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Possible String Theoretic Deviations from pQCD in Heavy Quark Energy Loss at LHC

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. pQCD Success at RHIC:.

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Possible String Theoretic Deviations from pQCD in Heavy Quark Energy Loss at LHC

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  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. CERN Heavy Ion Forum

  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 CERN Heavy Ion Forum

  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… 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 CERN Heavy Ion Forum

  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) • h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD • e- RAA ~ p, h RAA; e- RAA(f) • Mach wave-like structures • sstrong=(3/4) sweak, similar to Lattice T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) CERN Heavy Ion Forum

  6. Give up on pQCD? Old and Busted: pQCD New Hotness: AdS/CFT CERN Heavy Ion Forum

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

  8. 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 • 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! CERN Heavy Ion Forum

  9. Looking for a Robust, Detectable Signal erad~as L2 log(pT/Mq)/pT eST~ 1 - Exp(-m L), m = pl1/2T2/2Mq 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: epQCD 0 vs. eAdSindep of pT!! • dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST CERN Heavy Ion Forum

  10. 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 CERN Heavy Ion Forum

  11. Model Inputs • AdS/CFT Drag • “Obvious”: as = aSYM, TSYM = TQCD • D/2pT = 3 inspired: as = .05 • pQCD/Hydro inspired: as = .3 (D/2pT ~ 1) • “Alternative”: l = 5.5, TSYM = TQCD/31/4 • WHDG convolved radiative and collisional energy loss • as = .3 • WHDG radiative energy loss (similar to ASW) • = 40, 100 • All use realistic, nonuniform medium with Bjorken expansion • Two medium densities for LHC: • PHOBOS (dNg/dy = 1750); CGC (dNg/dy = 2900) CERN Heavy Ion Forum

  12. LHC c, b RAA pT Dependence • 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 CERN Heavy Ion Forum

  13. A Cleaner Signal RcAA(pT)/RbAA(pT) ~ 1 - as 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 CERN Heavy Ion Forum

  14. LHC RcAA(pT)/RbAA(pT) 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 pT CERN Heavy Ion Forum

  15. But There’s a Catch (I) • 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: (|) CERN Heavy Ion Forum

  16. LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits) • O: corrections unlikely for smaller momenta • |: corrections likely for higher momenta CERN Heavy Ion Forum

  17. But There’s a Catch (II) • Limited experimental pT reach? ALICE Physics Performance Report, Vol. II 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-pT CERN Heavy Ion Forum

  19. 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 ~ 2-3 times increase in this ratio by 30 GeV—this can be observed in year 1 at the LHC 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 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 CERN Heavy Ion Forum

  21. Backups CERN Heavy Ion Forum

  22. 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 CERN Heavy Ion Forum

  23. 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 CERN Heavy Ion Forum

  24. RHIC e- CERN Heavy Ion Forum

  25. RHIC c, b RAA(pT) CERN Heavy Ion Forum

  26. RHIC RcAA(pT)/RbAA(pT) CERN Heavy Ion Forum

  27. n(pT) CERN Heavy Ion Forum

  28. 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: CERN Heavy Ion Forum

  29. Drag Picture • The Heavy Quark Brachistochrone: J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007 CERN Heavy Ion Forum

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