Shock Treatment: Heavy Quark Energy Loss in a Novel Geometry William Horowitz The Ohio State University April 3, 2009 With many thanks to Yuri Kovchegov and Ulrich Heinz Quark Matter 2009

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 Quark Matter 2009

Trouble for High-pT wQGP Picture v2 too small NPE supp. too large p0 v2 WHDG C. Vale, QM09 Plenary (analysis by R. Wei) NPE v2 STAR, Phys. Rev. Lett. 98, 192301 (2007) Pert. at LHC energies? PHENIX, Phys. Rev. Lett. 98, 172301 (2007) Quark Matter 2009

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 Quark Matter 2009

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 2009

AdS/CFT Energy Loss Models I 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 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 Quark Matter 2009

AdS/CFT Energy Loss Models II String Drag calculation Embed string rep. quark/gluon in AdS geom. Includes all E-loss modes (difficult to interpret) Gluons and light quarks Empty space HQ calculation Previous HQ: thermalized QGP plasma, temp. T, Gubser, Gulotta, Pufu, Rocha, JHEP 0810:052, 2008 Chesler, Jensen, Karch, Yaffe, arXiv:0810.1985 [hep-th] Kharzeev, arXiv:0806.0358 [hep-ph] Gubser, Phys.Rev.D74:126005,2006 Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013, 2006 Quark Matter 2009

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) Quark Matter 2009

LHC RcAA(pT)/RbAA(pT) Prediction Individual c and b RAA(pT) predictions: 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) Quark Matter 2009

Universality and Applicability How universal are th. HQ drag results? Examine different theories Investigate alternate geometries Other AdS geometries Bjorken expanding hydro Shock metric Warm-up to Bj. hydro Can represent both hot and cold nuclear matter Quark Matter 2009

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 Quark Matter 2009

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) Quark Matter 2009

New in the Shock Find string solutions in HQ rest frame vHQ = 0 Assume static case (not new) Shock wave exists for all time String dragged for all time Xm = (t, x(z), 0,0, z) Simple analytic solutions: x(z) = x0, x0 ± m ½ z3/3 Quark Matter 2009

Shock Geometry Results Three t-ind. solutions (static gauge): Xm = (t, x(z), 0,0, z) x(z) = x0, x0 ± 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. x0 - m ½ z3/3 x0 + m ½ z3/3 x0 vshock Q z = 0 z = ¥ x Quark Matter 2009

HQ Momentum Loss x(z) = m ½ z3/3 => Relate m to nuclear properties Use AdS dictionary Metric in Fefferman-Graham form: m ~ T--/Nc2 T’00 ~ Nc2 L4 Nc2 gluons per nucleon in shock L is typical mom. scale; L-1 typical dist. scale Quark Matter 2009

Frame Dragging HQ Rest Frame Shock Rest Frame Mq L vsh vq = -vsh Mq 1/L vq = 0 i i vsh = 0 Change coords, boost Tmn into HQ rest frame: T-- ~ Nc2 L4 g2 ~ Nc2 L4 (p’/M)2 p’ ~ gM: HQ mom. in rest frame of shock Boost mom. loss into shock rest frame p0t = 0: Quark Matter 2009

Put Together This leads to We’ve generalized the BH solution to both cold and hot nuclear matter E-loss Recall for BH: Shock gives exactly the same drag as BH for L = p T Quark Matter 2009

Shock Metric Speed Limit Local speed of light (in HQ rest frame) Demand reality of point-particle action Solve for v = 0 for finite mass HQ z = zM = l½/2pMq Same speed limit as for BH metric when L = pT Quark Matter 2009

Conclusions and Outlook Use data to test E-loss mechanism RcAA(pT)/RbAA(pT) wonderful tool Calculated HQ drag in shock geometry For L = p T, drag and speed limit identical to BH Generalizes HQ drag to hot and cold nuclear matter Unlike BH, quark mass unaffected by shock Quark always heavy from strong coupling dressing? BH thermal adjustment from plasma screening IR? Future work: Time-dependent shock treatment AdS E-loss in Bjorken expanding medium Quark Matter 2009

Backup Slides Quark Matter 2009

Canonical Momenta Quark Matter 2009

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 Quark Matter 2009

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 Quark Matter 2009

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 2009

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 Quark Matter 2009

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) Quark Matter 2009

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) Quark Matter 2009

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 Quark Matter 2009

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 Quark Matter 2009

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 Quark Matter 2009

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 = ¥ Quark Matter 2009

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 = ¥ Quark Matter 2009

Trouble for High-pT wQGP Picture v2 too small NPE supp. too large p0 v2 WHDG dN/dy = 1400 C. Vale, QM09 Plenary (analysis by R. Wei) NPE v2 STAR, Phys. Rev. Lett. 98, 192301 (2007) Pert. at LHC energies? PHENIX, Phys. Rev. Lett. 98, 172301 (2007) Quark Matter 2009

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 Quark Matter 2009

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 Quark Matter 2009

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 Quark Matter 2009

HQ Momentum Loss in the Shock Must boost into shock rest frame: Relate m to nuclear properties Use AdS dictionary Metric in Fefferman-Graham form: m ~ T--/Nc2 T00 ~ Nc2 L4 Nc2 gluons per nucleon in shock L is typical mom. scale; L-1 typical dist. Scale Change coords, boost into HQ rest frame: T-- ~ Nc2 L4 (p/M)2 => m = L4 (p/M)2 x(z) = m ½ z3/3 => Quark Matter 2009

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 Quark Matter 2009

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 Quark Matter 2009

HQ Momentum Loss x(z) = m ½ z3/3 => Relate m to nuclear properties Use AdS dictionary Metric in Fefferman-Graham form: m ~ T--/Nc2 T’00 ~ Nc2 L4 Nc2 gluons per nucleon in shock L is typical mom. scale; L-1 typical dist. scale Change coords, boost into HQ rest frame: T-- ~ Nc2 L4 g2 ~ Nc2 L4 (p’/M)2 p’ ~ gM: HQ mom. in rest frame of shock Quark Matter 2009

Shocking Drag Boost mom. loss into shock rest frame Therefore HQ Rest Frame Shock Rest Frame Mq L vsh vq = -vsh Mq 1/L vq = 0 i i vsh = 0 Boost mom. loss into shock rest frame Therefore p0t = 0: Recall for BH: Shock gives exactly the same drag as BH for L = p T Quark Matter 2009