Transcript Diffusion of transverse correlations and shear viscosity in heavy ion

Diffusion of transverse
correlations and shear viscosity
in heavy ion collisions
Qun Wang (王群)
Univ of Sci & Tech of China
(中国科技大学)
With L.G.Pang,X.N.Wang,R.Xu
IWND2009, Shanghai, August 22-25,2009
What is shear viscosity
shear viscosity = resistance of liquid to
shear forces (and hence to flow)
Shear viscosity in ideal gas and liquid
• ideal gas, high T
• ideal liquid, low T
Frenkel, 1955
• lower bound by uncertainty principle
Danielewicz, Gyulassy, 1985
Ratio of Shear Viscosity to entropy density
Lacey et al,
PRL98,
092301
(2007)
Correlation from interaction:example
number density
momentum correlation
Interaction
potential
Momentum fluctuation as tool to measure
shear viscosity (1)
Cylindrical coordinate
EM tensor for fluid
[Gavin, Abdel-Aziz,
PRL 2006]
EM conservation of fluid to equation for fluctuation
local
rest
frame
Momentum fluctuation as tool to measure
shear viscosity (2)
Diffusion equation for momentum density
Diffusion equation for momentum density in rapidity
and proper time
Momentum fluctuation as tool to measure
shear viscosity (3)
Correlation of momentum fluctuation
Diffusion equation for correlation
is broadened by momentum diffusion
Momentum fluctuation as tool to measure
shear viscosity (4)
Connection to observable
• i labels particles
from each event
• brackets represent
the event average
Shear viscosity can broaden the rapidity correlations of
the momentum current. This broadening can be observed
by measuring the transverse momentum
covariance as a function of rapidity acceptance.
Momentum fluctuation as tool to measure
shear viscosity (5)
Rapidity correlations to measure the shear viscosity
[Gavin, Abdel-Aziz, PRL 2006]
Azimuthal correlation in transverse momenta
Transverse plane can be
separated to -bins
Focus on two -bins 1 and 2,
define correlation function
particle numbers in bins 1 and 2
i,j: particles in bins 1 and 2
average is taken over events
Diffusion equation for azimuthal correlation
in central collisions
Cylindrical coordinates, metrics and velocity
central collision
Diffusion equation for azimutha correlation
Diffusion equation for azimuthal correlation
in central collisions
In the co-moving frame without fluid velocity,
diffusion equation is in a simple form
with solution
Solve diffusion equation in general frame
1. Initial condition given by HIJING
2. Solve fluid equation to determine thermodynamic quantities
as input to diffusion equation
3. Average over freeze-out hyper-surface
freeze-out
energy density
Azimuthal correlation in transverse momenta
result from HIJING
Results for azimuthal correlation (1)
Free Gas
Results for azimuthal correlation (2)
First order phase transition
Results for azimuthal correlation (3)
Results for azimuthal correlation (4)
Results for azimuthal correlation (5)
Results for azimuthal correlation (6)
Summary and conclusion
1. A diffusion equation for azimuthal correlation for
transverse momentum is derived a general Lorentz
frame.
2. Mini-jet thermalization is shown in the correlation
3. Azimuthal correaltion as a measure for shear
viscosity