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Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss

Delve into the theoretical framework of AdS/CFT and its implications in understanding heavy ion physics. Discover the latest research on pQCD, energy loss, and connections to experimental data.

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Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss

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  1. Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss William Horowitz The Ohio State University Columbia University Frankfurt Institute for Advanced Studies (FIAS) October 28, 2008 LHC Predictions: Phys. Lett. B666:320, 2008 (arXiv:0706.2336) RHIC Predictions: J. Phys. G35:044025, 2008 (arXiv:0710.0703) With many thanks to Miklos Gyulassy and Simon Wicks Nuclear Seminar, McGill University

  2. Outline • Motivation for studying AdS/CFT • Introduction to Heavy Ion Physics • pQCD vs. AdS Drag: Expectations, Results, Limitations • Conclusions Nuclear Seminar, McGill University

  3. Motivation Nuclear Seminar, McGill University

  4. Lattice QCD pQCD Limited Toolbox for QCD Calculations Previously only two, restricted methods: • Any quantity • Small coupling (large momenta) Two 10 Tflops QCDOC Computers: RBRC and DOE • All momenta • Euclidean correlators Nuclear Seminar, McGill University

  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 J Maldacena, Adv.Theor.Math.Phys.2:231-252,1998 Bosonic part of IIB low energy effective action Geometry of bosonic part of 10D supergravity, near horizon limit Nuclear Seminar, McGill University

  6. Regime of Applicability Q.M. SSYM => C.M. SNG • 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) J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007 Nuclear Seminar, McGill University

  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, McGill University

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

  9. Introduction to Heavy Ion Physics Nuclear Seminar, McGill University

  10. Geometry of a HI Collision M Kaneta, Results from the Relativistic Heavy Ion Collider (Part II) • Hydro propagates IC • Results depend strongly on initial conditions • Viscosity reduces eventual momentum anisotropy T Ludlum and L McLerran, Phys. Today 56N10:48 (2003) Nuclear Seminar, McGill University

  11. Perfect Fluidity:AdS + Hydro’s Most Famous Success D. Teaney, Phys. Rev. C68, 034913 (2003) • Hydro h/s small ~ .1 • QGP fluid near-perfect liquid • Naïve pQCD => h/s ~ 1 • New estimates ~ .1 Z Xu, C Greiner, and H Stoecker, PRL101:082302 (2008) • Lowest order AdS result: h/s = 1/4p • Universality? P Kovtun, D Son, and A Starinets, Phys.Rev.Lett.94:111601 (2005) P Kats and P Petrov, arXiv:0712.0743 M Brigante et al., Phys. Rev. D77:126006 (2008) Nuclear Seminar, McGill University

  12. IC, Viscosity, and Hydro • Sharper IC (CGC) => viscosity • Softer IC (Glauber) => “perfect” T Hirano, et al., Phys. Lett. B636:299-304, 2006 Nuclear Seminar, McGill University

  13. Why High-pT Jets? 2D Transverse directions Longitudinal (beam pipe) direction • 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 Figures from http://www.star.bnl.gov/central/focus/highPt/ Nuclear Seminar, McGill University

  14. Jet Physics Terminology 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, McGill University

  15. 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, McGill University

  16. 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, McGill University

  17. 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, McGill University

  18. AdS/CFT Energy Loss Models • 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, McGill University

  19. AdS/CFT Drag • Model heavy quark jet energy loss by embedding string in AdS space dpT/dt = - m pT m = pl1/2T2/2Mq J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007 Nuclear Seminar, McGill University

  20. 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 • Similar to Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT • Very different from LPM dpT/dt ~ -LT3 log(pT/Mq) Nuclear Seminar, McGill University

  21. 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, McGill University

  22. 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, McGill University

  23. 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, McGill University

  24. LHC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0706.2336 • LHC Prediction Zoo: What a Mess! • Let’s go through step by step • 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 met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST Nuclear Seminar, McGill University

  25. 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, McGill University

  26. 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, McGill University

  27. Not So Fast! 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) • No Single 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, McGill University

  28. 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, McGill University

  29. 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, McGill University

  30. 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, McGill University

  31. 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, McGill University

  32. Conclusions • Previous AdS qualitative successes inconclusive • AdS/CFT Drag observables calculated • Generic differences (pQCD vs. AdS/CFT Drag) seen in RAA • Masked by extreme pQCD • Enhancement from ratio of c to b RAA • Discovery potential in Year 1 LHC Run • Understanding regions of self-consistency crucial • RHIC measurement possible Nuclear Seminar, McGill University

  33. Backups Nuclear Seminar, McGill University

  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, McGill University

  35. 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, McGill University

  36. 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, McGill University

  37. 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, McGill University

  38. 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, McGill University

  39. 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, McGill University

  40. 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, McGill University

  41. 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, McGill University

  42. 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, McGill University

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

  44. 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, McGill University

  45. 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, McGill University

  46. 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, McGill University

  47. 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, McGill University

  48. Conclusions • AdS/CFT Drag observables calculated • Generic differences (pQCD vs. AdS/CFT Drag) seen in RAA • Masked by extreme pQCD • Enhancement from ratio of c to b RAA • Discovery potential in Year 1 LHC Run • Understanding regions of self-consistency crucial • RHIC measurement possible Nuclear Seminar, McGill University

  49. Shameless self-promotion by the presenter Nuclear Seminar, McGill University

  50. 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, McGill University

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