1. 2/9/08 William Horowitz Quark Matter 2008 1 Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) February 9, 2008 With many thanks to Miklos Gyulassy and Simon Wicks arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions)

2. 2/9/08 William Horowitz Quark Matter 2008 2 Motivation –Many heavy quark energy loss models –Hope to distinguish between two broad classes: Standard Model pQCD AdS/CFT Drag –Comparison difficult: nontrivial mapping of AdS/CFT to QCD predictions for LHC –Look for robust signal

3. 2/9/08 William Horowitz Quark Matter 2008 3 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)

4. 2/9/08 William Horowitz Quark Matter 2008 4 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

5. 2/9/08 William Horowitz Quark Matter 2008 5 Intro to AdS/CFT 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

6. 2/9/08 William Horowitz Quark Matter 2008 6 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 classical SUGRA

7. 2/9/08 William Horowitz Quark Matter 2008 7 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

8. 2/9/08 William Horowitz Quark Matter 2008 8 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!

9. 2/9/08 William Horowitz Quark Matter 2008 9 AdS/CFT Drag Model heavy quark jet energy loss by embedding string in AdS space dp T /dt = -  p T  =    T 2 /2M q

10. 2/9/08 William Horowitz Quark Matter 2008 10 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

11. 2/9/08 William Horowitz Quark Matter 2008 11 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

12. 2/9/08 William Horowitz Quark Matter 2008 12 –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

13. 2/9/08 William Horowitz Quark Matter 2008 13 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)

14. 2/9/08 William Horowitz Quark Matter 2008 14 –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

15. 2/9/08 William Horowitz Quark Matter 2008 15 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 )

16. 2/9/08 William Horowitz Quark Matter 2008 16 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]

17. 2/9/08 William Horowitz Quark Matter 2008 17 –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

18. 2/9/08 William Horowitz Quark Matter 2008 18 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]

19. 2/9/08 William Horowitz Quark Matter 2008 19 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

20. 2/9/08 William Horowitz Quark Matter 2008 20 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]

21. 2/9/08 William Horowitz Quark Matter 2008 21 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

22. 2/9/08 William Horowitz Quark Matter 2008 22 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

23. 2/9/08 William Horowitz Quark Matter 2008 23 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 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

24. 2/9/08 William Horowitz Quark Matter 2008 24 Backups

25. 2/9/08 William Horowitz Quark Matter 2008 25 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

26. 2/9/08 William Horowitz Quark Matter 2008 26 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

27. 2/9/08 William Horowitz Quark Matter 2008 27 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

28. 2/9/08 William Horowitz Quark Matter 2008 28 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

29. 2/9/08 William Horowitz Quark Matter 2008 29 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

30. 2/9/08 William Horowitz Quark Matter 2008 30 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)

31. 2/9/08 William Horowitz Quark Matter 2008 31 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”

32. 2/9/08 William Horowitz Quark Matter 2008 32 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

33. 2/9/08 William Horowitz Quark Matter 2008 33 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

34. 2/9/08 William Horowitz Quark Matter 2008 34 T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007) WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

35. 2/9/08 William Horowitz Quark Matter 2008 35 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)

36. 2/9/08 William Horowitz Quark Matter 2008 36 –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

37. 2/9/08 William Horowitz Quark Matter 2008 37 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)