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

First, a Perturbative Detour High-pT Physics at LHC

pQCD Success in High-pT at RHIC: (circa 2005) Y. Akiba for the PHENIX collaboration, hep-ex/0510008 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

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 S. A. Bass, et al., arXiv:0808.0908 [nucl-th]. S. Wicks, et al., Nucl. Phys. A784, 426 (2007) T. Renk and K. J. Eskola, PoS LHC07, 032 (2007) High-pT Physics at LHC

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

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

Quantitative Extraction PHENIX, PRC77, 064907 (2008) 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: https://wiki.bnl.gov/TECHQM/index.php/WHDG S. Wicks, et al., Nucl. Phys. A783, 493 (2007) High-pT Physics at LHC

Trouble for High-pT wQGP Picture v2 too small NPE supp. too large 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

Back to the Future Fifth Dimension High-pT Physics at LHC

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

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

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

Energy Loss Comparison D7 Probe Brane t z = 0 x v AdS/CFT Drag: dpT/dt ~ -(T2/Mq) pT Q, m zm = l1/2/2pm 3+1D Brane Boundary 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

RAA Approximation 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) y=0 RHIC LHC High-pT Physics at LHC

Looking for a Robust, Detectable Signal 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. eAdS indep of pT!! dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST erad ~ as L2 log(pT/Mq)/pT eST ~ 1 - Exp(-m L), m = pl1/2 T2/2Mq S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006 High-pT Physics at LHC

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

LHC c, b RAA pT Dependence WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008) Naïve expectations met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST Significant rise in RAA(pT) for pQCD Rad+El Large suppression leads to flattening Use of realistic geometry and Bjorken expansion allows saturation below .2 LHC Prediction Zoo: What a Mess! Let’s go through step by step Unfortunately, large suppression pQCD similar to AdS/CFT High-pT Physics at LHC

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 - as n(pT) L2 log(Mb/Mc) ( /pT) High-pT Physics at LHC

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

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

Worldsheet boundary Spacelike if g > gcrit 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 Spacelike if g > gcrit z Trailing String “Brachistochrone” x D3 Black Brane High-pT Physics at LHC

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

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 E Q 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

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 Mrest ¹ Mkin Note that M >> T Minkowski Boundary z = 0 F.v = dp/dt E Q 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

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

New Geometries 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) Q vshock x z vshock x z Q Bjorken-Expanding Medium High-pT Physics at LHC

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

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

Shock Geometry Results Three t-ind. solutions (static gauge): Xm = (t, x(z), 0,0, z) x(z) = c, ± m ½ 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

HQ Momentum Loss in the Shock x(z) = m ½ z3/3 => 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 High-pT Physics at LHC

HQ Drag in the Shock HQ Rest Frame Shock Rest Frame Recall for BH: Mq L vsh vq = -vsh Mq 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

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

Backup Slides High-pT Physics at LHC

Measurement at RHIC Future detector upgrades will allow for identified c and b quark measurements RHIC production spectrum significantly harder than LHC y=0 RHIC 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

RHIC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well High-pT Physics at LHC

RHIC Rcb Ratio pQCD pQCD AdS/CFT AdS/CFT WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] Wider distribution of AdS/CFT curves due to large n: increased sensitivity to input parameters Advantage of RHIC: lower T => higher AdS speed limits High-pT Physics at LHC

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

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

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

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

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

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

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

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

Elastic Remains Important High-pT Physics at LHC

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

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

More Geometry pT dependence of surface bias Nontrivial a posteriori fixed length dependence (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