1. 21/05/07 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) May 21, 2007 With many thanks to Miklos Gyulassy.

2. 21/05/07 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. 21/05/07 William Horowitz CERN Heavy Ion Forum 3 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 D. Teaney, Phys. Rev. C68, 034913 (2003) Hydro  /s too small e - R AA too small M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632 :81-86 (2006)

4. 21/05/07 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. 21/05/07 William Horowitz CERN Heavy Ion Forum 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 Give up on pQCD? Qualitative AdS/CFT Successes:

6. 21/05/07 William Horowitz CERN Heavy Ion Forum 6 pQCD elastic:  /s ~ 1 –pQCD r+e PC:  /s ~.1? AdS: universal lower bound for all infinitely coupled systems  /s ~ 1/4  Ideal Hydro? T. Hirano, U. W. Heinz, D. Kharzeev, R. Lacy, Y. Nara, Phys. Lett. B636 :299-304 (2006) Hydro merely propagates initial conditions; its results are highly dependent on them Glauber initial state => ideal (ST) hydro CGC initial state => viscous (pQCD) hydro Must understand initial state better before reaching a conclusion: A. Adil, M. Gyulassy, T. Hirano, Phys. Rev. D73 :074006 (2006)

7. 21/05/07 William Horowitz CERN Heavy Ion Forum 7 Simultaneous , e - Suppression pQCD is not falsified: –Elastic loss? –Uncertainty in c, b contributions –In-medium fragmentation? –Resonances? S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 A. Adil and I. Vitev, hep-ph/0611109 H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, 034913 (2006) Naïve pQCD => large mass, small loss But ,  R AA ~ e - R AA !

8. 21/05/07 William Horowitz CERN Heavy Ion Forum 8 PHENIX, Phys. Rev. Lett. 98, 172301 (2007) Simultaneous R AA, v 2 Description –Energy loss translates spatial anisotropy of medium to jets R AA and v 2 are thus anti- correlated First seen for pions, no nonperturbative model reproduces both R AA and v 2 Observed for e -, too No known solution to the puzzle WH, Acta Phys. Hung. A27 :221-225 GREL 40-50% MPC 30%

9. 21/05/07 William Horowitz CERN Heavy Ion Forum 9 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!

10. 21/05/07 William Horowitz CERN Heavy Ion Forum 10 Drag Picture The Heavy Quark Brachistochrone: J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 :106003, 2007

11. 21/05/07 William Horowitz CERN Heavy Ion Forum 11 –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)

12. 21/05/07 William Horowitz CERN Heavy Ion Forum 12 A Note on LHC p T Reach More on p T limits from the AdS side later ALICE Physics Performance Report, Vol. II

13. 21/05/07 William Horowitz CERN Heavy Ion Forum 13 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

14. 21/05/07 William Horowitz CERN Heavy Ion Forum 14 Models –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 extrapolations to LHC: –PHOBOS (dN g /dy = 1750); CGC (dN g /dy = 2900)

15. 21/05/07 William Horowitz CERN Heavy Ion Forum 15 –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

16. 21/05/07 William Horowitz CERN Heavy Ion Forum 16 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 )

17. 21/05/07 William Horowitz CERN Heavy Ion Forum 17 LHC R c AA (p T )/R b AA (p T ) Prediction Recall the Prediction 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) –ST ratio is flat and many times smaller than pQCD at only moderate p T

18. 21/05/07 William Horowitz CERN Heavy Ion Forum 18 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 : (|)

19. 21/05/07 William Horowitz CERN Heavy Ion Forum 19 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

20. 21/05/07 William Horowitz CERN Heavy Ion Forum 20 Zooming In –Factor ~2-3 increase in ratio for pQCD –Possible distinction for Rad only vs. Rad+El at low-p T

21. 21/05/07 William Horowitz CERN Heavy Ion Forum 21 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

22. 21/05/07 William Horowitz CERN Heavy Ion Forum 22 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

23. 21/05/07 William Horowitz CERN Heavy Ion Forum 23 Conclusions (cont’d) Additional LHC 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 –Mach cone may be due to radiated gluons: from pQCD the away-side dip should widen with increasing parton mass –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