Transcript Document

Energy dependence of
anisotropic flow
Raimond Snellings
RHIC: the first 3 years
RHIC Scientists Serve Up “Perfect” Liquid
New state of matter more remarkable than predicted -- raising many
new questions
April 18, 2005
5 July 2006
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Outline
 The perfect liquid at RHIC
 How do we approach the perfect liquid?
 What can we expect at the LHC?
 What can we learn from higher
harmonics?
5 July 2006
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Anisotropic Flow

d3 N
1 d2 N 





E 3 
1

2
v
(
p
,
y
)
cos
n





n
t
r 
d p 2 pt dpt dy 
n 1

 Anisotropic flow ≡ azimuthal correlation
with the reaction plane




vn  cosn  r 
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the cleanest signal of final-state
reinteractions
Unavoidable consequence of
thermalization
Natural description in hydrodynamic
language, however when we talk about
flow we do not necessary imply (ideal)
hydrodynamic behavior
Flow in cascade models: depends on
constituent cross sections and densities,
partonic and/or hadronic
 Non-flow ≡ contribution to vn from
azimuthal correlations between particles
not due to their correlation with the
reaction plane (HBT, resonances, jets,
etc)
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Measuring Anisotropic Flow
vn  cos n(  r )   ein(  ψ r )
ein (1 2 )  ein (1  r ) ein ( r 2 )  ein (1  r )
ein ( r 2 )  (vn {2}) 2
Assumption: all correlations between particles due to flow
Non flow correlation contribute order (1/N), problem if vn≈1/√N
v2 2 
v22
ein (1 2 3 4 )  ein (1 2 ) ein (3 4 )  ein (1 4 ) ein (3 2 )  (vn {4}) 4
Non flow correlation contribute order (1/N3), problem if vn≈1/N¾
v2 4   2 v

2 2
2
1/ 4
 v 

4
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Measuring the cumulants of different order provides constraints on both fluctuations
and non-flow. Can be conveniently calculated using generating functions, extended
to vn{∞} using Lee-Yang zeros, reliable vn>1/N
N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001) 054906
5 July 2006
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The perfect liquid
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The “nearly perfect” liquid
HYDRO: Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909
STAR PRL 86, 402 (2001)
P.F. Kolb et al., PLB 500
(2001) 0012137

v2{4} 130 GeV

Zhixu Liu
5 July 2006
Magnitude and transverse
momentum dependence of v2
A strongly interacting, more
thermalized system which is for
more central collisions behaves
consistent with ideal fluid
behavior!
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Viscosity and parton cascade
D. Molnar and P. Huovinen,
PRL94:012302,2005
D. Teaney PRC68:034913,2003
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Viscosity needs to be small
Parton cascades need huge opacities
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Partially solved by coalescence
Microscopic picture responsible for large v2 still not understood (E. Shuryak
sQGP is being understood)
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Strong Collective Motion, v2(m,pt)
 Particles flow with a common velocity
 The most compact representation of the strong radial
flow and its azimuthal variation
 Best described by QGP EoS!?
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The QCD EoS and Cs
F. Karsch and E. Laermann, arXiv:hep-lat/0305025

Test the effect of four different
EoS; qp is lattice inspired, Q
has first order phase
transition, H is hadron gas
with no phase transition and T
a smooth parameterization
between hadron and QGP
phase
Pasi Huovinen, arXiv:nucl-th/0505036
5 July 2006
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v2(m,pt) and the softest point
Pasi Huovinen, arXiv:nucl-th/0505036
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EoS Q and EoS T (both have
significant softening) do provide the
best description of the magnitude of
the mass scaling in v2(pt)
The lattice inspired EoS (EoS qp) in
ideal hydro does as poorly as a
hadron gas EoS! (opposite to
conclusion Kämpfer)
Elliptic flow as function of pt and mass
very sensitive to EoS (particular the
heavier particles)
Before we can draw conclusions about
the EoS much more work needed in
theory (test different EoS, influence
viscosity, hadronic phase)
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Energy dependence
NA49, Phys. Rev. C(68), 034903 (2003)
Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909
Heiselberg and Levi PRC 59
D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nuclth/0011058; Phys. Rev. Lett 86, 4783 (2001).
v2 
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S
 tr
dN
dy
Energy dependence missed by ideal hydro
Hydro + cascade describes v2 from SPS to
RHIC
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At higher energies ideal hydro contribution
dominates
Hydro + cascade follows “low density limit”??
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v2, eccentricity and fluctuations
M. Miller and RS, arXiv:nucl-ex/0312008

y 2  x2
y 2  x2
v2  
v2 {2} 
v22

2 2
2
v2 {4}  2 v
v2 {6} 
 v
1
4
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2
 v
4
2
 9 v24

1/ 4
2 3
2
v22  12 v

1/ 6
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v2, eccentricity and fluctuations
M. Miller and RS, arXiv:nucl-ex/0312008
“standard”
v2{2}
overestimates
v2 by 10%,
higher order
cumulant
underestimate
v2 by 10% at
intermediate
centralities
 Measuring the cumulants of different order provides
constraints on both fluctuations! and on non-flow
contributions!
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PHOBOS eccentricity fluctuations
y'  x'
2
 part 
2
y'
y
x'
y'  x'
2
2
x
S. Manly, QM2005
 Large effect for small systems over whole centrality range
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v2/ revisited
S. Voloshin CIPANP-’06
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By using participant eccentricity Cu+Cu and Au+Au at two
energies follow the v2/ scaling
Although fluctuations in part are reduced to compared to
”standard” using {2} and v2{4}/{4} could be an
improvement
Why does it work that well?
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Rapidity dependence
Hirano: Nucl Phys A715 821 824 2003
 No boost invariance!
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Rapidity dependence
PHOBOS nucl-ex/0509034
PHOBOS PRL 94, 122303 (2005)
 dN/dh scales versus h-ybeam
 v2/ ~ 1/S dN/dy
 Rapidity dependence no surprise?
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Rapidity dependence of eccentricity
 Is the /S independent of rapidity?
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LHC energies
E. Simili
v2
dNch
dh
 Using dN/dy scaling of multiplicity and v2/eps
extrapolation
 Values a bit above hydro predictions (from T. Hirano)
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Energy dependence
T. Hirano
D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nuclth/0011058; Phys. Rev. Lett 86, 4783 (2001).
 The higher the beam energy the more
dominant the QGP (here ideal hydro)
contribution becomes
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Viscosity/entropy versus T
Hirano and Gyulassy
arXiv:nucl-th/0506049
Csernai, Kapusta and McLerran
arXiv:nucl-th/0604032
 Important to quantitatively calculate the
effect of viscosity on v2
 Would reduce further the elliptic flow
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Higher Harmonics
Peter Kolb, PRC 68, 031902
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STAR, Phys. Rev. Lett.(92), 062301 (2004)
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Higher harmonics are expected to be
present, for smooth azimuthal
distributions the higher harmonics will
be small vn ~ v2n/2
v4 - a small, but sensitive observable
for heavy ion collisions (Peter Kolb,
PRC 68, 031902)
v4 - magnitude sensitive to ideal hydro
behavior (Borghini and Ollitrault,
arXiv:nucl-th/0506045)
 Ideal hydro v4/v22 = 0.5
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What do we learn from v4?
 Ratio v4/v22 is sensitive to degree of
thermalization (Borghini and Ollitrault nuclth/0506045)
 v4(pt)/v2(pt)2 is 1/2 for ideal hydro (more accurate
for increasing values of pt)
 Observed integrated ratio is larger than unity
 Do we have intuitive test if the ratio is
related to the degree of thermalization?
 ratio v4/v22 expected to decrease as the collisions
become more central
 ratio v4/v22 expected to increase as function of
transverse momenta
 rapidity & energy dependence
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v2 and v4 at 200 GeV
STAR preliminary
Y. Bai, AGS users meeting 2006
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200 GeV v4{EP2}/v2{4}2
Y. Bai, AGS users
meeting 2006
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v4/v22 decreases with pt below 1 GeV/c after which is starts to
increase again (expected)
Magnitude and centrality dependence do not follow intuitive
expectations
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62 GeV v4{EP2}/v2{4}2
Y. Bai, AGS users
meeting 2006
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
Centrality and pt dependence similar to 200 GeV magnitude
of v4/v22 even somewhat lower!
Energy dependence does not follow intuitive expectations
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Rapidity dependence
A. Tang
 Ratio increases towards midrapidity
contrary to expectations
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Conclusions

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Strong collective motion at RHIC energies, consistent with perfect
liquid behavior
 No microscopic picture available
 Constraining the EoS requires more detailed calculations
Energy dependence
 No obvious horns, kinks or steps
 Collapse of the proton v2 at SPS (next talk)
 Measurements of v2{2}, v2{4}, v2{6} allow for estimates of the
fluctuations and non flow as function of energy (detailed
measurement still needs to be done, strong argument for energy
scan)
 v2 measurement at LHC will provide critical test of our
understanding of the almost perfect liquid, testing the “hydro
limit”
Au+Au and Cu+Cu follow v2/ scaling when using part
 Why does it work that well?
v4 is promising new observable to test hydrodynamic behavior
 Detailed high statistics measurement available
 Are the non-flow and fluctuation contributions to v4 under control?
 Challenge to theory!
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