Transcript Document

Anisotropic Flow
and Ideal Hydrodynamic Limit
Yuting Bai
(for the
Collaboration)
International Conference on Strangeness in
Quark Matter 2008
Oct. 6 -10, 2008
Beijing, China
Outline
 Introduction
 Anisotropic flow
 The success and uncertainties in ideal
hydro calculations
 Results
 How much deviation from ideal hydro
 Conclusions
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Anisotropic Flow
y
py
x
y
x
z
v2  cos2  r 
 The spatial anisotropy is transformed into a momentum
anisotropy by the multiple interactions
 Established early, self-quenching, therefore sensitive to

the early stage of the collisions
 Depending on rescattering, sensitive to the degree of
thermalization
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Ideal hydro success and uncertainties
C. Alt et.al;
Phys.Rev.C68,034903(2003)
Hydro limits from P.Kolb,
J.Sollfrank,U.Heinz;
Phys.ReV.C62:054909,2000
 v2/e was considered to approach the ideal hydro limit in
central collisions
 Uncertainties:


Choice of EoS - affects Hydro limits
The initial conditions: Glauber, Color Glass Condensate
(CGC)
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Choices of v2 and e
y
y’

x’
x
Standard eccent ricity : ε std 
RP
y2  x 2
y2  x 2
(σ 2y  σ 2x ) 2  4σ 2xy
P articipant eccent ricity : ε part 
σ 2y  σ 2x

,
σ 2x  x 2  x , σ 2y  y 2  y , σ xy  xy  x y
2
ε{2} 
2
ε2
M.Miller and R.Snellings;nucl-ex/0312008
R.Bhalerao and J- Y.Ollitrault; Phys.Lett.B 614(2006)260
S.Voloshin, A.Poskanzer, A.Tang and G.Wang;
Phys.Lett.B 659(2008)537

The number of individual
nucleons participating in
the collision as well as
their position could
fluctuate from event to
event. The center of the
overlap zone can be
shifted and the
orientation of the
principal axes of the
interaction zone can be
rotated
v2{EP}, v2{2}, epart and
e{2} sensitive to
anisotropy w.r.t the
participant plane PP
v2{4},v2{ZDCSMD} and
estd sensitive to
anisotropy w.r.t the
reaction plane RP
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Flow increases
STAR Preliminary
standard eccentricity from
Glauber model



eccentricity from CGC
(nucl-th/0605012)
Scaled v2 increases with centrality over large pt range
Peak position of v2/e shifts to higher pt in more central collision
The system seems more close to thermalization for most
central collisions
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How much deviation from ideal hydro
 Try to use the data to
constrain the hydro
limit
 Use relativistic
Boltzmann calculations
to calculate how v2
approaches hydro as
function of cross
section and density
 Based on these
calculations the v2/e
dependence has been
parameterized as
function of K
 Fit data to extract
v2hydro/e and s
hydro
v2 v2

ε
ε
1
1 K K0
Knudsen number : K  λ R
T henumber of collisionsper part icle:
1 K  (σ S)(dN dy )cs
σ : part oniccross sect ion
K 0  0.7,c s  1
K  0:
v2
3
hydro
Hydrodynamic limit
ε
K   : c ss
1 dN
Low densit y limit (LDL)
S dy
R.Bhalerao,J-P.Blaizot,N.Borghini and JY.Ollitrault;Phys.Lett.B 627:49-54,2005
C.Gombeaud and J-Y.Ollitrault;
Phys. Rev. C 77, 054904 (2008)
H-J.Drescher, A.Dumitru, C.Gombeaud, JY.Ollitrault; Phys. Rev. C 76, 024905 (2007)
Yuting Bai, SQM2008
How much deviation from ideal hydro


STAR Preliminary

The estimates depend
on the initial conditions.
A softer EoS is required
for CGC
Ideal hydro limit is not
reached at top RHIC
energy. The ratio of
v2/e is considerably
away from hydro limit
independent of choices
of e
K decreases with the
increasing of particle
density. But still finite
in the most central
collisions
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Hiroshi Masui Parallel Session I: 15:40—16:00
How much deviation from ideal hydro
STAR Preliminary
PHENIX p, K and p: nucl-ex/0604011, STAR Ks0, L: Phys. ReV. C 77 054901 (2008)
 With the assumption that parton cross section (s) is same
for all identified particles, a universal trend of approaching
hydro limit is established. In central collisions, the ratio of
v2/e is considerably away from hydro limit
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Constraint on EoS
STAR Preliminary
 cs 
s   K 0  const.
c
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Constraint on h/s
Temperature from:
A.Adare nucl-ex/08044168
STAR Preliminary
η
λT
T
T
T
1
 0.316  0.316
 0.316
 0.316 
1
dN
1
s
c
csn
σcs 1 dN
cσ

S dy R/(cs /c)
SR dy
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Charged particle v4/v22
STAR Preliminary
Hydro, Boltzmann calculations:J-Y. Ollitrault
 It’s expected that v4/v22 decreases with K-1.
 Consistent with Boltzmann calculation with K> 0.5
 Measured ratios indicate that ideal hydro limit is not
reached
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Conclusions
 v2/e, examined with transport motivated formula,
approaches ideal hydro limit for all identified
hadrons. In central Au+Au collisions, v2/e is still
considerably away from Hydro limit. The conclusion
is independent of initial conditions.
 Results of charged hadron v4/v22 are consistent with
above
 Constraint on EoS obtained.
 For the first time, h/s versus centrality is extracted.
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Choices of v2 and e
G. Wang QM2005
Au +Au 200 GeV
STAR Preliminary
 v2{4}: measured with the 4-particle cumulant method
 v2{ZDCSMD}: measured with the first order event plane
reconstructed with STAR’s ZDC-SMD
 non-flow effects are reduced in both methods
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