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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) January 10, 2008.

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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) January 10, 2008 With many thanks to Miklos Gyulassy, and Simon Wicks Nuclear Seminar, OSU

  2. Outline • Motivation for studying AdS/CFT • Introduction to Jet Physics • AdS Drag: Expectations, Results, Limitations • Conclusions Nuclear Seminar, OSU

  3. Motivation Nuclear Seminar, OSU

  4. Lattice QCD pQCD Limited Toolbox for QCD Calculations Previously only two: • All momenta • Euclidean correlators • Any quantity • Small coupling Nuclear Seminar, OSU

  5. 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 Nuclear Seminar, OSU

  6. 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) Q.M. SSYM => C.M. SNG J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007 Nuclear Seminar, OSU

  7. 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 Nuclear Seminar, OSU

  8. Connection to Experiment a.k.a. the Reality Check for Theory Nuclear Seminar, OSU

  9. Introduction to Jet Physics Nuclear Seminar, OSU

  10. Why High-pT Jets? • Compare unmodified p+p collisions to A+A: • Use suppression pattern to either: • Learn about medium (requires detailed understanding of energy loss): jet tomography • Learn about energy loss pT pT 2D Transverse direction Longitudinal (beam pipe) direction Figures from http://www.star.bnl.gov/central/focus/highPt/ Nuclear Seminar, OSU

  11. High-pT Observables 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: Nuclear Seminar, OSU

  12. 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 Nuclear Seminar, OSU

  13. 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? Nuclear Seminar, OSU

  14. 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) Nuclear Seminar, OSU

  15. pQCD vs. AdS Drag: Expectations, Results, Limitations Nuclear Seminar, OSU

  16. pQCD Energy Loss Mechanisms • Radiative bremsstrahlung • Reduced from Bethe-Heitler limit by in-medium rescattering/interference: • Landau-Pomeranchuk-Migdal (LPM) effect • Elastic (collisional) • Original thought: El << Rad • But El ~ Rad at RHIC/LHC • Importance under debate WHDG (Wicks, Horowitz, Djordjevic, Gyulassy), Nucl.Phys.A784:426-442,2007, and refs. therein Nuclear Seminar, OSU

  17. AdS/CFT Drag • Model heavy quark jet energy loss by embedding in AdS space dpT/dt = - m pT • AdS Result: dpT/dt ~ -(T2/Mq) pT Nuclear Seminar, OSU

  18. Energy Loss Comparison D7 Probe Brane t x v Q, m 3+1D Brane Boundary zm = 2pm / l1/2 D3 Black Brane (horizon) zh = pT Black Hole z = 0 • AdS/CFT Drag: dpT/dt ~ -(T2/Mq) pT • Compare to Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT • Compare to LPM dpT/dt ~ -LT3 log(pT/Mq) Nuclear Seminar, OSU

  19. RAA Approximation y=0 RHIC LHC • Above a few GeV, quark production spectrum is approximately power law: • dN/dpT ~ 1/pT(n+1), where n(pT) has some momentum dependence • We can approximate RAA(pT): • RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. e = 1-pf/pi) Nuclear Seminar, OSU

  20. 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 between pQCD, AdS/CFT • 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 Nuclear Seminar, OSU

  21. 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) Nuclear Seminar, OSU

  22. LHC c, b RAA pT Dependence WH, M. Gyulassy, arXiv: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 Nuclear Seminar, OSU

  23. 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) Nuclear Seminar, OSU

  24. LHC RcAA(pT)/RbAA(pT) Prediction • Recall the Zoo: WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] • 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, arXiv:0706.2336 [nucl-th] Nuclear Seminar, OSU

  25. But There’s a Catch x5 “z” • Speed limit estimate for applicability of AdS drag • 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 = T(t0, x=y=0): “(” • largest gcrit for smallest T T = Tc: “]” D7 Probe Brane Q Worldsheet boundary Spacelikeif g > gcrit Trailing String “Brachistochrone” D3 Black Brane Nuclear Seminar, OSU

  26. LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits) WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] • T(t0): (O), corrections unlikely for smaller momenta • Tc: (|), corrections likely for higher momenta Nuclear Seminar, OSU

  27. 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 Nuclear Seminar, OSU

  28. 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, arXiv:0710.0703 [nucl-th] Nuclear Seminar, OSU

  29. 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, arXiv:0710.0703 [nucl-th] Nuclear Seminar, OSU

  30. 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 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 Nuclear Seminar, OSU

  31. 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 Nuclear Seminar, OSU

  32. 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 Nuclear Seminar, OSU

  33. Backups Nuclear Seminar, OSU

  34. 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 Nuclear Seminar, OSU

  35. 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! Nuclear Seminar, OSU

  36. 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: Nuclear Seminar, OSU

  37. 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 Nuclear Seminar, OSU

  38. 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 Nuclear Seminar, OSU

  39. 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 Nuclear Seminar, OSU

  40. 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) Nuclear Seminar, OSU

  41. Pion RAA • Is it a good measurement for tomography? • Yes: small experimental error • Claim: we should not be so immediately dis-missive of the pion RAA as a tomographic tool • Maybe not: some models appear “fragile” Nuclear Seminar, OSU

  42. Fragility: A Poor Descriptor • All energy loss models with a formation time saturate at some RminAA > 0 • The questions asked should be quantitative : • Where is RdataAA compared to RminAA? • How much can one change a model’s controlling parameter so that it still agrees with a measurement within error? • Define sensitivity, s = min. param/max. param that is consistent with data within error Nuclear Seminar, OSU

  43. Different Models have Different Sensitivities to the Pion RAA • GLV: s < 2 • Higher Twist: s < 2 • DGLV+El+Geom: s < 2 • AWS: s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Nuclear Seminar, OSU

  44. T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007) WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Nuclear Seminar, OSU

  45. A Closer Look at ASW The lack of sensitivity needs to be more closely examined because (a) unrealistic geometry (hard cylinders) and no expansion and (b) no expansion shown against older data (whose error bars have subsequently shrunk (a) (b) 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) Nuclear Seminar, OSU

  46. Surface Bias vs. Surface Emission • Surface Emission: one phrase explanation of fragility • All models become surface emitting with infinite E loss • Surface Bias occurs in all energy loss models • Expansion + Realistic geometry => model probes a large portion of medium A. Majumder, HP2006 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 Nuclear Seminar, OSU

  47. A Closer Look at ASW • Difficult to draw conclusions on inherent surface bias in AWS from this for three reasons: • No Bjorken expansion • Glue and light quark contributions not disentangled • Plotted against Linput (complicated mapping from Linput to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) Nuclear Seminar, OSU

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