Viscosity of Quark-Gluon Plasma!

Transcription

1 Viscosity of Quark-Gluon Plasma! Rajendra Pokharel Advisor: Prof. Sean Gavin 2 nd Graduate Research Day " Wayne State University " "Apr 24, 2011!

2 Outlines " " Background Hydrodynamics The Model Results

3 Background " " "What is QGP?! " What is quark- gluon plasma (QGP)? This is how RHIC has defined QGP: (RHIC White Paper, 2005)

4 Background" " Quarks and Gluons! " MaQer is made up of quarks, leptons and gluons the force carrier bosons (and their ansparscles). Quarks and gluons have an extra degree of freedom color. 3 types of color charge: red, green and blue (ans- colors too!) Color Confinement α s Asympto1c freedom Energy scale V)

5 Background " " " Where to get QGP? " In order to get free quarks and gluons, we need to extreme compression and heat the nucleons. Where to find? Early universe (< 10-4 s) Heavy Ion Colliders: RHIC, LHC Deep inside neutron stars?

6 Background " " " " Early Universe"

7 Background " " " QCD Phase Diagram "

8 Background " " " Heavy Ion Collision " RHIC Au-Au at snn = 200 GeV LHC Pb-Pb at snn = 5.4TeV

9 Background " " " Did RHIC create QGP? " Experiments point to YES! QGP created at RHIC behaves like a liquid rather than a gas, as was expected (large ellipsc flow) QGP appears to be the most perfect fluid ever known (calculason based on ideal hydrodynamics fit the data, for p t < 2GeV)

10 Background" "How perfect is this perfect fluid? " Measure of how perfect (ideal) is given in terms of, η/s. It appears that QGP is the most perfect fluid we have known. TheoreScal bound? AdS/CFT and also uncertainty principle - > η/s =1/4π (k B = = c = 1)

11 Hydrodynamics Success of ideal hydrodynamic simulasons lead to go step further. How perfect fluid is QGP? A detailed dissipasve hydrodynamics should give the answer.

12 Hydrodynamics " "Ideal hydrodynamic equations First, applicability of hydrodynamics: T 200MeV n π 4fm 3 λ =1/σn 0.08fm (Huovinen, nucl- th/ ) This is much less than the size of gold nucleus ~ 7 fm. Basically, Hydrodynamics model = conservason of energy- momentum + equason of state. conservason of energy- momentum: µ T µν =0 Ideal (perfect fluid): T µν = u µ u ν p µν µν = g µν u µ u ν EquaSons of ideal hydrodynamics: D +( + p) µ u µ =0 ( + p)du λ λ p =0 D = u µ µ λ = λµ µ

13 Hydrodynamics "Viscous hydrodynamic equations "! T µν = u µ u ν p µν + Π µν ideal part dissipasve part T zx =! "v x "z Viscous hydrodynamic equasons: D +( + p) µ u µ Π µν (µ u ν) =0 ( + p)du λ λ p + λ ν µ Π µν =0 (µ u ν) = 1 2 ( µu ν + ν u µ ) Π µν = π µν + Π µν shear bulk (traceless) 1 st order (relasvissc Navier- Stoke): π µν =2η( (µ u ν) 1 3 µν α u α ) Π = ζ α u α 2 nd order (Israel- Stewart): π αβ = η <α u β> π αβ TD( β 2 T ) 2β 2Dπ αβ β 2 π αβ µ u µ Π = ζ 2 α u α β0 ΠTD β 0 Π µ u µ 2β 0 DΠ T β 2 = τ π 2η β 0 = τ Π 2ζ

14 Hydrodynamics "Diffusion of flow perturbation "! Linearize Navier- Stoke EquaSons ( + p)du y y p + y ν µ Π µν =0 Π zy = η( y u z + z u y )+(ζ 2 = 0 + δ(t, z),p= p 0 + δp(t, z),u µ =(1,0) + δu µ 3 η) zy α u α (t, z) One obtains: ( 0 + p 0 ) t δu y + z δπ zy =0 δπ zy = η 0 z δu y t δuy = ν 2 z 2 δuy ν = η 0 /( + p) Well known diffusion equa2on! But diffusion equason violates causality and not suitable for relasvissc fluid elements! SoluSon? Causal diffusion equason or second order diffusion equason. Follows from Israel the hydrodynamic equason and Israel- Stewart reln. τ π 2 δu y t 2 + t δuy = ν 2 z 2 δuy The relaxason Sme saves the causality.

15 Hydrodynamics "Fluctuation in transverse momentum current "! g t = δt 0y ( 0 + p 0 )δu y The causal diffusion equason becomes τ π 2 δt 0y t 2 + δt 0y t = ν 2 δt 0y Momentum current diffuses in collision volume. Viscosity informason is in the diffusion coefficient. Two- parscle momentum current correlason funcson r = T 0y 1 T 0y 2 0y 0y T1 T2 The last two relasons give τ π 2 r t 2 + r t = ν( ) r r = r r eql

16 The Model" " "Equations and Assumptions "! We assume Brorken boost invariance. Bjorken flow: u µ = x µ /τ =(t/τ, 0, 0,z/τ) Diffusion of correlason: τ" 2 r π τ 2 " + r τ Use kinesc theory: τ π = β η Ts, β =5 = ν( 2 η η2 2 ) r ν = η/( 0 + p 0 )=η/t s [e.g., Guy D. Moore et al. [hep- ph] ] For entropy, we use energy (hydro) equason with Bjorken flow and thermodynamics ( + p = Ts, Tds = d ) with the results: s τ + s τ = Φ T τ Perfect fluid: 1 st order viscous: 2 nd order viscous: Φ =0 Φ = 4 3 η τ Φ τ = Φ τ π Φ 2 1 τ + T β 2 τ β2 T + 2 3β 2 τ

17 The Model " Assumptions and main equations (contd ) "! Note 1: apidity of a parscle: spacesme rapidity: y = tanh 1 v z = tanh 1 (p z /E) = 1 2 lne + p z E p z η = 1 2 ln t + z t z We use mixed phase as s = fs Q +(1 f)s H For viscosity we use temperature dependent profile auer Hirano and Gyulassy. Minumum is corresponding to the KSS bound. Fixed freezeout temperature is assumed. Hirano & Gyulassy nucl-th/

18 The Model " "Parameters and initial conditions "! IniSal proper Sme: Fixed freezeout temperature: τ 0 =1fm T f = 150 MeV The equasons are then numerically solved. The solusons are then used to calculate the width of the distribuson, which is assumed to be Gaussian inisally. The width are then matched with recent STAR data. (Sharma, Pruneau, 2010)

19 Results" " "First order diffusion, first order entropy "! First order diffusion first order entropy STAR preliminary Sharma, Pruneau

20 Results" " Second order diffusion, second order entropy "! First order diffusion first order entropy

21 Summary " Viscosity diffuses fluctuason in transverse flow. This leads to diffusion of transverse momentum two- correlason funcson, above the background noise. First order diffusion model violates causality and not suitable for fluid of relasvissc parscles. Remedy is the second order diffusion, which follows from Israel- Stewart theory. It gives some relaxason Sme and preserves causality. Diffusion leads to widening of the width. Second order diffusion and second order entropy flux equasons gives the widening that fit much beqer with STAR data.

22 Thank You! Graduate Research Day 2011 " Wayne State University " "Apr 24, 2011!

23 Backups ) + 3 +! " T C * + +, # $ % T T C & ' ( 3 T T C,T < T C # 1 + wln T & $ % T C ' ( 2,T > T C Hirano & Gyulassy nucl-th/ v2

24 Backups