1. 10/28/08 William Horowitz Nuclear Seminar, McGill University 1 LHC Predictions: Phys. Lett. B666:320, 2008 (arXiv:0706.2336) RHIC Predictions: J. Phys. G35:044025, 2008 (arXiv:0710.0703) Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss William Horowitz The Ohio State University Columbia University Frankfurt Institute for Advanced Studies (FIAS) October 28, 2008 With many thanks to Miklos Gyulassy and Simon Wicks

2. 10/28/08 William Horowitz Nuclear Seminar, McGill University 2 Outline Motivation for studying AdS/CFT Introduction to Heavy Ion Physics pQCD vs. AdS Drag: Expectations, Results, Limitations Conclusions

3. 10/28/08 William Horowitz Nuclear Seminar, McGill University 3 Motivation

4. 10/28/08 William Horowitz Nuclear Seminar, McGill University 4 Limited Toolbox for QCD Calculations Lattice QCDpQCD All momenta Euclidean correlators Any quantity Small coupling (large momenta) Previously only two, restricted methods: Two 10 Tflops QCDOC Computers: RBRC and DOE

5. 10/28/08 William Horowitz Nuclear Seminar, McGill University 5 Maldacena Conjecture Large N c 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 Bosonic part of IIB low energy effective action Geometry of bosonic part of 10D supergravity, near horizon limit J Maldacena, Adv.Theor.Math.Phys.2:231-252,1998

6. 10/28/08 William Horowitz Nuclear Seminar, McGill University 6 Regime of Applicability –Large N c, 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. S SYM => C.M. S NG J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 :106003, 2007

7. 10/28/08 William Horowitz Nuclear Seminar, McGill University 7 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

8. 10/28/08 William Horowitz Nuclear Seminar, McGill University 8 Connection to Experiment a.k.a. the Reality Check for Theory

9. 10/28/08 William Horowitz Nuclear Seminar, McGill University 9 Introduction to Heavy Ion Physics

10. 10/28/08 William Horowitz Nuclear Seminar, McGill University 10 Geometry of a HI Collision Hydro propagates IC –Results depend strongly on initial conditions Viscosity reduces eventual momentum anisotropy T Ludlum and L McLerran, Phys. Today 56N10 :48 (2003) M Kaneta, Results from the Relativistic Heavy Ion Collider (Part II)

11. 10/28/08 William Horowitz Nuclear Seminar, McGill University 11 –Hydro  /s small ~.1 QGP fluid near-perfect liquid –Naïve pQCD =>  /s ~ 1 New estimates ~.1 Z Xu, C Greiner, and H Stoecker, PRL101:082302 (2008) –Lowest order AdS result:  /s = 1/4  Universality? Perfect Fluidity: AdS + Hydro’s Most Famous Success D. Teaney, Phys. Rev. C68, 034913 (2003) P Kovtun, D Son, and A Starinets, Phys.Rev.Lett.94:111601 (2005) P Kats and P Petrov, arXiv:0712.0743 M Brigante et al., Phys. Rev. D77 :126006 (2008)

12. 10/28/08 William Horowitz Nuclear Seminar, McGill University 12 IC, Viscosity, and Hydro –Sharper IC (CGC) => viscosity –Softer IC (Glauber) => “perfect” T Hirano, et al., Phys. Lett. B636 :299-304, 2006

13. 10/28/08 William Horowitz Nuclear Seminar, McGill University 13 Compare unmodified p+p collisions to A+A: Use suppression pattern to either: –Learn about medium (requires detailed understanding of energy loss): jet tomography –Learn about energy loss Why High-p T Jets? pTpT pTpT Figures from http://www.star.bnl.gov/central/focus/highPt/ Longitudinal (beam pipe) direction 2D Transverse directions

14. 10/28/08 William Horowitz Nuclear Seminar, McGill University 14 Jet Physics Terminology pTpT  Naïvely: if medium has no effect, then R AA = 1 Common variables used are transverse momentum, p T, and angle with respect to the reaction plane,  Common to Fourier expand R AA :

15. 10/28/08 William Horowitz Nuclear Seminar, McGill University 15 pQCD Success at RHIC: –Consistency: R AA (  )~R AA (  ) –Null Control: R AA (  )~1 –GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dN g /dy~dN  /dy Y. Akiba for the PHENIX collaboration, hep-ex/0510008 (circa 2005)

16. 10/28/08 William Horowitz Nuclear Seminar, McGill University 16 e - R AA too small M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632 :81-86 (2006) wQGP not ruled out, but what if we try strong coupling? D. Teaney, Phys. Rev. C68, 034913 (2003) Hydro  /s too small v 2 too large A. Drees, H. Feng, and J. Jia, Phys. Rev. C71 :034909 (2005) (first by E. Shuryak, Phys. Rev. C66 :027902 (2002)) Trouble for wQGP Picture

17. 10/28/08 William Horowitz Nuclear Seminar, McGill University 17 Mach wave-like structures s strong =(3/4) s weak, similar to Lattice  /s AdS/CFT ~ 1/4  << 1 ~  /s pQCD e - R AA ~ ,  R AA ; e - R AA (  ) T. Hirano and M. Gyulassy, Nucl. Phys. A69 :71-94 (2006) Qualitative AdS/CFT Successes: PHENIX, Phys. Rev. Lett. 98, 172301 (2007) J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 AdS/CFT S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213

18. 10/28/08 William Horowitz Nuclear Seminar, McGill University 18 AdS/CFT Energy Loss Models Langevin model –Collisional energy loss for heavy quarks –Restricted to low p T –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!

19. 10/28/08 William Horowitz Nuclear Seminar, McGill University 19 AdS/CFT Drag Model heavy quark jet energy loss by embedding string in AdS space dp T /dt = -  p T  =    T 2 /2M q J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 :106003, 2007

20. 10/28/08 William Horowitz Nuclear Seminar, McGill University 20 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 = 0 z h =  T z m = 2  m / 1/2

21. 10/28/08 William Horowitz Nuclear Seminar, McGill University 21 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

22. 10/28/08 William Horowitz Nuclear Seminar, McGill University 22 –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 :126005 (2006); C. Herzog et al. JHEP 0607:013,2006

23. 10/28/08 William Horowitz Nuclear Seminar, McGill University 23 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)

24. 10/28/08 William Horowitz Nuclear Seminar, McGill University 24 –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, M. Gyulassy, arXiv:0706.2336

25. 10/28/08 William Horowitz Nuclear Seminar, McGill University 25 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 )

26. 10/28/08 William Horowitz Nuclear Seminar, McGill University 26 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 WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]

27. 10/28/08 William Horowitz Nuclear Seminar, McGill University 27 –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 smallest  crit for largest T T = T(  0, x=y=0): “(” largest  crit for smallest T T = T c : “]” Not So Fast! D3 Black Brane D7 Probe Brane Q Worldsheet boundary Spacelike  if  >  crit Trailing String “Brachistochrone” “z” x5x5

28. 10/28/08 William Horowitz Nuclear Seminar, McGill University 28 LHC R c AA (p T )/R b AA (p T ) Prediction (with speed limits) –T(  0 ): (O), corrections unlikely for smaller momenta –T c : (|), corrections likely for higher momenta WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]

29. 10/28/08 William Horowitz Nuclear Seminar, McGill University 29 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

30. 10/28/08 William Horowitz Nuclear Seminar, McGill University 30 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:0710.0703 [nucl-th]

31. 10/28/08 William Horowitz Nuclear Seminar, McGill University 31 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:0710.0703 [nucl-th] pQCD AdS/CFT pQCD AdS/CFT

32. 10/28/08 William Horowitz Nuclear Seminar, McGill University 32 Conclusions Previous AdS qualitative successes inconclusive AdS/CFT Drag observables calculated Generic differences (pQCD vs. AdS/CFT Drag) seen in R AA –Masked by extreme pQCD Enhancement from ratio of c to b R AA –Discovery potential in Year 1 LHC Run Understanding regions of self-consistency crucial RHIC measurement possible

33. 10/28/08 William Horowitz Nuclear Seminar, McGill University 33 Backups

34. 10/28/08 William Horowitz Nuclear Seminar, McGill University 34 Geometry of a HI Collision Medium density and jet production are wide, smooth distributions Use of unrealistic geometries strongly bias results M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005 1D Hubble flow =>  (  ) ~ 1/  => T(  ) ~ 1/  1/3 S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007

35. 10/28/08 William Horowitz Nuclear Seminar, McGill University 35 Langevin Model –Langevin equations (assumes  v ~ 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

36. 10/28/08 William Horowitz Nuclear Seminar, McGill University 36 But There’s a Catch (II) Limited experimental p T reach? –ATLAS and CMS do not seem to be limited in this way (claims of year 1 p T reach of ~100 GeV) but systematic studies have not yet been performed ALICE Physics Performance Report, Vol. II

37. 10/28/08 William Horowitz Nuclear Seminar, McGill University 37 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

38. 10/28/08 William Horowitz Nuclear Seminar, McGill University 38 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Asymptopia at the LHC Asymptotic pocket formulae:  E rad /E   3 Log(E/  2 L)/E  E el /E   2 Log((E T) 1/2 /m g )/E

39. 10/28/08 William Horowitz Nuclear Seminar, McGill University 39 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)

40. 10/28/08 William Horowitz Nuclear Seminar, McGill University 40 Pion R AA Is it a good measurement for tomography? –Yes: small experimental error Claim: we should not be so immediately dis- missive of the pion R AA as a tomographic tool –Maybe not: some models appear “fragile”

41. 10/28/08 William Horowitz Nuclear Seminar, McGill University 41 Fragility: A Poor Descriptor All energy loss models with a formation time saturate at some R min AA > 0 The questions asked should be quantitative : –Where is R data AA compared to R min AA ? –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

42. 10/28/08 William Horowitz Nuclear Seminar, McGill University 42 Different Models have Different Sensitivities to the Pion R AA GLV: s < 2 Higher Twist: s < 2 DGLV+El+Geom: s < 2 AWS: s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

43. 10/28/08 William Horowitz Nuclear Seminar, McGill University 43 T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007) WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

44. 10/28/08 William Horowitz Nuclear Seminar, McGill University 44 A Closer Look at ASW 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) 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)

45. 10/28/08 William Horowitz Nuclear Seminar, McGill University 45 –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 Surface Bias vs. Surface Emission A. Majumder, HP2006S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

46. 10/28/08 William Horowitz Nuclear Seminar, McGill University 46 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 L input (complicated mapping from L input to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005)

47. 10/28/08 William Horowitz Nuclear Seminar, McGill University 47 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

48. 10/28/08 William Horowitz Nuclear Seminar, McGill University 48 Conclusions AdS/CFT Drag observables calculated Generic differences (pQCD vs. AdS/CFT Drag) seen in R AA –Masked by extreme pQCD Enhancement from ratio of c to b R AA –Discovery potential in Year 1 LHC Run Understanding regions of self- consistency crucial RHIC measurement possible

49. 10/28/08 William Horowitz Nuclear Seminar, McGill University 49 Shameless self-promotion by the presenter

50. 10/28/08 William Horowitz Nuclear Seminar, McGill University 50 Geometry of a HI Collision Medium density and jet production are wide, smooth distributions Use of unrealistic geometries strongly bias results M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005 1D Hubble flow =>  (  ) ~ 1/  => T(  ) ~ 1/  1/3 S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007