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pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss

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

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pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss

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

  2. pQCD Success 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 SQM 2007

  3. Trouble for wQGP Picture • e- RAA too small • Hydro h/s 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) • wQGP not ruled out, but what if we try… 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 SQM 2007

  5. Qualitative AdS/CFT Successes: AdS/CFT 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 PHENIX, Phys. Rev. Lett. 98, 172301 (2007) • sstrong=(3/4) sweak, similar to Lattice • h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD • e- RAA ~ p, h RAA; e- RAA(f) • Mach wave-like structures T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) SQM 2007

  6. AdS/CFT vs. pQCD with Jets • 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 • 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! SQM 2007

  7. Looking for a Robust, Detectable Signal erad~as L2 log(pT/Mq)/pT • Use LHC’s large 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: epQCD 0 vs. eAdSindep of pT!! • dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST eST~ 1 - Exp(-m L), m = pl1/2T2/2Mq S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006 SQM 2007

  8. Model Inputs • AdS/CFT Drag: nontrivial mapping of QCD to SYM • “Obvious”: as = aSYM = const., TSYM = TQCD • D/2pT = 3 inspired: as = .05 • pQCD/Hydro inspired: as = .3 (D/2pT ~ 1) • “Alternative”: l = 5.5, TSYM = TQCD/31/4 • Start loss at thermalization time t0; end loss at Tc • WHDG convolved radiative and elastic energy loss • as = .3 • WHDG radiative energy loss (similar to ASW) • = 40, 100 • Use realistic, diffuse medium with Bjorken expansion • PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900) SQM 2007

  9. LHC c, b RAA pT Dependence WH, M. Gyulassy, nucl-th/0706.2336 • Large suppression leads to flattening • Use of realistic geometry and Bjorken expansion allows saturation below .2 • Significant rise in RAA(pT) for pQCD Rad+El • Naïve expectations born out in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST • LHC Prediction Zoo: What a Mess! • Let’s go through step by step SQM 2007

  10. A Cleaner Signal • 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. Simple analytic approx. of uniform medium gives RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27 • Ratio starts below 1; independent of pT RcbpQCD(pT) ~ 1 - asn(pT) L2 log(Mb/Mc) ( /pT) SQM 2007

  11. LHC RcAA(pT)/RbAA(pT) Prediction • Recall the Zoo: WH, M. Gyulassy, nucl-th/0706.2336 • 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 pT WH, M. Gyulassy, nucl-th/0706.2336 SQM 2007

  12. But There’s a Catch Induced horizon Appearsif g > gcrit x5 “z” • Speed limit estimate for applicability of AdS/CFT drag computation • g < gcrit = (1 + 2Mq/l1/2 T)2 ~ 4Mq2/(l T2) • Limited by Mcharm ~ 1.2 GeV • Ambiguous T for QGP • smallest gcrit for largest T = T(t0, x=y=0): (O) • largest gcrit for smallest T = Tc: (|) D7 Probe Brane Q Trailing String “Brachistochrone” Black D3 Brane SQM 2007

  13. LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits) WH, M. Gyulassy, nucl-th/0706.2336 • T(t0): (O), corrections unlikely for smaller momenta • Tc: (|), corrections likely for higher momenta SQM 2007

  14. Identified c and b at RHIC y=0 RHIC LHC • Index of power law production spectrum: • NOT slowly varying • No longer expect pQCD dRAA/dpT > 0 • Large n requires corrections to naïve Rcb ~ Mc/Mb SQM 2007

  15. RHIC c, b RAA pT Dependence • Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well WH, M. Gyulassy, to be published SQM 2007

  16. RHIC Rcb 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 pQCD AdS/CFT AdS/CFT WH, M. Gyulassy, to be published SQM 2007

  17. Conclusions • 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, Rcb, 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 Rcb 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 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 RcAA/RbAA with the possibility of breaching 1 and asymptotically approaching 1 from above • Surface emission models (although already unlikely as per v2(pT) data) predict flat in pTc, b RAA, with a ratio of 1 • Moderately suppressed radiative only energy loss shows a dip in the ratio at low pT; 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 SQM 2007

  19. Backups SQM 2007

  20. 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 SQM 2007

  21. Asymptopia at the LHC Asymptotic pocket formulae: DErad/E ~a3 Log(E/m2L)/E DEel/E ~a2 Log((E T)1/2/mg)/E WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation SQM 2007

  22. n(pT) SQM 2007

  23. Langevin Model AdS/CFT 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: SQM 2007

  24. But There’s a Catch (II) • Limited experimental pT reach? ALICE Physics Performance Report, Vol. II SQM 2007

  25. Zoom In • Factor ~2-3 increase in ratio for pQCD • Possible distinction for Rad only vs. Rad+El at low-pT SQM 2007

  26. 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); D/2pT ~ 3 => aSYM ~ .05 SQM 2007

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