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The LHC to Test pQCD vs. AdS/CFT Heavy Quark Energy Loss

The LHC to Test pQCD vs. AdS/CFT Heavy Quark Energy Loss. William Horowitz Columbia University FIAS April 26, 2007. With many thanks to Miklos Gyulassy. Good Signs for pQCD at RHIC:. Y. Akiba for the PHENIX collaboration , hep-ex/0510008. (circa 2005).

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The LHC to Test pQCD vs. AdS/CFT Heavy Quark Energy Loss

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  1. The LHC to Test pQCD vs. AdS/CFT Heavy Quark Energy Loss William Horowitz Columbia University FIAS April 26, 2007 With many thanks to Miklos Gyulassy. 44th RNM Workshop

  2. Good Signs for pQCD at RHIC: Y. Akiba for the PHENIX collaboration, hep-ex/0510008 (circa 2005) • Consistency: RAA(h)~RAA(p) • Null Control: RAA(g)~1 • GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy 44th RNM Workshop

  3. Trouble for wQGP Picture • Hydro h/s too small • e- too small • v2 too large A. Drees, H. Feng, and J. Jia, Phys. Rev. C71:034909 (2005) (first by E. Shuryak, Phys. Rev. C66:027902 (2002)) M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006) D. Teaney, Phys. Rev. C68, 034913 (2003) 44th RNM Workshop

  4. Strong Coupling • The supergravity double conjecture: QCD  SYM  IIB • IF super Yang-Mills (SYM) is not too different from QCD, & • IF Maldecena conjecture is true • Then a tool exists to calculate strongly-coupled QCD in SUGRA 44th RNM Workshop

  5. Ideal Hydro? Hydro merely propagates initial conditions; its results are highly dependent on them • pQCD: h/s ~ 1 • AdS: universal lower bound for all infinitely coupled systems h/s ~ 1/4p • AdS success? • Glauber initial state => • ideal (ST) hydro • CGC initial state => • viscous (pQCD) hydro T. Hirano, U. W. Heinz, D. Kharzeev, R. Lacy, Y. Nara, Phys. Lett. B636:299-304 (2006) Must understand initial state better before reaching a conclusion: A. Adil, M. Gyulassy, T. Hirano, Phys. Rev. D73:074006 (2006) 44th RNM Workshop

  6. Simultaneous p, e- Suppression A. Adil and I. Vitev, hep-ph/0611109 H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, 034913 (2006) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 • pQCD is not falsified: • Elastic loss? • Uncertainty in c, b contributions • In-medium fragmentation? • Resonances? • Naïve pQCD => large mass, small loss • But p, h RAA ~ e- RAA! 44th RNM Workshop

  7. Simultaneous RAA, v2 Description WH, Acta Phys. Hung. A27:221-225 PHENIX, Phys. Rev. Lett. 98, 172301 (2007) • Energy loss translates spatial anisotropy of medium to jets • RAA and v2 are thus anti-correlated • First seen for pions, no nonperturbative model reproduces both RAA and v2 • Observed for e-, too • No known solution to the puzzle 44th RNM Workshop

  8. Strings, Jets, and the LHC • Langevin model • Collisional energy loss for heavy quarks • Restricted to low pT • 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 • Considerable debate over its 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! 44th RNM Workshop

  9. Regimes of Applicability • String Regime • Large Nc, 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 Nc to SYM is easy, but coupling is hard aS runs whereas aSYM does not: aSYM is something of an unknown constant • Taking aSYM = aS = .3 (D/2pT~1); aSYM ~ .05 => D/2pT~3 • LHC medium density predictions vary by factor of 2 44th RNM Workshop

  10. Looking for a Robust, Detectable Signal erad~a3 L2 log(pT/Mq)/pT eST~ 1 - Exp(-m L), m = plT2/2Mq S. Gubser, Phys.Rev.D74:126005 (2006) • Use large LHC pT reach and identification of c and b to distinguish • RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. e = 1-pf/pi) • Asymptotic pQCD momentum loss: • String theory drag momentum loss: • Independent of pT and strongly dependent on Mq! • T2 dependence in exponent makes for a very sensitive probe • Expect: eQCD 0 vs. eAdSindep of pT!! • dRAA(pT)/dpT > 0 => pQCD ; dRAA(pT)/dpT < 0 => ST 44th RNM Workshop

  11. Models • AdS/CFT Drag • “Obvious”: as = aSYM, TSYM = TQCD • D/2pT = 3 inspired: as = .05, t0 = 1 • Hydro inspired: as = .3, t0 = .6 • “Alternative”: l = 5.5, TSYM = TQCD/31/4 • WHDG convolved radiative and collisional energy loss • as = .3, t0 = .2 • WHDG radiative energy loss (similar to ASW) • = 40, 100 • All use realistic, nonuniform medium with Bjorken expansion 44th RNM Workshop

  12. LHC c, b RAA pT Dependence • Full numerical calculation shows ST RAA decreases with pT (as compared to strong increase for pQCD) • Saturation, or fragility, occurs at a much smaller RAA due to realistic modeling of the medium 44th RNM Workshop

  13. A Cleaner Signal RcAA(pT)/RbAA(pT) ~ 1 - a3 n(pT) L2 log(Mb/Mc) ( /pT) • But what about the interplay between mass and momentum? • Take ratio of c to b RAA(pT) • pQCD: Mass effects die out with increasing pT • Ratio starts below 1, asymptotically approaches 1. Approach is slower for higher quenching • ST: drag independent of pT, inversely proportional to mass • Ratio starts below 1, independent of pT 44th RNM Workshop

  14. LHC RcAA(pT)/RbAA(pT) Prediction • Recall the previous plot: • 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 pT 44th RNM Workshop

  15. Conclusions • PID and large pT 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: • dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST • Ratio of charm to bottom RAA 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 Mq • A measurement of this ratio NOT going to 1 will be a clear sign of new physics: pQCD predicts ~ 3 times increase in this ratio by 30 GeV—this can be observed in year 1 at the LHC 44th RNM Workshop

  16. Conclusions (cont’d) • Additional LHC Goodies: • Adil Vitev in-medium fragmentation results in a much more rapid rise to 1 for RcAA/RbAA with the possibility of breaching 1 and asymptotically approaching 1 from above • Surface emission models (although already unlikely as per p v2(pT) data) predict flat in pT c, b RAA, 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 pT; convolved loss is monotonic 44th RNM Workshop

  17. Backups: LHC p Predictions 44th RNM Workshop

  18. Suppression of AWS • AWS pQCD-based controlling parameter must be nonperturbatively large to fit RHIC data -pQCD gives = c e3/4, where c ~ 2; c ~ 8-20 required for RHIC data -Needed because radiative only energy loss (and > 1? R = (1/2) L3) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) 44th RNM Workshop

  19. LHC p Predictions • Our predictions show a significant increase in RAA as a function of pT • This rise is robust over the range of predicted dNg/dy for the LHC that we used • This should be compared to the flat in pT curves of AWS-based energy loss (next slide) • We wish to understand the origin of this difference WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation 44th RNM Workshop

  20. Comparison of LHC p Predictions Curves of ASW-based energy loss are flat in pT (a) (b) 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) 44th RNM Workshop

  21. Why ASW is Flat • Flat in pT curves result from extreme suppression at the LHC • When probability leakage P(e > 1) is large, the (renormalized or not) distribution becomes insensitive to the details of energy loss • Enormous suppression due to: • Already (nonperturbatively) large suppression at RHIC for ASW • Extrapolation to LHC assumes 7 times RHIC medium densities (using EKRT) • Note: even if LHC is only ~ 2-3 times RHIC, still an immoderate ~ 30-45 • As seen on the previous slide, Vitev predicted a similar rise in RAA(pT) as we do • Vitev used only radiative loss, Prad(e), but assumed fixed path • WHDG similar because elastic and path fluctuations compensate 44th RNM Workshop

  22. Conclusions • LHC RAA(pT) data will distinguish between energy loss models • GLV Rad+El+Geom predicts significant rise in pT • ASW type models predict flat pT dependence 44th RNM Workshop

  23. Backup Slides 44th RNM Workshop

  24. RHIC e- 44th RNM Workshop

  25. RHIC c, b RAA(pT) 44th RNM Workshop

  26. RHIC RcAA(pT)/RbAA(pT) 44th RNM Workshop

  27. n(pT) 44th RNM Workshop

  28. Hydro Initial State Hirano and Nara(’04), Hirano et al.(’06)‏ Kuhlman et al.(’06), Drescher et al.(’06)‏ 44th RNM Workshop

  29. Regimes of Applicability • String Regime • Large Nc, 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 Nc to SYM is easy, but coupling is hard aS runs whereas aSYM does not: aSYM is something of an unknown constant • Taking aSYM = aS = .3 gives l ~ 10 Taking aSYM ~ .05 => l ~ 1.8 (keep in mind for later) 44th RNM Workshop

  30. Langevin Scheme ST here • Langevin equations (assumes gv ~ 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: 44th RNM Workshop

  31. Plugging in Numbers • Langevin pT reach: • gv(8 GeV e- from c) ~ 11 • D/(2pT) = 4/l1/2 from ST: • aSYM = aS = .3 => D/(2pT) ~ 1 • Oversuppresses RAA • aSYM ~ .05 required for D/(2pT) ~ 3 • Mass constraint, (for T = 350 MeV) • aSYM = .3 this gives ~ .6 GeV • aSYM = .05 this gives ~ .25 GeV • Both charm and bottom satisfy this condition • Not entirely unreasonable 44th RNM Workshop

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  36. Strings, Jet Physics, and the LHC:Looking for a Signal erad~a3 L2 log(pT/Mq)/pT eST~ 1 - Exp(-m L), m = plT2/2m S. Gubser, Phys.Rev.D74:126005 (2006) • Use large LHC pT reach and identification of c and b to distinguish • RAA ~ (1-e(pT))n(pT), pf = (1-e)pi • Asymptotic pQCD momentum loss: • String theory drag momentum loss: • Independent of pT and strongly dependent on m!! • T2 dependence makes for a very sensitive probe 44th RNM Workshop

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