Strongly interacting quantum fluids: Experimental status

Transcription

1 Strongly interacting quantum fluids: Experimental status Thomas Schaefer North Carolina State University

2 Perfect fluids: The contenders QGP (T=180 MeV) Liquid Helium (T=0.1 mev) Trapped Atoms (T=0.1 nev)

3 I. Experiment (liquid helium) η [µp] T [K] Kapitza (1938) viscosity vanishes below T c capillary flow viscometer Hollis-Hallett (1955) roton minimum, phonon rise rotation viscometer η/s 0.8 /k B

4 II. Heavy ion collision: Geometry R Au /γ y R Au x b z rapidity : y = 1 2 log ( E + pz E p z ) transverse momentum : p 2 T = p 2 x + p 2 y

5 Bjorken expansion Experimental observation: At high energy ( y ) rapidity distributions of produced particles (in both pp and AA) are flat dn dy const Physics depends on proper time τ = t 2 z 2, not on y All comoving (v = z/t) observers are equivalent Analogous to Hubble expansion

6 Bjorken expansion τ =const t η =const hadrons QGP pre equilibrium projectile target z

7 Bjorken expansion: Hydrodynamics Boost invariant expansion u µ = γ(1,0,0, v z ) = (t/τ, 0,0, z/τ) solves Euler equation (no longitudinal acceleration) µ (su µ ) = 0 Solution for ideal Bj hydrodynamics s(τ) = s 0τ 0 τ d dτ [τs(τ)] = 0 T = const τ 1/3 Exact boost invariance, no transverse expansion, no dissipation,...

8 Numerical estimates Total entropy in rapidity interval [y, y + y] S = sπr 2 z = sπr 2 τ y = (s 0 τ 0 )πr 2 y R Use S/N 3.6 s 0 τ 0 = 1 πr 2 S y z = τ y s 0 = ǫ 0 = 3.6 ( dn ) πr 2 τ 0 dy 1 ( det ) πr 2 τ 0 dy Bj estimate Depends on initial time τ 0

9 BNL and RHIC

10 Multiplicities 400 Au+Au 19.6 GeV 600 Au+Au 130 GeV dn ch /dη dn ch /dη η η % 6-15% Au+Au 200 GeV 25-35% 35-45% dn ch /dη % 45-55% η Phobos White Paper (2005)

11 Bjorken expansion

12 Chemical equilibrium at freezeout Ratio 1 s NN =130 GeV T (MeV) crossover quark gluon plasma end point π - π + Data Model T=165.5, µ b =38 MeV - K K + p p Λ Λ Ξ Ξ Ω Ω K + π + - K π - p π - Λ π - Ξ π - Ω π - φ K - * K K NA49 SIS, AGS RHIC hadrons µ B (MeV) Andronic et al. (2006)

13 Collective behavior: Radial flow Radial expansion leads to blue-shifted spectra in Au+Au Au+Au p+p 1/(2π) d 2 N / (m T dm T dy) [c 4 /GeV 2 ] STAR preliminary Au+Au central s NN = 200 GeV K - π - 1/(2π) d 2 N / (m T dm T dy) [c 4 /GeV 2 ] K - STAR preliminary p+p min. bias s NN = 200 GeV π - p 10-2 p m T - m 0 [GeV/c 2 ] m T - m 0 [GeV/c 2 ] v T 0.6c! m T = p 2 T + m2

14 Collective behavior: Elliptic flow Hydrodynamic expansion converts coordinate space anisotropy to momentum space anisotropy Anisotropy Parameter v Hydro model π K p Λ PHENIX Data π + +π K +K p+p STAR Data 0 K S Λ+Λ b Transverse Momentum p T source: U. Heinz (2005) dn p 0 d 3 p = v 0 (p ) (1 + 2v 2 (p ) cos(2φ) +...) pz =0 (GeV/c)

15 Elliptic flow II: Multiplicity scaling v 2 /ε 0.25 HYDRO limits E lab /A=11.8 GeV, E877 E lab /A=40 GeV, NA E lab /A=158 GeV, NA49 s NN =130 GeV, STAR s NN =200 GeV, STAR Prelim (1/S) dn ch /dy source: U. Heinz (2005)

16 Viscous Corrections Longitudinal expansion: Bj expansion solves Navier-Stokes equation ( 4 entropy equation 1 ds s dτ = η + ζ ) τ stτ Viscous corrections small if 4 3 η s + ζ s (Tτ) early Tτ τ 2/3 η/s const η/s < τ 0 T 0 late Tτ const η T/σ τ 2 /σ < 1 Hydro valid for τ [τ 0, τ fr ]

17 Viscous corrections to T ij (radial expansion) T zz = P 4 3 η τ T xx = T yy = P increases radial flow (central collision) decreases elliptic flow (peripheral collision) Modification of distribution function δf = 3 8 Correction to spectrum grows with p 2 Γ s T 2 f 0(1 + f 0 )p α p β α u β η τ δ(dn) dn 0 = Γ s 4τ f ( p T ) 2

18 Elliptic flow III: Viscous effects v 2 (percent) ideal η/s=0.03 η/s=0.08 η/s=0.16 STAR p T [GeV] Romatschke (2007), Teaney (2003)

19 Elliptic flow IV: Systematic trends Deviation from ideal hydro increases for more peripheral events increases with p source: R. Snellings (STAR)

20 Elliptic flow V: Predictions for LHC e p /e x ( v 2 /e x ) η/s = 10-4 η/s = 0.08 η/s = 0.16 RHIC Glauber RHIC CGC LHC Glauber LHC CGC PHOBOS/CGC PHOBOS/Glauber (1/S overlap )(dn ch /dy)[fm -2 ] Romatschke, Luzum (2009) Busza (QM 2009)

21 Elliptic flow VI: Recombination quark number scaling of elliptic flow Anisotropy Parameter v Hydro model π K p Λ PHENIX Data STAR Data π + +π h +h + - K +K K 0 S p+ p Λ+ Λ Transverse Momentum p T (GeV/c) v 2 /n Polynomial Fit π + +π - 0 K S p+ p Λ+Λ STAR Preliminary + - K +K Ξ+Ξ (qq) (mes) p mes = 2pqu Data/Fit (qqq) (bar) p bar = 3pqu p T /n (GeV/c)

22 Jet quenching R AA = n AA N coll n pp source: Akiba [Phenix] (2006)

23 Jet quenching II Disappearance of away-side jet φ) dn/d( φ) dn/d( 1/N 1/NTRIGGER Trigger d+au FTPC-Au 0-20% p+p min. bias Au+Au Central φ (radians) source: Star White Paper (2005)

24 Jet quenching III: The Mach cone azimuthal multiplicity dn/dφ (high energy trigger particle at φ = 0) wake of a fast quark in N = 4 plasma Chesler and Yaffe (2007) source: Phenix (PRL, 2006), W. Zajc (2007)

25 Jet quenching: Theory 10.0 energy loss governed by RHIC data ˆq = ρ q 2 dq 2 dσ dq 2 q (GeV 2 /fm) pion gas QGP (GeV/fm 3 ) 0.1 cold nuclear matter larger than pqcd predicts? relation to η? (ˆq 1/η?) also: large energy loss of heavy quarks source: R. Baier (2004)

26 Where are we? observe almost ideal fluid behavior, initial conditions well above critical energy density. systematics require 0 < η/s < 0.4; more studies needed, LHC elliptic flow will be very interesting. jet quenching large; very detailed studies under way. LHC will provide unprecedented range. heavy flavors: large energy loss seen, flavor studies (c/b) under way.

27 III. Experiment: Cold gases transverse expansion expansion (rotating trap) collective modes n t + (n v) = 0 mn v ( t + mn v ) v = P n V

28 Scaling flows Universal equation of state P = n5/3 m f ( mt n 2/3 ) Equilibrium density profile (local density approximation) ( n 0 (x) = n(µ(x), T) µ(x) = µ 0 1 x2 Rx 2 y2 Ry 2 z2 R 2 z ) Scaling Flow: Stretch and rotate profile µ 0 µ 0 (t), T T 0 (µ 0 (t)/µ 0 ), R x R x (t),... Linear velocity profile v(x, t) = 1 2 ( α x x 2 + α y y 2 + α z z 2 + αxy ) + ωẑ x. Hubble flow

29 Almost ideal fluid dynamics Hydrodynamic expansion converts σ σ µ coordinate space anisotropy σ σ to momentum space anisotropy O Hara et al. (2002)

30 Almost ideal fluid dynamics Radial breathing mode Ideal fluid hydrodynamics (P n 5/3 ) n t + (n v) = 0 v ( t + v ) P v = mn V m Frequency (ω/ω ) B (Gauss) Hydro frequency at unitarity 10 ω = 3 ω experiment: Kinast et al. (2005) /k F a

31 Dissipation (scaling flows) Energy dissipation (η, ζ, κ: shear, bulk viscosity, heat conductivity) Ė = 1 d 3 x η(x) ( i v j + j v i 23 ) 2 2 δ ij k v k d 3 x ζ(x) ( i v i ) 2 1 d 3 x κ(x) ( i T) 2 T Have ζ = 0 and T(x) = const. Universality implies ( ) T η(x) = s(x) α s µ(x) d 3 x η(x) = S α s

32 Collective modes: Small viscous correction exponentiates a(t) = a 0 cos(ωt) exp( Γ t) ( ) ( Γ η/s = (3Nλ) 1/3 E0 ω E F ) ( N S ) 1.5 η/s T/T F Kinast et al. (2006), Schaefer (2007)

33 Navier-Stokes equation Option 1: Moment method d 3 x x k (ρ v i +...) = d 3 x x k ( i P j δπ ij ) Only involves η /E 0. Option 2: Scaling ansatz for η(µ, T) Option 3: Numerical solutions. η(n, T) = η 0 (mt) 3/2 + η 1 P(n, T) T

34 Dissipation R i [µm] R 80 θ [ ] E/E F = 0.56 E/E F = R z t[ms] t [ms] R θ R R z O Hara et al (2002), Kinast et al (2005), Clancy et al (2007)

35 Dissipation R i [µm] R 80 θ [ ] E/E F = 0.56 E/E F = R z t[ms] t [ms] (δt 0 )/t 0 (δa)/a = ( ) ( ) αs /3 ( S/N 1/(4π) N 2.3 ) ( 0.85 E 0 /E F ) t 0 : Crossing time (b = b z, θ = 45 ) a: amplitude

36 Time Scales t acc t diss t fr t cross R i [µm] 300 R R z t[ms]

37 Where are we? high temperature (T > 2.5T c ) dominated by corona low temperature (T T c ): evidence for low viscosity (η/s < 0.4) core also seen in irrotational flow data full (2nd order hydro or hydro+kin) analysis needed

38 The bottom-line Remarkably, the best fluids that have been observed are the coldest and the hottest fluid ever created in the laboratory, cold atomic gases (10 6 K) and the quark gluon plasma (10 12 K ) at RHIC. Both of these fluids come close to a bound on the shear viscosity that was first proposed based on calculations in string theory, involving nonequilibrium evolution of back holes in 5 (and more) dimensions.