Richard Seto University of California, Riverside 2010 APS April Meeting Thurgood Marshall East Feb 13, 2010 *aka AdS5/CFT experimentalist 10:45 am 1

 Some thoughts about what we are looking for  Introduction to heavy ions and RHIC  Several Topics ◦ Elliptic flow   /s ◦ Jet (quark) energy loss ◦ Heavy quark diff coefficient ◦ τ 0 (thermalization time) and T init ◦ Mention others  Summarize (Scorecard) and conclude 2

Phase Transition: T c = 170 ± 15% MeV  ~ 0.6 GeV/fm 3 T TcTc 3

Collide Au + Au ions for maximum volume  s = 200 GeV/nucleon pair, p+p and d+A to compare BNL-RHIC Facility STAR Soon to Come – the LHC 4

 Old paradigm ◦ RHIC – “weakly” interacting gas- Quark gluon plasma  Everything “easy” to calculate using pQCD and stat mech.  What we found ◦ Strongly interacting fluid- the sQGP Strong elliptic flow Jet quenching Everything “hard” to calculate Naïve expectations 5

 Right Theory  Wrong approx αS αS pQCD Weak coupling limit Strong coupling limit Gauge String duality aka AdS5/CFT sQGP  Wrong Theory  “Right” approx  But we Model ~ala condensed matter  Capture essential features Gauge –String Duality 6

 Problems:  conformal theory (no running coupling) ◦ BUT! ◦ RHIC in a region T>Tc where α s is ~constant (T is only scale)  What about the coupling size? ◦ expansion on the strong coupling side is in 1/ λ  RHIC α S ~ ½  1/λ ~ 1/20 λ=4  N colors α s (N C =3~LARGE!)  What about all those extra super-symmetric particles, the fact that there are no quarks… ◦ Find universal features ◦ Pick parameters insensitive to differences ◦ Make modifications to the simplest theory (  =4) to make it look more like QCD  Ultimately find a dual to QCD 7

RHIC data field theory e.g.  =4 Supersymmetry a “model” Parameters Fits to data Hydro/QCD based model Compare And learn Gravity String Theory QCD Gauge- String Duality aka AdS5/CFT 8 More modeling rescaling

transverse momentum p t time Relativistic Heavy Ion Collisions Lorenz contracted pancakes Pre-equilibrium <  ~1fm/c ?? QGP and hydrodynamic expansion  ~ few fm/c ?? Stages of the Collision Tc ~ 190 MeV T time T init =? Pure sQGP τ0τ0 9

dn/d  ~ v 2 (p T ) cos (2  ) +... Initial spatial anisotropy converted into momentum anisotropy. Efficiency of conversion depends on the properties of the medium. x y z  Coordinate space: initial asymmetry pressure pypy pxpx Momentum space: final asymmetry 10

Hydrodynamic Equations Energy-momentum conservation Charge conservations (baryon, strangeness, etc…) For perfect fluids (neglecting viscosity!), Energy densityPressure4-velocity Within ideal hydrodynamics, pressure gradient dP/dx is the driving force of collective flow. 11

 If system free streams ◦ spatial anisotropy is lost ◦ v 2 is not developed PHENIX Huovinen et al detailed hydro calculations (QGP+mixed+RG, zero viscosity)  0 ~ fm/c  ~15-25GeV/fm 3 (ref: cold matter 0.16 GeV/fm 3 ) 12

Strongly Coupled fluids have small viscosity! 13

Anisotropic Flow l Conversion of spatial anisotropy to momentum anisotropy depends on viscosity l Same phenomena observed in gases of strongly interacting atoms (Li6) weakly coupled finite viscosity strongly coupled viscosity=0 The RHIC fluid behaves like this, that is, viscocity~0 M. Gehm, et al Science (2002) 14

the low-brow sheer force(stress) is: energy momentum stress tensor 15

σ(0)=area of horizon “The key observation… is that the right hand side of the Kubo formula is known to be proportional to the classical absorption cross section of gravitons by black three-branes.” dual Gravity  =4 SYM “QCD”strongcoupling Policastro, Son, Starinets hep-th  =4 Supersymmetry Gravity 16

Entropy black hole “branes”  Entropy  =4 SYM “QCD” Entropy black hole Bekenstetein, Hawking = Area of black hole horizon Kovtun, Son, Starinets hep-th =σ(0) k=8.6 E -5 eV/K This is believed to be a universal lower bound for a wide class of Gauge theories with a gravity dual 17

 Data from STAR ◦ Note – “non-flow contribution subtraction (resonances, jets…)  Use Relativistic- Viscous hydrodynamics  Fit data to extract  ◦ Will depend on initial conditions Task was completed recently by Paul Romatschke after non-flow Subtraction was done on the data STAR “non-flow” subtracted data 18

 Best fit is to  /s ~0.08 = 1/4  ◦ With glauber initial conditions  Using CGC (saturated gluon) initial conditions  /s ~0.16  Note: Demir and Bass ◦ hadronic stages of the collision do not change the fact that the origin of the low viscosity matter is in the partonic phase (arXiv: ) STAR “non-flow” subtracted 19 Phys.Rev.C78: (2008)

lowest viscosity possible? helium water nitrogen viscosity bound? 20

 See “A Viscosity Bound Conjecture”, P. Kovtun, D.T. Son, A.O. Starinets, hep- th/ P. KovtunD.T. SonA.O. Starinetshep- th/ ◦ THE SHEAR VISCOSITY OF STRONGLY COUPLED N=4 SUPERSYMMETRIC YANG-MILLS PLASMA., G. Policastro, D.T. Son, A.O. Starinets, Phys.Rev.Lett.87:081601,2001 hep-th/ THE SHEAR VISCOSITY OF STRONGLY COUPLED N=4 SUPERSYMMETRIC YANG-MILLS PLASMA., G. Policastro, D.T. Son, A.O. Starinets, Phys.Rev.Lett.87:081601,2001 hep-th/ lowest viscosity possible? helium water nitrogen viscosity bound? Meyer Lattice:  /s = (33)  RHIC arXiv:

22

“ Spectators” “Participants” Impact Parameter  Hard interactions ~ N collisions Use a Glauber model Centrality def’n head on – central glancing - peripheral Participant Binary Collisions 23

direct photons scale as N coll    suppressed by 5! AuAu 200 GeV R AA Direct γ π0π0 η 0.2 Direct γ 00 24

  =4 SYM- no running of coupling  no hard probes (a quark would not form a jet- just a soft glow of gluons)  Various schemes ◦ Introduce heavy quark ◦ Start with jet as an initial state ◦ Formulate the problem in pQCD  Non perturbative coupling to medium is embodied in one constant ( /length)   =4 SYM  (Liu, Rajagopal, Wiedemann)  QCD – hard probes (jets)  Assumption - Quark energy loss by radiation of gluons 25

  =4 SYM- no running of coupling  no hard probes (a quark would not form a jet- just a soft glow of gluons)  Various schemes ◦ Introduce heavy quark ◦ Start with jet as an initial state ◦ Formulate the problem is pQCD  Non perturbative coupling to medium is embodied in one constant ( /length)   =4 SYM  (Liu, Rajagopal, Wiedemann) Formulate in terms of Wilson loop and calculate In N=4 SYM using Ads/CFT 26 hep-ph/

 solution was for static medium at temperature T  But the temperature is falling at RHIC as a function of time. Tq 0.3 GeV4.5 GeV 2 /fm 0.4 GeV GeV20.7 t T 27

 Use PQM model (parton quenching model) ◦ Realistic model of energy loss (BDMPS) ◦ Realistic geometry 28 arXiv:

throw a pebble in the stream see if it moves m u ~3 MeV m d ~5 MeV m s ~100 MeV m c ~1,300 MeV m b ~4,700 MeV Λ QCD ~200 MeV 29

PRL 98, (2007) high p T non-photonic e ± suppression increases with centrality similar to light hadron suppression at high p T non-photonic e ± Flow  charm suppressed and thermalizes Can we describe this in the context of the sQGP? 30

 Make modification to  =4 ◦ Add heavy quark (adding a D7 Brane )  Drag a heavy quark at a constant velocity and see how much force is needed – calculate a drag coefficient  M μ =f/v D=T/ μM  Rescale to QCD ◦ Herzog: Gubser: alternate set of parameters ( λ=5.5, 3 ¼ T SYM =T QCD )  D HQ (AdS)=0.6/T 31 hep-th/ , hep-th/

 Rapp and vanHees  model has “non- pertubative” features ◦ resonant scattering  fits flow and R AA  D HQ =4-6/2  T = /T PRL 98, (2007) Cf D(AdS)=0.6/T 32

33

 Equilibration time ( τ 0 ) from AdS model Rapidly expanding Spherical plasma Ball Black hole in AdS5 τ e-fold =1/8.6T max dual Perturb it Study rate of equilibration to hydrodynamical description ~ hydro-like modes ~non hydro-like Find rate of decay Of non hydo-like modes τ 0 (AdS)= 4 τ e-fold 34 arXiv:hep-th/

 Make a measure of low p T photons (black body radiation) Use a model of time dependence and fit data t T 35 pQCD See special symposium

 Models follow same trend depend on τ 0 5 e-fold 4 e-fold 3 e-fold 36

Liu, Rajagopal, Wiedermann “Hot Wind” + Hydro 37

STAR ΔϕΔϕ 38

SCORECARD quantityunitsTheoryExper iment datamethodCollabcomment s/s SB [1]0.77~0.8 Lattice1 st order correction  /s [2]0.1~0.08Charge d flow Viscous hydro[9] STARUniversal? 1 st order [3] GeV 2 /fm R_AA (pion) Fit to PQM [10] PHENIXAverage over time D HQ (τ HQ GeV [4] 0.6/T /T HQ decay e- Fit to[11] Rapp, vanHees PHENIXRescaled theory T(τ 0 =3fm) [5] GeV0.300 (4-efold) 0.380Fit to[12] models PHENIX τ 0 [6] fm Fit to flow [13] STAR/ PHENIX Init cond needed J/ ψ [7] stronger suppression pt>5Some inconsistency between experiments wait for more data [14] Mach cones, [8] diffusion wakes existsSomething is thereNeed more studies [15] 39

 There are complications and assumptions that I skipped over e.g. ◦ for Hydro  need to use Israel-Stewart as not to violate causality  need EOS (from lattice – at the moment various ones are used for the fits) ◦ The electrons from experiment are actually ~½ B mesons at high p T. For the AdS side we (I) typically assumed m=1.4  And the list goes on 40

 The Gauge-String Duality (AdS/CFT) is a powerful new tool  The various theoretical together are giving us a deeper understanding of the sQGP ◦ Can work hand in hand to with the experimentalists  pQCD, Gauge String Dualities, Lattice, Viscous Hydrodynamics, Cascade simulations, … ◦ Bring different strengths and weakness ◦ ALL are needed and must work together 41

 [1]hep-th/  [2]hep-th  [3]hep-ph/  [4]hep-th/ , hep-th/  [5]arXiv:hep-th/  [6]arXiv:  [7]hep-ph/  [8]arXiv:  [9]Phys.Rev.C78: (2008)  [10]arXiv:  [11]Phys. Rev. Lett. 98, (2007)  [12]arXiv:  [13]nucl-th/  [14]Phys. Rev. C 80 (2009)  [15]arXiv:

1 st order correction 20% 1 st order correction 3% 43

R2R2 2c  PHENIX: Central Au-Au yields Energy density far above transition value predicted by lattice. R~7fm Lattice: T C ~190 MeV (  C ~ 1 GeV/fm 3 ) Phase transition- fast cross over to experimentalist: 1 st order 44