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Testing AdS/CFT at LHC

Testing AdS/CFT at LHC. William Horowitz The Ohio State University February 6, 2009. With many thanks to Yuri Kovchegov and Ulrich Heinz. First, a Perturbative Detour. pQCD Success in High-p T at RHIC:. Y. Akiba for the PHENIX collaboration , hep-ex/0510008. (circa 2005).

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Testing AdS/CFT at LHC

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  1. Testing AdS/CFT at LHC William Horowitz The Ohio State University February 6, 2009 With many thanks to Yuri Kovchegov and Ulrich Heinz High-pT Physics at LHC

  2. First, a Perturbative Detour High-pT Physics at LHC

  3. pQCD Success in High-pT at RHIC: Y. Akiba for the PHENIX collaboration, hep-ex/0510008 (circa 2005) • Consistency: RAA(h)~RAA(p) • Null Control: RAA(g)~1 • GLV Calculation: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy • Assuming pQCD E-loss, let’s clear up some myths High-pT Physics at LHC

  4. Surface Emission: Red Herring? • If you believe in pQCD E-loss, observed jets come from deep in the medium HT, AMY, ASW WHDG BDMPS + Hydro T. Renk and K. J. Eskola, PoS LHC07, 032 (2007) S. Wicks, et al., Nucl. Phys. A784, 426 (2007) S. A. Bass, et al., arXiv:0808.0908 [nucl-th]. High-pT Physics at LHC

  5. Fragility is Fragile • Linear-linear plot of RAA(qhat) is the incorrect way to think about the problem PHENIX, Phys. Rev. C77, 064907 (2008) K. J. Eskola, et al., Nucl. Phys. A747, 511 (2005) High-pT Physics at LHC

  6. Fragility is Fragile (cont’d) • If you believe in pQCD E-loss, RAA is NOT a fragile probe of the medium • Linear on a log-log plot • Double => halve RAA • Similar results for WHDG, GLV, AMY, ZOWW, etc. PHENIX, Phys. Rev. C77, 064907 (2008) High-pT Physics at LHC

  7. Quantitative Extraction • Model params to within ~20% • Experimental error only!! • Sys. theor. err. could be quite large • Running coupling uncertainties • Smaller at LHC? • Multi-gluon correlations? • Larger at LHC? • Handling of geometry • … • See also TECHQM wiki: PHENIX, PRC77, 064907 (2008) https://wiki.bnl.gov/TECHQM/index.php/WHDG S. Wicks, et al., Nucl. Phys. A783, 493 (2007) High-pT Physics at LHC

  8. v2 too small NPE supp. too large Trouble for High-pT wQGP Picture p0 v2 M Tannenbaum, High-pT Physics at LHC ‘09 NPE v2 STAR, Phys. Rev. Lett. 98, 192301 (2007) Pert. at LHC energies? PHENIX, Phys. Rev. Lett. 98, 172301 (2007) High-pT Physics at LHC

  9. Back to the FutureFifth Dimension High-pT Physics at LHC

  10. Motivation for High-pT AdS • Why study AdS E-loss models? • Many calculations vastly simpler • Complicated in unusual ways • Data difficult to reconcile with pQCD • pQCD quasiparticle picture leads to dominant q ~ m ~ .5 GeV mom. transfers => Nonperturbatively large as • Use data to learn about E-loss mechanism, plasma properties • Domains of self-consistency crucial for understanding High-pT Physics at LHC

  11. 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 High-pT Physics at LHC

  12. AdS/CFT Energy Loss Models • Langevin Diffusion • Collisional energy loss for heavy quarks • Restricted to low pT • pQCD vs. AdS/CFT computation of D, the diffusion coefficient • ASW/LRW model • Radiative energy loss model for all parton species • pQCD vs. AdS/CFT computation of • Debate over its predicted magnitude • Heavy Quark Drag calculation • Embed string representing HQ into AdS geometry • Includes all E-loss modes • Empty space calculation: • Previously: thermalized QGP plasma, temp. T, gcrit<~Mq/T Moore and Teaney, Phys.Rev.C71:064904,2005 Casalderrey-Solana and Teaney, Phys.Rev.D74:085012,2006; JHEP 0704:039,2007 BDMPS, Nucl.Phys.B484:265-282,1997 Armesto, Salgado, and Wiedemann, Phys. Rev. D69 (2004) 114003 Liu, Ragagopal, Wiedemann, PRL 97:182301,2006; JHEP 0703:066,2007 Kharzeev, arXiv:0806.0358 [hep-ph] Gubser, Phys.Rev.D74:126005,2006 Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013,2006 High-pT Physics at LHC

  13. Energy Loss Comparison D7 Probe Brane • AdS/CFT Drag: dpT/dt ~ -(T2/Mq) pT t x z = 0 v Q, m 3+1D Brane Boundary zm = l1/2/2pm D3 Black Brane (horizon) zh = 1/pT Black Hole z = ¥ • Similar to Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT • Very different from LPM dpT/dt ~ -LT3 log(pT/Mq) High-pT Physics at LHC

  14. 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) High-pT Physics at LHC

  15. 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 High-pT Physics at LHC

  16. 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) High-pT Physics at LHC

  17. LHC c, b RAA pT Dependence WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008) • 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 High-pT Physics at LHC

  18. 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) High-pT Physics at LHC

  19. LHC RcAA(pT)/RbAA(pT) Prediction • Recall the Zoo: WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008) • 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 • Distinguish rad and el contributions? WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008) High-pT Physics at LHC

  20. Additional Discerning Power • Consider ratio for ALICE pT reach mc = mb = 0 • Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1 • Does not include partonic E-loss, which will be nonnegligable as ratio goes to unity • Higgs (non)mechanism => Rc/Rb ~ 1 ind. of pT High-pT Physics at LHC

  21. Not So Fast! D7 Probe Brane Q • 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 Worldsheet boundary Spacelikeif g > gcrit z Trailing String “Brachistochrone” x D3 Black Brane High-pT Physics at LHC

  22. LHC RcAA(pT)/RbAA(pT) Prediction(with speed limits) WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008) • T(t0): (, highest T—corrections unlikely for smaller momenta • Tc: ], lowest T—corrections likely for higher momenta High-pT Physics at LHC

  23. Derivation of BH Speed Limit I • Constant HQ velocity • Assume const. v kept by F.v • Critical field strength Ec = M2/l½ • E > Ec: Schwinger pair prod. • Limits g < gc ~ T2/lM2 • Alleviated by allowing var. v • Drag similar to const. v Minkowski Boundary z = 0 F.v = dp/dt Q E v zM = l½ / 2pM D7 dp/dt J. Casalderrey-Solana and D. Teaney, JHEP 0704, 039 (2007) D3 zh = 1/pT Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013 (2006) z = ¥ High-pT Physics at LHC

  24. Derivation of BH Speed Limit II • Local speed of light • BH Metric => varies with depth z • v(z)2 < 1 – (z/zh)4 • HQ located at zM = l½/2pM • Limits g < gc ~ T2/lM2 • Same limit as from const. v • Mass a strange beast • Mtherm < Mrest • Mrest¹ Mkin • Note that M >> T Minkowski Boundary z = 0 F.v = dp/dt Q E v zM = l½ / 2pM D7 S. S. Gubser, Nucl. Phys. B 790, 175 (2008) dp/dt D3 zh = 1/pT z = ¥ High-pT Physics at LHC

  25. Universality and Applicability • How universal are drag results? • Examine different theories • Investigate alternate geometries • When does the calculation break down? • Depends on the geometry used High-pT Physics at LHC

  26. New Geometries vshock Q vshock z Q z x x Constant T Thermal Black Brane Shock Geometries Nucleus as Shock J Friess, et al., PRD75:106003, 2007 DIS Embedded String in Shock Before After Albacete, Kovchegov, Taliotis, JHEP 0807, 074 (2008) Bjorken-Expanding Medium High-pT Physics at LHC

  27. Shocking Motivation • Warm-up for full Bjorken metric R. A. Janik and R. B. Peschanski, Phys. Rev. D 73, 045013 (2006) • No local speed of light limit! • Metric yields -1 < v < 1 • In principle, applicable to all quark masses for all momenta • Subtlety in exchange of limits? High-pT Physics at LHC

  28. Standard Method of Attack • Parameterize string worldsheet • Xm(t, s) • Plug into Nambu-Goto action • Varying SNG yields EOM for Xm • Canonical momentum flow (in t, s) High-pT Physics at LHC

  29. Shock Geometry Results • Three t-ind. solutions (static gauge): Xm = (t, x(z), 0,0, z) • x(z) = c, ± m½ z3/3 • Constant solution unstable • Time-reversed negative x solution unphysical • Sim. to x ~ z3/3, z << 1, for const. T BH geom. Q z = 0 vshock + m ½ z3/3 - m ½ z3/3 c x z = ¥ High-pT Physics at LHC

  30. HQ Momentum Loss in the Shock Relate m to nuclear properties • Use AdS dictionary: m ~ T--/Nc2 • T-- = (boosted den. of scatterers) x (mom.) • T-- = Nc2 (L3 p+/L) x (p+) • Nc2 gluons per nucleon in shock • L is typical mom. scale; L-1 typical dist. scale • p+: mom. of shock gluons as seen by HQ • p: mom. of HQ as seen by shock => m = L2p+2 x(z) = m½ z3/3 => High-pT Physics at LHC

  31. HQ Rest Frame Shock Rest Frame HQ Drag in the Shock Mq L vsh Mq vq = -vsh 1/L vq = 0 i i vsh = 0 • Recall for BH: • Shock gives exactly the same drag as BH for L = p T High-pT Physics at LHC

  32. Conclusions and Outlook for • the LHC Experiment: • Use data to test E-loss mechanism • RcAA(pT)/RbAA(pT) wonderful tool • p+Pb and Direct-g Pb+Pb critical null controls • the AdS Drag: • Applicability and universality crucial • Both investigated in shock geom. • Shock geometry reproduces BH momentum loss • Unrestricted in momentum reach • Variable velocity case nontrivial • Future work • Time-dependent shock treatment • AdS E-loss in Bjorken expanding medium High-pT Physics at LHC

  33. Backup Slides High-pT Physics at LHC

  34. 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 High-pT Physics at LHC

  35. 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] High-pT Physics at LHC

  36. 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] High-pT Physics at LHC

  37. Simultaneous p, e- Suppression A. Adil and I. Vitev, hep-ph/0611109 H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, 034913 (2006) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 • pQCD is not falsified: • Elastic loss? • Uncertainty in c, b contributions • In-medium fragmentation? • Resonances? • Naïve pQCD => large mass, small loss • But p, h RAA ~ e- RAA! High-pT Physics at LHC

  38. Zooming In • Factor ~2-3 increase in ratio for pQCD • Possible distinction for Rad only vs. Rad+El at low-pT High-pT Physics at LHC

  39. Additional Discerning Power • Consider ratio for ALICE pT reach • 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 High-pT Physics at LHC

  40. Consider ratio for ALICE pT reach High-pT Physics at LHC

  41. 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 High-pT Physics at LHC

  42. Comparison of LHC p Predictions Curves of ASW-based energy loss are flat in pT (a) (b) 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) High-pT Physics at LHC

  43. Why ASW is Flat • Flat in pT curves result from extreme suppression at the LHC • When probability leakage P(e > 1) is large, the (renormalized or not) distribution becomes insensitive to the details of energy loss • Enormous suppression due to: • Already (nonperturbatively) large suppression at RHIC for ASW • Extrapolation to LHC assumes 7 times RHIC medium densities (using EKRT) • Note: even if LHC is only ~ 2-3 times RHIC, still an immoderate ~ 30-45 • As seen on the previous slide, Vitev predicted a similar rise in RAA(pT) as we do • Vitev used only radiative loss, Prad(e), but assumed fixed path • WHDG similar because elastic and path fluctuations compensate High-pT Physics at LHC

  44. Elastic Can’t be Neglected! M. Mustafa, Phys. Rev. C72:014905 (2005) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 High-pT Physics at LHC

  45. Elastic Remains Important High-pT Physics at LHC

  46. A Closer Look at PQM • Difficult to draw conclusions on inherent surface bias in PQM 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) High-pT Physics at LHC

  47. Direct g: A+A IS Well Understood PHENIX, Phys. Rev. Lett. 94, 232301 (2005) High-pT Physics at LHC

  48. pT dependence of surface bias Nontrivial a posteriori fixed length dependence More Geometry (not surface emission!) S. A. Bass, et al., arXiv:0808.0908 [nucl-th]. S. Wicks, WH, M. Djordjevic and M. Gyulassy, Nucl. Phys. A784, 426 (2007) High-pT Physics at LHC

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