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Falsifying AdS/CFT Drag or pQCD Heavy Quark Energy Loss with A+A at RHIC and LHC

arXiv:0706.2336  (LHC predictions) arXiv:0710.0703 (RHIC predictions). Falsifying AdS/CFT Drag or pQCD Heavy Quark Energy Loss with A+A at RHIC and LHC. William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) November 2, 2007.

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Falsifying AdS/CFT Drag or pQCD Heavy Quark Energy Loss with A+A at RHIC and LHC

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  1. arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions) Falsifying AdS/CFT Drag or pQCD Heavy Quark Energy Loss with A+A at RHIC and LHC William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) November 2, 2007 With many thanks to Miklos Gyulassy, Simon Wicks, and Ivan Vitev Heavy Quark Workshop, LBNL

  2. Shameless Web Self Promotion Hello Online Viewers! Scary! Heavy Quark Workshop, LBNL

  3. pQCD Success at RHIC: Y. Akiba for the PHENIX collaboration, nucl-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 Heavy Quark Workshop, LBNL

  4. 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 strong coupling? Heavy Quark Workshop, LBNL

  5. Strong Coupling Calculation • 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 Heavy Quark Workshop, LBNL

  6. Qualitative AdS/CFT Successes: AdS/CFT S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213 J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 PHENIX, Phys. Rev. Lett. 98, 172301 (2007) • Mach wave-like structures • sstrong=(3/4) sweak, similar to Lattice • h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD • e- RAA ~ p, h RAA; e- RAA(f) T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) Heavy Quark Workshop, LBNL

  7. Quantitative AdS/CFT 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! Heavy Quark Workshop, LBNL

  8. Energy Loss Comparison • ST Drag dpT/dt = -(pl1/2T2/2Mq)pT • Compare to Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT • Compare to LPM dpT/dt ~ -LT3 log(pT/Mq) Heavy Quark Workshop, LBNL

  9. Looking for a Robust, Detectable Signal erad~as L2 log(pT/Mq)/pT • Use future detectors’ identification of c and b to distinguish between pQCD, AdS/CFT • 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 Heavy Quark Workshop, LBNL

  10. Model Inputs for LHC Predictions • 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) Heavy Quark Workshop, LBNL

  11. LHC c, b RAA pT Dependence WH, M. Gyulassy, nucl-th/0706.2336 • Unfortunately, large suppression pQCD similar to AdS/CFT • 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 Heavy Quark Workshop, LBNL

  12. An Enhanced 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) Heavy Quark Workshop, LBNL

  13. 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 Heavy Quark Workshop, LBNL

  14. But There’s a Catch 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 • Similar to BH LPM • gcrit ~ Mq/(lT) • Ambiguous T for QGP • smallest gcrit for largest T = T(t0, x=y=0): “(” • largest gcrit for smallest T = Tc: “]” D7 Probe Brane Q Worldsheet boundary Spacelikeif g > gcrit Trailing String “Brachistochrone” D3 Black Brane Heavy Quark Workshop, LBNL

  15. 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 Heavy Quark Workshop, LBNL

  16. Measurement at RHIC y=0 RHIC LHC • Future detector upgrades will allow for identified c and b quark measurements • RHIC production spectrum significantly harder than LHC • NOT slowly varying • No longer expect pQCD dRAA/dpT > 0 • Large n requires corrections to naïve Rcb ~ Mc/Mb Heavy Quark Workshop, LBNL

  17. 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 Heavy Quark Workshop, LBNL

  18. 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 Heavy Quark Workshop, LBNL

  19. 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 Heavy Quark Workshop, LBNL

  20. 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 Heavy Quark Workshop, LBNL

  21. 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+p baseline and p+A control Heavy Quark Workshop, LBNL

  22. Backups Heavy Quark Workshop, LBNL

  23. 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 Heavy Quark Workshop, LBNL

  24. 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 Heavy Quark Workshop, LBNL

  25. 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: Heavy Quark Workshop, LBNL

  26. But There’s a Catch (II) • Limited experimental pT reach? • ATLAS and CMS do not seem to be limited in this way (claims of year 1 pT reach of ~100 GeV) but systematic studies have not yet been performed ALICE Physics Performance Report, Vol. II Heavy Quark Workshop, LBNL

  27. K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) 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) Heavy Quark Workshop, LBNL

  28. Introduction to Jargon pT f Naïvely: if medium has no effect, then RAA = 1 Common variables used are transverse momentum, pT, and angle with respect to the reaction plane, f Common to Fourier expand RAA: Heavy Quark Workshop, LBNL

  29. Geometry of a HI Collision Medium density and jet production are wide, smooth distributions Use of unrealistic geometries strongly bias results S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007 1D Hubble flow => r(t) ~ 1/t => T(t) ~ 1/t1/3 M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005 Heavy Quark Workshop, LBNL

  30. Lattice QCD pQCD QCD Calculations Previously only two tools: • All momenta • Euclidean correlators • Any quantity • Small coupling Heavy Quark Workshop, LBNL

  31. Maldacena Conjecture Large Nc limit of d-dimensional conformal field theory dual to string theory on the product of d+1-dimensional Anti-de Sitter space with a compact manifold 3+1 SYM z = 0 Heavy Quark Workshop, LBNL

  32. Regime of Applicability • 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) D7 Probe Brane t x v Q, m 3+1D Brane Boundary zm = 2pm / l1/2 Q.M. SSYM => C.M. SNG D3 Black Brane (horizon) zh = pT Black Hole z = 0 Heavy Quark Workshop, LBNL

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