Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano Viscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate Quark Matter 2011 May 27 th 2011, Annecy, France AM and T. Hirano, arXiv:1102.5053 [nucl-th]
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V iscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate
AM and T. Hirano, arXiv:1102.5053 [ nucl-th ]. V iscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate. Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano. Quark Matter 2011 May 27 th 2011, Annecy , France. - PowerPoint PPT Presentation
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Akihiko MonnaiDepartment of Physics, The University of Tokyo
Collaborator: Tetsufumi Hirano
Viscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate
Quark Matter 2011May 27th 2011, Annecy, France
AM and T. Hirano, arXiv:1102.5053 [nucl-th]
Quark Matter 2011, May 27, Annecy, France
Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate
Next slide: 2 / 12
Introduction Quark-gluon plasma (QGP) at relativistic heavy ion collisions
Hadron phase QGP phase
(crossover) sQGP (wQGP?)
The QGP quantified as a nearly-perfect fluid
RHIC experiments (2000-)
Viscosity is important for “improved” inputs (initial conditions, equation of state, etc.)
Consistent modeling is necessary to extract physical properties from experimental data
Introduction
Quark Matter 2011, May 27, Annecy, France
Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate
Next slide: 3 / 12
Introduction Modeling a high-energy heavy ion collision
First Results from LHC
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)
Quark Matter 2011, May 27, Annecy, France
Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate
Next slide: 4 / 12
First Results from LHC LHC experiments (2010-)
Mid-rapidity multiplicity
CGC in Heavy Ion Collisions
ALICE data (most central 0-5%)
CGC; fit to RHIC data but no longer valid at LHC?
CGC
Pb+Pb, 2.76 TeV at η = 0
K. Aamodt et al. PRL105 252301
Heavy ion collisions of higher energies
Will the RHIC modeling of heavy ion collisions be working intact at LHC?
Quark Matter 2011, May 27, Annecy, France
Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate
Next slide: 5 / 12
CGC in Heavy Ion Collisions Saturation scale in MC-KLN model
CGC + Hydrodynamic Model
Hydrodynamic Model
Initial conditionfrom the CGC
Hydrodynamic evolution
Observed particle distribution
a missing piece!
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
Initial conditionfrom the CGC
Observed particle distribution
dN/dy
λ=0.28λ=0.18
λ=0.38
We need to estimate hydrodynamic effects with(i) non-boost invariant expansion(ii) viscous corrections for the CGC
Quark Matter 2011, May 27, Annecy, France
Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate
Next slide: 6 / 12
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:
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
Quark Matter 2011, May 27, Annecy, France
Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Evolution with Non-Boost Invariant Flow for the Color Glass Condensate
Next slide: 7 / 12
Hydrodynamic Model Full 2nd order viscous hydrodynamic equations
Model Input for Hydro
Solve in (1+1)-D relativistic coordinates (= no transverse flow)with piecewise parabolic + iterative method
EoM for bulk pressure
EoM for shear tensor
Energy-momentum conservation +AM and T. Hirano, NPA 847, 283