1. 6/26/07 William Horowitz SQM 2007 1 pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) June 26, 2007 With many thanks to Miklos Gyulassy, Simon Wicks, Jorge Casalderrey-Solana, and Urs Wiedemann. arXiv:0706.2336 (LHC predictions)

2. 6/26/07 William Horowitz SQM 2007 2 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)

3. 6/26/07 William Horowitz SQM 2007 3 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… 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

4. 6/26/07 William Horowitz SQM 2007 4 Strong Coupling 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

5. 6/26/07 William Horowitz SQM 2007 5 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 (  ) Mach wave-like structures T. Hirano and M. Gyulassy, Nucl. Phys. A69 :71-94 (2006) Qualitative AdS/CFT Successes: PHENIX, Phys. Rev. Lett. 98, 172301 (2007) J. J. Friess, S. S. Gubser, G. Michalogiorgakis, S. S. Pufu, Phys. Rev. D75 :106003 (2007) J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 AdS/CFT

6. 6/26/07 William Horowitz SQM 2007 6 AdS/CFT vs. pQCD 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!

7. 6/26/07 William Horowitz SQM 2007 7 –Use LHC’s large p T reach and identification of c and b to distinguish 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

8. 6/26/07 William Horowitz SQM 2007 8 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)

9. 6/26/07 William Horowitz SQM 2007 9 –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

10. 6/26/07 William Horowitz SQM 2007 10 A Cleaner 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 )

11. 6/26/07 William Horowitz SQM 2007 11 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

12. 6/26/07 William Horowitz SQM 2007 12 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 : (|) Black D3 Brane D7 Probe Brane Q Induced horizon Appears  if  >  crit Trailing String “Brachistochrone” “z” x5x5

13. 6/26/07 William Horowitz SQM 2007 13 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

14. 6/26/07 William Horowitz SQM 2007 14 Identified c and b at RHIC –Index of power law production spectrum: 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

15. 6/26/07 William Horowitz SQM 2007 15 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

16. 6/26/07 William Horowitz SQM 2007 16 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

17. 6/26/07 William Horowitz SQM 2007 17 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

18. 6/26/07 William Horowitz SQM 2007 18 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

19. 6/26/07 William Horowitz SQM 2007 19 Backups

20. 6/26/07 William Horowitz SQM 2007 20 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

21. 6/26/07 William Horowitz SQM 2007 21 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

22. 6/26/07 William Horowitz SQM 2007 22 n(pT)n(pT)

23. 6/26/07 William Horowitz SQM 2007 23 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

24. 6/26/07 William Horowitz SQM 2007 24 But There’s a Catch (II) Limited experimental p T reach? ALICE Physics Performance Report, Vol. II

25. 6/26/07 William Horowitz SQM 2007 25 Zoom In –Factor ~2-3 increase in ratio for pQCD –Possible distinction for Rad only vs. Rad+El at low-p T

26. 6/26/07 William Horowitz SQM 2007 26 Regimes of Applicability String Regime –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) RHIC/LHC Regime –Mapping QCD N c to SYM is easy, but coupling is hard  S runs whereas  SYM does not:  SYM is something of an unknown constant Taking  SYM =  S =.3 (D/2  T ~ 1); D/2  T ~ 3 =>  SYM ~.05