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Shock Treatment: Heavy Quark Energy Loss in a Novel Geometry

Explore the impact of geometries on heavy quark energy loss mechanisms with strong coupling calculations and AdS/CFT models. Includes comparisons with pQCD predictions and the study of shock geometries.

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Shock Treatment: Heavy Quark Energy Loss in a Novel Geometry

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  1. 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

  2. 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 Quark Matter 2009

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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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) Quark Matter 2009

  9. 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

  10. 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

  11. 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 Quark Matter 2009

  12. 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

  13. 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 ± m½ z3/3 Quark Matter 2009

  14. Shock Geometry Results Q z = 0 vshock x0+ m ½z3/3 x0 - m ½z3/3 x0 x z = ¥ • Three t-ind. solutions (static gauge): Xm = (t, x(z), 0,0, z) • x(z) = x0, x0 ± m½ z3/3 • Constant solution unstable • Time-reversed negative x solution unphysical • Sim. to x ~ z3/3, z << 1, for const. T BH geom. Quark Matter 2009

  15. HQ Momentum Loss 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 x(z) = m½ z3/3 => Quark Matter 2009

  16. Frame Dragging • HQ Rest Frame • Shock Rest Frame • 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 Mq L vsh Mq vq = -vsh 1/L vq = 0 i i vsh = 0 • p0t = 0: Quark Matter 2009

  17. 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

  18. 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

  19. 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

  20. Backup Slides Quark Matter 2009

  21. Canonical Momenta Quark Matter 2009

  22. 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 2009

  23. 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 2009

  24. 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

  25. 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 Quark Matter 2009

  26. 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 2009

  27. 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

  28. 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

  29. 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 Quark Matter 2009

  30. 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

  31. 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 = ¥ Quark Matter 2009

  32. 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 = ¥ Quark Matter 2009

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

  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 Quark Matter 2009

  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] Quark Matter 2009

  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] Quark Matter 2009

  37. 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) = m½ z3/3 => Quark Matter 2009

  38. 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 => Quark Matter 2009

  39. 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 Quark Matter 2009

  40. HQ Momentum Loss 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 x(z) = m½ z3/3 => Quark Matter 2009

  41. HQ Rest Frame Shock Rest Frame Shocking Drag Mq L vsh Mq vq = -vsh 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

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