1. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 1 pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) August 31, 2007 With many thanks to Miklos Gyulassy, Simon Wicks, and Ivan Vitev arXiv:0706.2336 (LHC predictions)

2. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 2 QCD Calculations Lattice QCDpQCD All momenta Euclidean correlators Any quantity Small coupling Previously only two tools:

3. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 3 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 3+1 SYM z = 0

4. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 4 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) t x Q, m v D7 Probe Brane D3 Black Brane (horizon) 3+1D Brane Boundary Q.M. S SYM => C.M. S NG Black Hole z = 0 z h =  T z m = 2  m / 1/2

5. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 5 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

6. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 6 Connection to Experiment a.k.a. the Reality Check for Theory

7. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 7 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)

8. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 8 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

9. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 9 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

10. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 10 Quantitative AdS/CFT with Jets 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!

11. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 11 –Use LHC’s large p T reach and identification of c and b to distinguish between pQCD, AdS/CFT R AA ~ (1-  (p T )) n(p T ), where p f = (1-  )p i (i.e.  = 1-p f /p i ) 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

12. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 12 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)

13. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 13 –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 born out 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 –LHC Prediction Zoo: What a Mess! –Let’s go through step by step WH, M. Gyulassy, nucl-th/0706.2336

14. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 14 An Enhanced Signal 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 R cb pQCD (p T )  1 -  s n (p T ) L 2 log(M b /M c ) ( /p T )

15. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 15 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, nucl-th/0706.2336

16. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 16 But There’s a Catch –Speed limit estimate for applicability of AdS/CFT drag computation  <  crit = (1 + 2M q / 1/2 T) 2 ~ 4M q 2 /(  T 2 ) –Limited by M charm ~ 1.2 GeV –Ambiguous T for QGP smallest  crit for largest T = T(  0, x=y=0): (O) largest  crit for smallest T = T c : (|) D3 Black Brane D7 Probe Brane Q Worldsheet boundary Spacelike  if  >  crit Trailing String “Brachistochrone” “z” x5x5

17. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 17 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, nucl-th/0706.2336

18. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 18 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

19. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 19 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, to be published

20. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 20 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 pQCD AdS/CFT pQCD AdS/CFT WH, M. Gyulassy, to be published

21. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 21 Conclusions Year 1 of LHC could show qualitative differences between energy loss mechanisms: –dR AA (p T )/dp T > 0 => pQCD; dR AA (p T )/dp T ST Ratio of charm to bottom R AA, R cb, 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 R cb 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?

22. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 22 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

23. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 23 Conclusions (cont’d) Additional c, b PID Goodies: –Adil Vitev in-medium fragmentation results in a much more rapid rise to 1 for R c AA /R b AA with the possibility of breaching 1 and asymptotically approaching 1 from above –Surface emission models (although already unlikely as per v 2 (p T ) data) predict flat in p T c, b R AA, with a ratio of 1 –Moderately suppressed radiative only energy loss shows a dip in the ratio at low p T ; 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

24. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 24 Backups

25. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 25 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

26. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 26 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

27. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 27 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

28. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 28 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

29. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 29 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)

30. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 30 Introduction to Jargon 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 :

31. 8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 31 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