1. 6/1/07 William Horowitz CERN Heavy Ion Forum 1 Possible String Theoretic Deviations from pQCD in Heavy Quark Energy Loss at LHC William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) June 1, 2007 With many thanks to Miklos Gyulassy, Simon Wicks, Ivan Vitev, Jorge Casalderrey-Solana.

2. 6/1/07 William Horowitz CERN Heavy Ion Forum 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. 6/1/07 William Horowitz CERN Heavy Ion Forum 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. 6/1/07 William Horowitz CERN Heavy Ion Forum 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. 6/1/07 William Horowitz CERN Heavy Ion Forum 5  /s AdS/CFT ~ 1/4  << 1 ~  /s pQCD e - R AA ~ ,  R AA ; e - R AA (  ) Mach wave-like structures s strong =(3/4) s weak, similar to Lattice 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. 6/1/07 William Horowitz CERN Heavy Ion Forum 6 Give up on pQCD? Old and Busted: pQCD New Hotness: AdS/CFT

7. 6/1/07 William Horowitz CERN Heavy Ion Forum 7 If You Ask Me… Use the LHC to Test the Two! Let’s look at Heavy Quark Jet Suppression

8. 6/1/07 William Horowitz CERN Heavy Ion Forum 8 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 –Equation for infinitely massive quark moving with constant v through infinitely coupled SYM at uniform T –not yet used to calculate observables: let’s do it!

9. 6/1/07 William Horowitz CERN Heavy Ion Forum 9 –Use large LHC 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)

10. 6/1/07 William Horowitz CERN Heavy Ion Forum 10 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

11. 6/1/07 William Horowitz CERN Heavy Ion Forum 11 Model Inputs –AdS/CFT Drag “Obvious”:  s =  SYM, 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 –WHDG convolved radiative and collisional energy loss  s =.3 –WHDG radiative energy loss (similar to ASW) = 40, 100 –All use realistic, nonuniform medium with Bjorken expansion Two medium densities for LHC: –PHOBOS (dN g /dy = 1750); CGC (dN g /dy = 2900)

12. 6/1/07 William Horowitz CERN Heavy Ion Forum 12 –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

13. 6/1/07 William Horowitz CERN Heavy Ion Forum 13 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 –Ratio starts below 1; independent of p T R c AA (p T )/R b AA (p T )  1 -  s n(p T ) L 2 log(M b /M c ) ( /p T )

14. 6/1/07 William Horowitz CERN Heavy Ion Forum 14 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

15. 6/1/07 William Horowitz CERN Heavy Ion Forum 15 But There’s a Catch (I) –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 : (|)

16. 6/1/07 William Horowitz CERN Heavy Ion Forum 16 LHC R c AA (p T )/R b AA (p T ) Prediction (with speed limits) –O: corrections unlikely for smaller momenta –|: corrections likely for higher momenta

17. 6/1/07 William Horowitz CERN Heavy Ion Forum 17 But There’s a Catch (II) Limited experimental p T reach? ALICE Physics Performance Report, Vol. II

18. 6/1/07 William Horowitz CERN Heavy Ion Forum 18 Zoom In –Factor ~2-3 increase in ratio for pQCD –Possible distinction for Rad only vs. Rad+El at low-p T

19. 6/1/07 William Horowitz CERN Heavy Ion Forum 19 Conclusions –PID and large p T reach will give the LHC a unique position to make discoveries in the heavy quark sector 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 will be an important observable –Ratio is: flat in ST; asymptotically approaching 1 from below in pQCD While future AdS/CFT calculations could well alter the ST predictions shown here, it is highly unlikely that a pQCD mechanism can be found that allows mass effects to persist out to momenta orders of magnitude larger than M q –A measurement of this ratio NOT going to 1 will be a clear sign of new physics: pQCD predicts ~ 2-3 times increase in this ratio by 30 GeV—this can be observed in year 1 at the LHC

20. 6/1/07 William Horowitz CERN Heavy Ion Forum 20 Conclusions (cont’d) Additional LHC 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

21. 6/1/07 William Horowitz CERN Heavy Ion Forum 21 Backups

22. 6/1/07 William Horowitz CERN Heavy Ion Forum 22 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

23. 6/1/07 William Horowitz CERN Heavy Ion Forum 23 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

24. 6/1/07 William Horowitz CERN Heavy Ion Forum 24 RHIC e -

25. 6/1/07 William Horowitz CERN Heavy Ion Forum 25 RHIC c, b R AA (p T )

26. 6/1/07 William Horowitz CERN Heavy Ion Forum 26 RHIC R c AA (p T )/R b AA (p T )

27. 6/1/07 William Horowitz CERN Heavy Ion Forum 27 n(pT)n(pT)

28. 6/1/07 William Horowitz CERN Heavy Ion Forum 28 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

29. 6/1/07 William Horowitz CERN Heavy Ion Forum 29 Drag Picture The Heavy Quark Brachistochrone: J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 :106003, 2007