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AM and T. Hirano, arXiv:1102.5053 [nucl-th]. V iscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate. Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano. Standard and Novel QCD Phenomena at Hadron Colliders - PowerPoint PPT Presentation
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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
Next slide: / 18
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
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
Next slide: / 18
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
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
Next slide: / 18
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
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
Next slide: / 18
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
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
Next slide: / 18
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
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
Next slide: / 18
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!
Initial conditionfrom the CGC
Observed particle distribution
H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903
: thickness function: momentum fraction of incident particles
7
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
Next slide: / 18
CGC in Heavy Ion Collisions CGC + Hydrodynamic Model
Viscous Hydrodynamic Model
Initial conditionfrom the CGC
Hydrodynamic evolution
Observed particle distribution
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
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
Next slide: / 18
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
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
Next slide: / 18
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
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
Next slide: / 18
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
11
Solve in (1+1)-D relativistic coordinates (= no transverse flow)
Note: (2+1)-D viscous hydro assumes boost invariance in the longitudinal direction
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
Next slide: / 18
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
12
Energy distribution: MC-KLN type CGC model H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903
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
Next slide: / 18
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
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
Next slide: / 18
Results CGC initial distributions + longitudinal viscous hydro
Results
Outward entropy flux FlatteningEntropy production Enhancement
14
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
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
Next slide: / 18
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
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
Next slide: / 18
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
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
Next slide: / 18
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
17
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
Next slide: / 18
The End Thank you for listening! Website: http://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/index.html
18Appendices
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
Next slide: / 18
Results Parameter dependences
Comparison to boost-invariant flow
19
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
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
Next slide: / 18
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
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