Understanding Strongly Interacting Fluids in Relativistic Heavy Ion Collisions at RHIC

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

2.  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 ◦ τ0 (thermalization time) and Tinit ◦ Mention others  Summarize (Scorecard) and conclude ˆ q 2

3. T Tc Phase Transition: Tc= 170  15% MeV e e ~ 0.6 GeV/fm3 3

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

5.  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 Jet quenching Naïve expectations Everything “hard” to calculate Strong elliptic flow 5

6. Gauge –String Duality  Wrong Theory  “Right” approx  Right Theory  Wrong approx  But we Model ~ala condensed matter  Capture essential features sQGP Gauge String duality aka AdS5/CFT pQCD t Hooft   Strong coupling limit ' αS 4 N Weak coupling limit colors 6

7. e e  Problems:  conformal theory (no running coupling) ◦ BUT! ◦ RHIC in a region T>Tc where αsis ~constant (T is only scale)  What about the coupling size? ◦ expansion on the strong coupling side is in 1/λ  RHIC αS~ ½  1/λ ~ 1/20 λ=4Ncolorsαs (NC=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 ~ 0.8 SB 7

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

9. Stages of the Collision transverse momentum pt time T Pure sQGP Pure sQGP  Relativistic Heavy Ion Collisions  Lorenz contracted pancakes  Pre-equilibrium < ~1fm/c ??  QGP and hydrodynamic expansion ~ few fm/c ?? Tinit=? Tc ~ 190 MeV time τ0 9

10.   2 2 p p p p x y      cos2 py v 2 2 2 x y pressure  z y x Coordinate space: initial asymmetry Momentum space: final asymmetry dn/d ~ 1 + 2 v2(pT) cos (2 ) + ... Initial spatial anisotropy converted into momentum anisotropy. Efficiency of conversion depends on the properties of the medium. 10

11. Hydrodynamic Equations Energy-momentum conservation Charge conservations (baryon, strangeness, etc…) For perfect fluids (neglecting viscosity!), Energy density Pressure 4-velocity Within ideal hydrodynamics, pressure gradient dP/dx is the driving force of collective flow. 11

12.  If system free streams ◦ spatial anisotropy is lost ◦ v2is not developed PHENIX PHENIX Huovinen et al Huovinen et al ( ) e  e 0  detailed hydro calculations (QGP+mixed+RG, zero viscosity)  0~ 0.6 -1.0 fm/c  e~15-25GeV/fm3  (ref: cold matter 0.16 GeV/fm3) max  / fm c 0 12

13. Strongly Coupled fluids have small viscosity! 13

14. 14 Anisotropic Flow Anisotropic Flow  Conversion of spatial anisotropy to momentum Conversion of spatial anisotropy to momentum anisotropy depends on viscosity anisotropy depends on viscosity  Same phenomena observed in gases of strongly Same phenomena observed in gases of strongly interacting atoms (Li6) interacting atoms (Li6) M. Gehm, et al Science 298 2179 (2002) strongly coupled strongly coupled viscosity=0 viscosity=0 weakly coupled weakly coupled finite viscosity finite viscosity The RHIC fluid behaves like this, The RHIC fluid behaves like this, that is, viscocity~0 that is, viscocity~0

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

16. =4 SYM “QCD” strong coupling Gravity dual   8 G  Policastro, Son, Starinets hep-th 0104066 =4 Supersymmetry Gravity “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.” σ(0)=area of horizon 16

17. Entropy =4 SYM “QCD” Entropy   black hole “branes” Entropy black hole Bekenstetein, Hawking = Area of black hole horizon   =σ(0) black holearea 4G   6 10   13 SYM " s Ks " QCD  4 s k B This is believed to be a universal lower bound for a wide class of Gauge theories with a gravity dual k=8.6 E -5 eV/K Kovtun, Son, Starinets hep-th 0405231 17

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

19. STAR “non-flow” subtracted  Best fit is to /s ~0.08 = 1/4 ◦ With glauber initial conditions  Using CGC (saturated gluon) initial conditions /s ~0.16 Phys.Rev.C78:034915 (2008)  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:0812.22422) 19

20.  4 s       cos Vis ity   4 Entropy Density k B RHIC lowest viscosity possible? helium viscosity bound? nitrogen water 20

21.  4 s       cos Vis ity   4 Entropy Density k B RHIC lowest viscosity possible? helium Meyer Lattice: /s = 0.134 (33) viscosity bound?  See “A Viscosity Bound Conjecture”, P. Kovtun, D.T. Son, A.O. Starinets, hep- th/0405231 arXiv:0704.1801 nitrogen water RHIC   ◦ 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/0104066 21

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23. Hard interactions ~ Ncollisions “Spectators” Use a Glauber model Centrality def’n Centrality def’n head on head on – – central glancing glancing - - peripheral central peripheral “Participants” “Spectators” AuAu yield N pp yield N Binary Collisions  AuAu coll 1000 N AuAu coll  R AA  pp coll 1 N pp coll Participant 23

24. AuAu 200 GeV direct photons scale as Ncoll 0suppressed by 5! Direct γ Direct γ 0 0.2 π0 η RAA 24

25.  QCD – hard probes (jets)  Assumption - Quark energy loss by radiation of gluons ˆ q  0 =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 (<pT2>/length) ˆ q  ˆ q =4 SYM (Liu, Rajagopal, Wiedemann)  25

26. Formulate in terms of Wilson loop and calculate In N=4 SYM using Ads/CFT ˆ q  0             3 4  3/2   3 ˆ q T SYM 5 4 =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 (<pT2>/length) ˆ q  ˆ q =4 SYM (Liu, Rajagopal, Wiedemann) hep-ph/0605178  26

27.  solution was for static medium at temperature T T T 0.3 GeV 0.4 GeV 0.5 GeV T q q 4.5 GeV2/fm 10.6 20.7 t  But the temperature is falling at RHIC as a function of time.   2 ˆ( q AdS ) 5 15 / GeV fm 27

28.  Use PQM model (parton quenching model) ◦ Realistic model of energy loss (BDMPS) ◦ Realistic geometry ˆ q 5 15   2 ˆ q cf / GeV fm     2.1 3.1  6.3 5.2  ˆ q 13.2 2 arXiv:0801.1665 28

29. m m m m m mu u~3 MeV md d~5 MeV ms s~100 MeV mc c~1,300 MeV mb b~4,700 MeV ~3 MeV ~5 MeV ~100 MeV ~1,300 MeV ~4,700 MeV ΛQCD QCD~200 MeV ~200 MeV throw a pebble in the stream see if it moves 29

30. PRL 98, 172301 (2007)  non-photonic e±Flow charm suppressed and thermalizes  high pTnon-photonic e± suppression increases with centrality  similar to light hadron suppression at high pT Can we describe this in the context of the sQGP? 30

31.  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  Mμ=f/v D=T/μM  Rescale to QCD D D   2 0.15 T   D   T D D D     , 0.5 , 0  19  QCD QCD D , SYM ~ ~ 4 Where s s ◦ Herzog:     , 0 , 0 , 0 QCD SYM SYM s Gubser: alternate set of parameters (λ=5.5, 3¼TSYM=TQCD) DHQ (AdS)=0.6/T  31 hep-th/0605158, hep-th/0605191

32.  Rapp and vanHees  model has “non- pertubative” features ◦ resonant scattering  fits flow and RAA  DHQ =4-6/2T = 0.6-0.9/T Cf D(AdS)=0.6/T PRL 98, 172301 (2007) 32

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34.  Equilibration time (τ0) from AdS Rapidly expanding Spherical plasma Ball Black hole in AdS5 dual model ~ hydro-like modes ~non hydro-like Perturb it Study rate of equilibration to hydrodynamical description Find rate of decay Of non hydo-like modes τe-fold =1/8.6Tmax τ0 (AdS)= 4 τe-fold arXiv:hep-th/0611005 34

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

36. 3 e-fold 4 e-fold 5 e-fold  Models follow same trend depend on τ0 36

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

38. STAR Δϕ 38

39. SCORECARD Exper iment ~0.8 SCORECARD quantity units units Theory Theory data method Collab comment s/sSB [1] 0.77 Lattice 1storder correction Universal? 1storder 0.1 ~0.08 Charge d flow R_AA (pion) HQ decay e- Viscous hydro[9] Fit to PQM [10] Fit to[11] Rapp, vanHees Fit to[12] models Fit to flow [13] STAR /s [2] GeV2 /fm 5-15 13 PHENIX Average ˆ q [3] over time 0.6/T 0.6-0.9 /T PHENIX Rescaled DHQ (τHQ) @T=0.300 GeV [4] theory GeV 0.300 (4-efold) 0.3 0.380 PHENIX T(τ0 =3fm) [5] fm 0.6 STAR/ PHENIX wait for more data [14] Need more studies [15] Init cond needed τ0 [6] stronger suppression pt>5 Some inconsistency between experiments Something is there J/ψ [7] Mach cones, [8] diffusion wakes exists 39

40.  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 pT. For the AdS side we (I) typically assumed m=1.4  And the list goes on 40

41.  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

42.  [1]hep-th/9805156  [2]hep-th 0405231  [3]hep-ph/0605178  [4]hep-th/0605158, hep-th/0605191  [5]arXiv:hep-th/0611005  [6]arXiv:0705.1234  [7]hep-ph/0607062  [8]arXiv:0706.4307  [9]Phys.Rev.C78:034915 (2008)  [10]arXiv:0801.1665  [11]Phys. Rev. Lett. 98, 172301 (2007)  [12]arXiv:0804.4168  [13]nucl-th/0407067  [14]Phys. Rev. C 80 (2009) 41902  [15]arXiv:0805.0622 42

43.  sQGP S  0.5 (0.35)    Supersym 4 ~19 (13) N colors S 1   0.05 (0.08)          1  (3)  1 15   ... 1storder correction 20% 3/2 4 s         3 4 15 8 (3) S    1 ... 1storder correction 3% 3/2 S SB ˆ q 43

44. Energy density far above transition value predicted by lattice.       1 R 1 c  dE dy e  2 T Bj  2 2 R~7fm R2 2c Lattice: TC~190 MeV (eC~ 1 GeV/fm3) Phase transition- fast cross over to experimentalist: 1storder PHENIX: Central Au-Au yields dET  GeV fm   503 GeV 2 e   ~15 @ 0.6 / ( ) fm c thermalization 3 d   0 44