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Theoretical Thoughts on Energy Loss at RHIC and LHC. William Horowitz The Ohio State University May 21, 2009. With many thanks to Brian Cole, Yuri Kovchegov, and Ulrich Heinz. Outline. Introduction pQCD AdS/CFT Conclusions. Introduction. p T. f. Heavy ion jet physics.

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## Theoretical Thoughts on Energy Loss at RHIC and LHC

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**Theoretical Thoughts on Energy Loss at RHIC and LHC**William Horowitz The Ohio State University May 21, 2009 With many thanks to Brian Cole, Yuri Kovchegov, and Ulrich Heinz Energy Loss at RHIC and LHC**Outline**• Introduction • pQCD • AdS/CFT • Conclusions Energy Loss at RHIC and LHC**Introduction**pT f Heavy ion jet physics Heavy ion collision Energy Loss at RHIC and LHC**Why High-pT Jets?**• Compare unmodified p+p collisions to A+A: • Use suppression pattern to either: • Learn about medium (requires detailed understanding of energy loss): jet tomography • Learn about energy loss pT pT 2D Transverse direction Longitudinal (beam pipe) direction Figures from http://www.star.bnl.gov/central/focus/highPt/ Energy Loss at RHIC and LHC**High-pT Observables**pT f Naïvely: if medium has no effect, then RAA = 1 Common variables used are transverse momentum, pT, and angle with respect to the reaction plane, f Fourier expand RAA: Energy Loss at RHIC and LHC**Part I: pQCD Eloss**Energy Loss at RHIC and LHC**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 Energy Loss at RHIC and LHC**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) Energy Loss at RHIC and LHC**Multiple Models**• Inconsistent medium properties • Distinguish between models Bass et al., Phys.Rev.C79:024901,2009 WHDG, Nucl.Phys.A784:426-442,2007 Bass et al. Energy Loss at RHIC and LHC**Vary input param.**Find “best” value Quantitative Parameter Extraction Need for theoretical error PHENIX, PRC77:064907,2008 Energy Loss at RHIC and LHC**Comparing Models**• Difficult at RAA • Many assumptions • Prod. spectra, FF, geometry, etc. • Focus on “Brick” • Fixed L, T, Ejet • Compare WHDG Rad to ASW-SH • WHDG Rad: DGLV opacity expansion • GLV + massive quarks, gluons • ASW-SH: opacity expansion Energy Loss at RHIC and LHC**Why WHDG Rad vs. ASW-SH?**• Examine ASW-SH = GLV claim • Warm-up for WHDG Rad vs. ASW-MS Energy Loss at RHIC and LHC**Main Results**• Implemented formulae very different • But, massless DGLV integrand same form (Modulo detail of scattering center distribution) • But, var. have very diff. physical meaning (!) • Strong cutoff dependence (!) • Massive gluon effect (!) • Pun intended Energy Loss at RHIC and LHC**Compared Quantities**• dNg/dx • Single inclusive radiated gluon spectrum • P(e) • Poisson convolution • Model multiple emission • Additional assumptions • Convolve dNg/dx to find P(e) • Ef = (1 – e)Ei • pdf Energy Loss at RHIC and LHC**Conclusions**• ASW-SH code no good for RAA • To be fair, hasn’t been used • RAA cutoff dep. likely => large th. err. • Must be overcome for tomography • Strong as dependence, too • Large gluon mass effect • Higher order diagrams likely important • Not to be confused with higher orders of opacity Energy Loss at RHIC and LHC**Part II: AdS/CFT**Energy Loss at RHIC and 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 Energy Loss at RHIC and LHC**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 Energy Loss at RHIC and LHC**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 Energy Loss at RHIC and LHC**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) Energy Loss at RHIC and LHC**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) Energy Loss at RHIC and LHC**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 Energy Loss at RHIC and LHC**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 Energy Loss at RHIC and 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) Energy Loss at RHIC and LHC**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 Energy Loss at RHIC and LHC**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. Energy Loss at RHIC and LHC**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 => Energy Loss at RHIC and LHC**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: Energy Loss at RHIC and LHC**Putting It All 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 Energy Loss at RHIC and LHC**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 Energy Loss at RHIC and LHC**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 Energy Loss at RHIC and LHC

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