Koichi MuraseA, Tetsufumi HiranoB

The University of TokyoA,Sophia UniversityB

Hydrodynamic fluctuations and dissipation in an integrated

dynamical model 2015/9/29,

QM2015

2015/9/29 1

PartX (1/1)

• Final observables– flow harmonics vn, etc.

• Initial-state fluctuations– nucleon distribution– quantum fluctuations

Fluctuations in heavy-ion collisions

2015/9/29 2

Response ofMatter

EoS, η, ζ, τR, λ, …

0collision axis

time

PartX (1/1)

• Final observables– flow harmonics vn, etc.

• Initial state fluctuation– nucleon distribution– quantum fluctuations

Fluctuations in heavy-ion collisions

2015/9/29 3

Other fluctuations+ hydro fluctuations+ jets/mini-jets+ critical phenomena+ …

0collision axis

time

Relativistic hydrodynamics

( ～ QGP)

PartX (1/1) Hydrodynamic FluctuationsHF ＝ Thermal fluctuations of dissipative currents

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ensemble/eventaveraged

thermal fluctuationsat each spacetime x

e.g.

V: 3+1 dim. volumedecreaseanisotropy

HF is important in e-by-e description of HIC

Balance

Fluctuation-Dissipation RelationFDR

HF

increaseanisotropy

Integrateddynamical model

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PartX (1/1) Integrated Dynamical Model

2015/9/29 6

0collision axis

time

2. (3+1)-dim. Relativistic Fluctuating HydrodynamicsEoS: lattice QCD&HRG, η/s = 1/4π

1. Initial conditionMC-KLN

5. Analysis of hadron distribution

3. Particlization at Tsw = 155 MeV

Cooper-Frye formula: f + δf

4. Hadronic cascades (JAM)

Updated version of T. Hirano, P. Huovinen, KM, Y. Nara, PPNP 70, 108 (2012) [arXiv:1204.5814]

PartX (1/1) Setup: Target

Collision system　 Au+Au, √sNN = 200 GeV

Fluctuations• Initial-state fluctuations from nucleon positions• Hydrodynamic fluctuations

Comparison between the effects of both fluctuations

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Au Au

PartX (1/1) Setup: IS Fluctuations and HF• Initial condition

Centrality: Minimum biasModel: MC-KLN (CGC)

• (3+1)-dim Relativistic Fluctuating Hydrodynamics:

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x-y plane ηs-x plane

Type η/s HF Hydro Cascades

Viscous 1/4π none 100 k events 10 M (100k 100)☓

Fluctuating 1/4π λ = 1.0 (fm) 100 k events 10 M (100k 100☓ )

λ: HF cutoff length scale (Gaussian width)

PartX (1/1)Numerical Simulation: Evolution

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Hydrodynamic evolution

ηs

x [f

m]

ηs

x [f

m]

y [f

m]

y [f

m]

x [fm]

x [fm]

without HF

with HF

conventional2nd-order

viscous hydro

2nd-orderfluctuating hydro

τT ττ

PartX (1/1) vn{EP} vs pT

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EP: η-sub,|η| = 1.0-2.8

0-5%

• HF increase anisotropies• larger effects in a higher order HF V∝ -1/2

PartX (1/1) vn{EP} vs pT

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EP: η-sub,|η| = 1.0-2.8

• Central: 　　 (IS Fluct.) + (HF)• Non-central: (IS Fluct.) + (HF) + (Collision geometry)

20-30%

PartX (1/1) vn{2m} vs pT

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• v{4}2 ＝ v{6}2 ＞ v{2}2

• flow fluctuations σ: larger with HF

～ flow fluct.

v{2}2

＝ v2 ＋ σ2,v{4}2 , v{6}2

～ v2 － σ2,

20-30%

PartX (1/1) E-by-E distribution of v2

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v{2}2

＝ v2 ＋ σ2,v{4}2 , v{6}2

～ v2 － σ2,

• Broader distribution of v2

20-30%

PartX (1/1)Event-plane fluctuations by HF

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• Event-plane decorrelation by HF

20-30%

CMS, arXiv:1503.01692

J. Jia, and P. Huo,

Phys. Rev. C 90, 034905 (2014),

Summary

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PartX (1/1) Summary• Hydrodynamic fluctuations

＝ thermal fluctuations of hydrodynamics• Relativistic fluctuating hydrodynamics

in an integrated dynamical model – increase of anisotropies– larger effects in higher order vns– larger flow fluctuationsHF: Important in extracting the transport properties

• Outlook– Scan viscosity η & cutoff λ, and compare them to data– Modifications of f(p, λ), η(λ), etc. by cutoff λ.

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Backup

2014/08/06 17

Setup A:HF only

2015/7/27 18

PartX (1/1) Setup A: HF only• Initial condition

b = 6.45 fm ( ～ Centrality 20%)Averaged MC-KLN (CGC)

• (3+1)-dim Relativistic Fluctuating Hydrodynamics:

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x-y plane ηs-x plane

Type η/s HF Hydro Cascades

Ideal 0 none 1 event 104 events

Viscous 1/4π none 1 event 104 events

Fluctuating 1/4π σ=0.8, 1.0, 1.2 (fm) ＊ 104 events 3☓ 104 events 3☓

σ: HF cutoff length scale

PartX (1/1)Numerical Simulation: Evolution

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A: Hydrodynamic evolution

ηs

x [f

m]

ηs

x [f

m]

y [f

m]

y [f

m]

x [fm]

x [fm]

without HF

with HF

conventional2nd-order

viscous hydro

2nd-orderfluctuating hydro

τT ττ

PartX (1/1) A: dNch/dη

• Increase entropy production by HF• Larger effect with a shorter cutoff length σ

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PartX (1/1) A: pT-spectra (pions)

• High-pt particles increase with HF accelerated by local flows

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local flows by HF

PartX (1/1) A: Elliptic flow v2{2}

• decreased by viscosity, unchanged by HF local flows do not change the global flow profile

2015/7/22 23local flows by HF

PartX (1/1) A: Elliptic flow v2{2}(η)

• Decrease with viscosity, increase with HF increase of high-pT particles

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v2(pT) in the last slide

High-pT particles

v2

η

PartX (1/1) B: pT-spectra (pions)

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• Points: PHENIX PRC69 (2004) 034909• Black lines: ideal hydrodynamics• Blue lines: viscous hydrodynamics• Red lines: fluctuating hydrodynamics0-4%, 5-10%, 10-15%, 15-20%, 20-30%,30-40%, 40-50%, 50-60%, 60-70%, 70-80%from top to bottom (multiplied by 104-10-5)

• Increase of high-pT pions:larger in peripheral collisions larger thermal fluctuationsin smaller systems

• Correction of distribution inCooper-Frye formula by HF?

Setup B:IS fluctuations + HF

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PartX (1/1) Elliptic flow v2(η)

• v2(fluctuating) > v2(ideal) in central collisionsCentral: 　　 (IS Fluct.) + (HF)Non-central: (IS Fluct.) + (HF) + (Collision geometry)

• Same order with IS fluctuations2015/9/29 27

ηp ηp

10-15%0-5%

PartX (1/1) v2{2}(pT), v3{2}(pT)

• v2 increase with HF in central collisions

• Similar behavior for v3

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v2 v3

PartX (1/1) v2{2} vs pT

• Calculations: η/s = 1/4pi2015/9/29 29