v iscous hydrodynamic expansion of the quark-gluon plasma for the color glass condensate

Akihiko MonnaiDepartment of Physics, The University of Tokyo

Collaborator: Tetsufumi Hirano

Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate

Standard and Novel QCD Phenomena at Hadron CollidersJune 1st 2011, ECT*, Trento, Italy

AM and T. Hirano, arXiv:1102.5053 [nucl-th]

Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate

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Outline1. Introduction

Models for relativistic heavy ion collisions

2. Hydrodynamic model for the CGCNon-boost invariant viscous hydro in the longitudinal direction

3. ResultsHydro deformation of the CGC rapidity distribution at RHIC and LHC

4. SummarySummary and Outlook

Introduction 2



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Introduction Quark-gluon plasma (QGP) at relativistic heavy ion collisions

Hadron phase QGP phase

　(crossover) sQGP (wQGP?)

Introduction 3

Quantification of the space-time evolution of the QGP by modeling the heavy ion collisions

Determination of the properties of the QCD matter from experimental data (e.g. transport coefficients)

In this work, we discuss the role of hydrodynamic models on the color glass condensate

Introduction 3



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Introduction “Standard model” of a high-energy heavy ion collision

particles

hadronic phase

QGP phase

Freezeout

Pre-equilibrium

Hydrodynamic stage

Color glass condensate

Hadronic cascade

Initial condition

Hydro to particles

ｔ

z

t

Color glass condensate (CGC)

Relativistic hydrodynamics

Description of saturated gluons in the nuclei before a collision (τ < 0 fm/c)

Description of collective motion of the QGP (τ ~ 1-10 fm/c)

4Introduction



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Introduction RHIC experiments (2000-)

LHC experiments (2010-)

†he First ALICE Result 5

The QGP is well-described by ideal hydro modelViscosity is important for 1st-principle-based inputs (equation of state, initial conditions, etc.)

Heavy ion collisions of higher energies

Will the RHIC modeling of heavy ion collisions be working intact at LHC?

The CGC itself has also been successful in explaining multiplicity

5

An unified picture would be necessary



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The First ALICE Result Mid-rapidity multiplicity

CGC in Heavy Ion Collisions

ALICE data (most central 0-5%) CGC; fit to RHIC data What is happening at LHC?

CGC

Pb+Pb, 2.76 TeV at η = 0K. Aamodt et al. PRL105 252301

6



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CGC in Heavy Ion Collisions Saturation scale in MC-KLN model

CGC in Heavy Ion Collisions

Fixed via direct comparison with data

dNch/dη gets steeper with increasing λ; RHIC data suggest λ~0.28

D. Kharzeev et al., NPA 730, 448

dN/dy

λ=0.28λ=0.18

λ=0.38

Initial conditionfrom the CGC

Hydrodynamic evolution

Observed particle distribution

secondary interactions!



H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903

: thickness function: momentum fraction of incident particles

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CGC in Heavy Ion Collisions CGC + Hydrodynamic Model

Viscous Hydrodynamic Model


Hydrodynamic evolution


secondary interactions!

8

The first time the CGC rapidity distribution is discussed in terms of viscous hydrodynamics

We need to estimate hydrodynamic effects with(i) non-boost invariant expansion(ii) viscous corrections for the CGC

Motivation



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Viscous Hydrodynamic Model Decomposition of the energy-momentum tensor by flow

Stability condition + frame fixing

10 dissipative currents2 equilibrium quantities

Energy density deviation:Bulk pressure:

Energy current:Shear stress tensor:

Energy density:Hydrostatic pressure:

Viscous Hydrodynamic Model

where is the projection operator

related in equation of state

Thermodynamic stability demands Identify the flow as local energy flux

This leaves and

9



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Viscous Hydrodynamic Model Physical meanings of and

Viscous Hydrodynamic Model 10

Naïve interpretation at the 1st order in gradient expansion

Shear viscosity: response to deformation

Bulk viscosity: response to expansion + cooling

- In actual calculations one includes 2nd order contributions for the sake of causality and stability

Bulk pressure

Shear stress tensor

Cross term in linear response theory



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Viscous Hydrodynamic Model Full 2nd order viscous hydrodynamic equations

Model Input for Hydro

EoM for bulk pressure

EoM for shear tensor

Energy-momentum conservation +AM and T. Hirano, NPA 847, 283

All the terms are kept

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Solve in (1+1)-D relativistic coordinates (= no transverse flow)

Note: (2+1)-D viscous hydro assumes boost invariance in the longitudinal direction



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Model Input for Hydro Equation of state and transport coefficients

Initial conditions

Results

Equation of State: Lattice QCD

Shear viscosity: η = s/4π

2nd order coefficients: Kinetic theory & η, ζ

Initial flow: Bjorken flow (i.e. flow rapidity Yf = ηs)

Bulk viscosity: ζ = (5/2)[(1/3) – cs2]η

Relaxation times: Kinetic theory & η, ζ

S. Borsanyi et al., JHEP 1011, 077

P. Kovtun et al., PRL 94, 111601A. Hosoya et al., AP 154, 229

AM and T. Hirano, NPA 847, 283

Dissipative currents: δTμν = 0

Initial time: τ = 1 fm/c

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Energy distribution: MC-KLN type CGC model H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903



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Results CGC initial distributions + longitudinal viscous hydro

Results

Outward entropy flux FlatteningEntropy production Enhancement

RHIC LHC

If the true λ is larger at RHIC, it enhances dN/dy at LHC;Hydro effect is an important factor in explaining the LHC data

13

AM and T. Hirano, arXiv:1102.5053



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Results CGC initial distributions + longitudinal viscous hydro

Results

Outward entropy flux FlatteningEntropy production Enhancement

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RHIC LHC

If the true λ is larger at RHIC, it enhances dN/dy at LHC;Hydro effect is an important factor in explaining the LHC dataIf the λ is unchanged at RHIC, dN/dy is still enhanced at LHC;Hydro effect is an important factor in explaining the LHC data

AM and T. Hirano, arXiv:1102.5053



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Results Deviation from boost-invariant flow

RHIC LHC

Flows exhibit similar trends at RHIC and LHC

τ = 30 fm/c τ = 50 fm/c

deceleration by suppression of total pressure P0 – Π + π at early stage andacceleration by enhancement of hydrostatic pressure P0 at late stage

Ideal flow ≈ viscous flow due to competition between

Flow rapidity:

Results 15



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Results Time evolution for the LHC settings

No sizable modification the on rapidity distribution after 20 fm/c, unlike the flow profile

Equal-time surface is close to isothermal surface for the current parameters

16Summary and Outlook

It could be accidental; isothermal entropic “freezeout” is coming soon



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Summary and Outlook We solved full 2nd order viscous hydro in (1+1)-dimensions

for the “shattered” color glass condensate

Future prospect includes:– Detailed analyses on parameter dependences, rcBK, etc…– A (3+1)-dimensional viscous hydrodynamic model

The End

AM & T. Hirano, in preparation

Non-trivial deformation of CGC rapidity distribution due to(i) outward entropy flux (non-boost invariant effect)

(ii) entropy production (viscous effect)

Viscous hydrodynamic effect may play an important role in understanding the seemingly large multiplicity at LHC

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The End Thank you for listening! Website: http://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/index.html

18Appendices

http://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/



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Results Parameter dependences

Comparison to boost-invariant flow

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Larger entropy production for more viscous systems

(ii) η/s = 1/4π, ζeff/s = (5/2)[(1/3) – cs2]/4π

(iii) η/s = 3/4π, ζeff/s = (15/2)[(1/3) – cs2]/4π

(i) η/s = 0, ζeff/s = 0

Longitudinal viscous hydro expansion is essential

preliminary

Appendices



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Introduction Relativistic hydrodynamics: macroscopic theory defined on

Flow

Temperature

20

Energy-momentum conservationLaw of increasing entropy

(in the limit of vanishing conserved currents)

driven by

Input Output

• Initial conditions • Equation of state• Transport coefficients

• Energy-momentum tensor• Flow field• Temperature field

Introduction

v iscous hydrodynamic expansion of the quark-gluon plasma for the color glass condensate

Documents

novel qcd phenomena

color glass condensatestandard

italyakihiko monnai

heavy ion collisionsalice

qcd matter

viscous hydrodynamic

hadron collidersjune

role of hydrodynamic