE v 2 Pert. at LHC energies?

2/7/09 William Horowitz High-p T Physics at LHC9 Back to the Future Fifth Dimension

2/7/09 William Horowitz High-p T Physics at LHC10 Motivation for High-p T AdS Why study AdS E-loss models? –Many calculations vastly simpler Complicated in unusual ways –Data difficult to reconcile with pQCD –pQCD quasiparticle picture leads to dominant q ~  ~.5 GeV mom. transfers => Nonperturbatively large  s Use data to learn about E-loss mechanism, plasma properties –Domains of self-consistency crucial for understanding

2/7/09 William Horowitz High-p T Physics at LHC11 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

2/7/09 William Horowitz High-p T Physics at LHC12 AdS/CFT Energy Loss Models –Langevin Diffusion Collisional energy loss for heavy quarks Restricted to low p T pQCD vs. AdS/CFT computation of D, the diffusion coefficient –ASW/LRW model Radiative energy loss model for all parton species pQCD vs. AdS/CFT computation of Debate over its predicted magnitude –Heavy Quark Drag calculation Embed string representing HQ into AdS geometry Includes all E-loss modes Empty space calculation: Previously: thermalized QGP plasma, temp. T,  crit <~M q /T Moore and Teaney, Phys.Rev.C71:064904,2005 Casalderrey-Solana and Teaney, Phys.Rev.D74:085012,2006; JHEP 0704:039,2007 BDMPS, Nucl.Phys.B484: ,1997 Armesto, Salgado, and Wiedemann, Phys. Rev. D69 (2004) Liu, Ragagopal, Wiedemann, PRL 97:182301,2006; JHEP 0703:066,2007 Gubser, Phys.Rev.D74:126005,2006 Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013,2006 Kharzeev, arXiv: [hep-ph]

2/7/09 William Horowitz High-p T Physics at LHC13 Energy Loss Comparison –AdS/CFT Drag: dp T /dt ~ -(T 2 /M q ) p T –Similar to Bethe-Heitler dp T /dt ~ -(T 3 /M q 2 ) p T –Very different from LPM dp T /dt ~ -LT 3 log(p T /M q ) t x Q, m v D7 Probe Brane D3 Black Brane (horizon) 3+1D Brane Boundary Black Hole z =  z h = 1/  T z m = 1/2 /2  m z = 0

2/7/09 William Horowitz High-p T Physics at LHC14 R AA Approximation –Above a few GeV, quark production spectrum is approximately power law: dN/dp T ~ 1/p T (n+1), where n(p T ) has some momentum dependence –We can approximate R AA (p T ): R AA ~ (1-  (p T )) n(p T ), where p f = (1-  )p i (i.e.  = 1-p f /p i ) y=0 RHIC LHC

2/7/09 William Horowitz High-p T Physics at LHC15 –Use LHC’s large p T reach and identification of c and b to distinguish between pQCD, AdS/CFT Asymptotic pQCD momentum loss: String theory drag momentum loss: –Independent of p T and strongly dependent on M q ! –T 2 dependence in exponent makes for a very sensitive probe –Expect:  pQCD 0 vs.  AdS indep of p T !! dR AA (p T )/dp T > 0 => pQCD; dR AA (p T )/dp T ST  rad   s L 2 log(p T /M q )/p T Looking for a Robust, Detectable Signal  ST  1 - Exp(-  L),  =    T 2 /2M q S. Gubser, Phys.Rev. D74 : (2006); C. Herzog et al. JHEP 0607:013,2006

2/7/09 William Horowitz High-p T Physics at LHC16 Model Inputs –AdS/CFT Drag: nontrivial mapping of QCD to SYM “Obvious”:  s =  SYM = const., T SYM = T QCD –D 2  T = 3 inspired:  s =.05 –pQCD/Hydro inspired:  s =.3 (D 2  T ~ 1) “Alternative”: = 5.5, T SYM = T QCD /3 1/4 Start loss at thermalization time  0 ; end loss at T c –WHDG convolved radiative and elastic energy loss  s =.3 –WHDG radiative energy loss (similar to ASW) = 40, 100 –Use realistic, diffuse medium with Bjorken expansion –PHOBOS (dN g /dy = 1750); KLN model of CGC (dN g /dy = 2900)

2/7/09 William Horowitz High-p T Physics at LHC17 –LHC Prediction Zoo: What a Mess! –Let’s go through step by step –Unfortunately, large suppression pQCD similar to AdS/CFT–Large suppression leads to flattening –Use of realistic geometry and Bjorken expansion allows saturation below.2 –Significant rise in R AA (p T ) for pQCD Rad+El–Naïve expectations met in full numerical calculation: dR AA (p T )/dp T > 0 => pQCD; dR AA (p T )/dp T ST LHC c, b R AA p T Dependence WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)

2/7/09 William Horowitz High-p T Physics at LHC18 But what about the interplay between mass and momentum? –Take ratio of c to b R AA (p T ) pQCD: Mass effects die out with increasing p T –Ratio starts below 1, asymptotically approaches 1. Approach is slower for higher quenching ST: drag independent of p T, inversely proportional to mass. Simple analytic approx. of uniform medium gives R cb pQCD (p T ) ~ n b M c / n c M b ~ M c /M b ~.27 –Ratio starts below 1; independent of p T An Enhanced Signal R cb pQCD (p T )  1 -  s n (p T ) L 2 log(M b /M c ) ( /p T )

2/7/09 William Horowitz High-p T Physics at LHC19 LHC R c AA (p T )/R b AA (p T ) 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 p T –Distinguish rad and el contributions? WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)

2/7/09 William Horowitz High-p T Physics at LHC20 Additional Discerning Power –Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1 »Does not include partonic E-loss, which will be nonnegligable as ratio goes to unity –Higgs (non)mechanism => R c /R b ~ 1 ind. of p T –Consider ratio for ALICE p T reach m c = m b = 0

2/7/09 William Horowitz High-p T Physics at LHC21 Speed limit estimate for applicability of AdS drag –  <  crit = (1 + 2M q / 1/2 T) 2 ~ 4M q 2 /(  T 2 ) Limited by M charm ~ 1.2 GeV Similar to BH LPM –  crit ~ M q /( T) No single T for QGP Not So Fast! Q D7 Probe Brane Worldsheet boundary Spacelike  if  >  crit Trailing String “Brachistochrone” z x D3 Black Brane

2/7/09 William Horowitz High-p T Physics at LHC22 LHC R c AA (p T )/R b AA (p T ) Prediction (with speed limits) –T(  0 ): (, highest T—corrections unlikely for smaller momenta –T c : ], lowest T—corrections likely for higher momenta WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)

2/7/09 William Horowitz High-p T Physics at LHC23 Derivation of BH Speed Limit I Constant HQ velocity –Assume const. v kept by F. v –Critical field strength E c = M 2 / ½ E > E c : Schwinger pair prod. Limits  <  c ~ T 2 / M 2 –Alleviated by allowing var. v Drag similar to const. v z = 0 z M = ½ / 2  M z h = 1/  T E F. v = dp/dt dp/dt Q Minkowski Boundary D7 D3 v J. Casalderrey-Solana and D. Teaney, JHEP 0704, 039 (2007) Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013 (2006) z = 

2/7/09 William Horowitz High-p T Physics at LHC24 Derivation of BH Speed Limit II Local speed of light –BH Metric => varies with depth z v(z) 2 < 1 – (z/z h ) 4 –HQ located at z M = ½ /2  M –Limits  <  c ~ T 2 / M 2 Same limit as from const. v –Mass a strange beast M therm < M rest M rest  M kin –Note that M >> T z = 0 z M = ½ / 2  M z h = 1/  T E F. v = dp/dt dp/dt Q Minkowski Boundary D7 D3 v S. S. Gubser, Nucl. Phys. B 790, 175 (2008) z = 

2/7/09 William Horowitz High-p T Physics at LHC25 Universality and Applicability How universal are drag results? –Examine different theories –Investigate alternate geometries When does the calculation break down? –Depends on the geometry used

2/7/09 William Horowitz High-p T Physics at LHC26 New Geometries Albacete, Kovchegov, Taliotis, JHEP 0807, 074 (2008) J Friess, et al., PRD 75 :106003, 2007 Constant T Thermal Black Brane Shock Geometries Nucleus as Shock Embedded String in Shock DIS Q v shock x z x z Q BeforeAfter Bjorken-Expanding Medium

2/7/09 William Horowitz High-p T Physics at LHC27 Shocking Motivation Warm-up for full Bjorken metric R. A. Janik and R. B. Peschanski, Phys. Rev. D 73, (2006) No local speed of light limit! –Metric yields -1 < v < 1 –In principle, applicable to all quark masses for all momenta –Subtlety in exchange of limits?

2/7/09 William Horowitz High-p T Physics at LHC28 Standard Method of Attack Parameterize string worldsheet –X  ( ,  ) Plug into Nambu-Goto action Varying S NG yields EOM for X  Canonical momentum flow (in ,  )

2/7/09 William Horowitz High-p T Physics at LHC29 Shock Geometry Results Three t-ind. solutions (static gauge): X  = (t, x(z), 0,0, z) –x(z) = c, ±   ½ z 3 /3 Constant solution unstable Time-reversed negative x solution unphysical Sim. to x ~ z 3 /3, z << 1, for const. T BH geom.  ½ z 3 /3  ½ z 3 /3 c v shock Q z = 0 z =  x

2/7/09 William Horowitz High-p T Physics at LHC30 HQ Momentum Loss in the Shock Relate  to nuclear properties –Use AdS dictionary:  ~ T -- /N c 2 –T -- = (boosted den. of scatterers) x (mom.) –T -- = N c 2 (  3 p + /  ) x (p + ) N c 2 gluons per nucleon in shock  is typical mom. scale;   typical dist. scale p + : mom. of shock gluons as seen by HQ p: mom. of HQ as seen by shock =>  =  2 p +2 x(z) =   ½ z 3 /3 =>

2/7/09 William Horowitz High-p T Physics at LHC31 HQ Drag in the Shock HQ Rest Frame Shock Rest Frame v sh MqMq 1/   v q = -v sh MqMq i i v sh = 0 v q = 0 –Recall for BH: –Shock gives exactly the same drag as BH for  =  T

2/7/09 William Horowitz High-p T Physics at LHC32 Conclusions and Outlook for the LHC Experiment: –Use data to test E-loss mechanism R c AA (p T )/R b AA (p T ) wonderful tool –p+Pb and Direct-  Pb+Pb critical null controls the AdS Drag: –Applicability and universality crucial Both investigated in shock geom. –Shock geometry reproduces BH momentum loss Unrestricted in momentum reach Variable velocity case nontrivial –Future work Time-dependent shock treatment AdS E-loss in Bjorken expanding medium

2/7/09 William Horowitz High-p T Physics at LHC33 Backup Slides

2/7/09 William Horowitz High-p T Physics at LHC34 Measurement at RHIC –Future detector upgrades will allow for identified c and b quark measurements y=0 RHIC LHC NOT slowly varying –No longer expect pQCD dR AA /dp T > 0 Large n requires corrections to naïve R cb ~ M c /M b –RHIC production spectrum significantly harder than LHC

2/7/09 William Horowitz High-p T Physics at LHC35 RHIC c, b R AA p T Dependence Large increase in n (p T ) overcomes reduction in E-loss and makes pQCD dR AA /dp T < 0, as well WH, M. Gyulassy, arXiv: [nucl-th]

2/7/09 William Horowitz High-p T Physics at LHC36 RHIC R cb Ratio Wider distribution of AdS/CFT curves due to large n : increased sensitivity to input parameters Advantage of RHIC: lower T => higher AdS speed limits WH, M. Gyulassy, arXiv: [nucl-th] pQCD AdS/CFT pQCD AdS/CFT

2/7/09 William Horowitz High-p T Physics at LHC37 Simultaneous , e - Suppression pQCD is not falsified: –Elastic loss? –Uncertainty in c, b contributions –In-medium fragmentation? –Resonances? S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/ A. Adil and I. Vitev, hep-ph/ H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, (2006) Naïve pQCD => large mass, small loss But ,  R AA ~ e - R AA !

2/7/09 William Horowitz High-p T Physics at LHC38 Zooming In –Factor ~2-3 increase in ratio for pQCD –Possible distinction for Rad only vs. Rad+El at low-p T

2/7/09 William Horowitz High-p T Physics at LHC39 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 Consider ratio for ALICE p T reach

2/7/09 William Horowitz High-p T Physics at LHC40 Consider ratio for ALICE p T reach

2/7/09 William Horowitz High-p T Physics at LHC41 LHC  Predictions WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Our predictions show a significant increase in R AA as a function of p T This rise is robust over the range of predicted dN g /dy for the LHC that we used This should be compared to the flat in p T curves of AWS- based energy loss (next slide) We wish to understand the origin of this difference

2/7/09 William Horowitz High-p T Physics at LHC42 Curves of ASW-based energy loss are flat in p T 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 : (2005) (a)(b) Comparison of LHC  Predictions

2/7/09 William Horowitz High-p T Physics at LHC43 Why ASW is Flat Flat in p T curves result from extreme suppression at the LHC –When probability leakage P(  > 1) is large, the (renormalized or not) distribution becomes insensitive to the details of energy loss Enormous suppression due to: –Already (nonperturbatively) large suppression at RHIC for ASW –Extrapolation to LHC assumes 7 times RHIC medium densities (using EKRT) »Note: even if LHC is only ~ 2-3 times RHIC, still an immoderate ~ As seen on the previous slide, Vitev predicted a similar rise in R AA (p T ) as we do –Vitev used only radiative loss, P rad (  ), but assumed fixed path –WHDG similar because elastic and path fluctuations compensate

2/7/09 William Horowitz High-p T Physics at LHC44 Elastic Can’t be Neglected! M. Mustafa, Phys. Rev. C72 : (2005) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/

2/7/09 William Horowitz High-p T Physics at LHC45 Elastic Remains Important

2/7/09 William Horowitz High-p T Physics at LHC46 A Closer Look at PQM –Difficult to draw conclusions on inherent surface bias in PQM from this for three reasons: No Bjorken expansion Glue and light quark contributions not disentangled Plotted against L input (complicated mapping from L input to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 : (2005)

2/7/09 William Horowitz High-p T Physics at LHC47 Direct  : A+A IS Well Understood PHENIX, Phys. Rev. Lett. 94, (2005)

2/7/09 William Horowitz High-p T Physics at LHC48 More Geometry p T dependence of surface bias Nontrivial a posteriori fixed length dependence S. Wicks, WH, M. Djordjevic and M. Gyulassy, Nucl. Phys. A784, 426 (2007) (not surface emission!) S. A. Bass, et al., arXiv: [nucl-th].