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Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss

This paper explores the comparison between the AdS/CFT Drag and pQCD models for heavy quark energy loss, with the goal of finding a robust signal that can distinguish between the two. The predictions for the LHC are examined, looking for a detectable and reliable signal.

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Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss

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  1. William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) February 9, 2008 arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions) With many thanks to Miklos Gyulassy and Simon Wicks Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss Quark Matter 2008

  2. Motivation • Many heavy quark energy loss models • Hope to distinguish between two broad classes: • Standard Model pQCD • AdS/CFT Drag • Comparison difficult: • nontrivial mapping of AdS/CFT to QCD • predictions for LHC • Look for robust signal Quark Matter 2008

  3. 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 Quark Matter 2008

  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? Quark Matter 2008

  5. Intro to AdS/CFT 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 Quark Matter 2008

  6. 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 classical SUGRA Quark Matter 2008

  7. 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) Quark Matter 2008

  8. 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! Quark Matter 2008

  9. AdS/CFT Drag • Model heavy quark jet energy loss by embedding string in AdS space dpT/dt = - m pT m = pl1/2T2/2Mq Quark Matter 2008

  10. 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) Quark Matter 2008

  11. 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) Quark Matter 2008

  12. 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 Quark Matter 2008

  13. 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) Quark Matter 2008

  14. 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 Quark Matter 2008

  15. 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) Quark Matter 2008

  16. 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] Quark Matter 2008

  17. 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 Quark Matter 2008

  18. 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 Quark Matter 2008

  19. 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 Quark Matter 2008

  20. 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] Quark Matter 2008

  21. 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] Quark Matter 2008

  22. 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 Quark Matter 2008

  23. 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 Quark Matter 2008

  24. Backups Quark Matter 2008

  25. 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 Quark Matter 2008

  26. 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: Quark Matter 2008

  27. 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 Quark Matter 2008

  28. 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 Quark Matter 2008

  29. 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 Quark Matter 2008

  30. 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) Quark Matter 2008

  31. 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” Quark Matter 2008

  32. 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 Quark Matter 2008

  33. 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 Quark Matter 2008

  34. T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007) WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Quark Matter 2008

  35. 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) Quark Matter 2008

  36. 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 Quark Matter 2008

  37. 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) Quark Matter 2008

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