Wang Meijuan Liu Lianshou Wu Yuanfang

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Is there hydrodynamic flow at RHIC?

• Wang Meijuan Liu Lianshou Wu Yuanfang
• IOPP, Huazhong Normal University

• Motivation
• Neighboring angular-bin multiplicity correlation
  pattern in transport models
• Anisotropic correlation coefficient(ACC)
• Summary

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1. Motivation
Some form of a quark-gluon plasma is formed at
RHIC, and one of the evidences is the
anisotropic collective flow behavior observed.
The successful hydrodynamic description on the
observed mass dependence of v2 at pt lt 2GeV
shows that observed dense matter behaves like a
perfect fluid, and is referred as sQGP.
Experimentally Hydrodynamic
model can still not quantitatively fit the
observed mass dependence of v2 for CuCu data.
PRL98, 242302(2007)

• Theoreticallly
• local thermal equilibrium is required.
• Viscosity0 is hard to be understood.

However
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1. Motivation
The main experimental physical quantity v2
1)it only globally characterizes the possible
direction and strength of anisotropic
distribution. 2) The intrinsic interaction of
final state particles is absent.
2-particle azimuthal corr.
How the particles in different azimuthal
directions interact with each other can not be
drawn from them either.
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2. Introduction of the corr. pattern
A spatial-dependent neighboring correlation
pattern is suggested
Wu Yuanfang, Lianshou Liu, Yingdan Wang, Yuting
Bai and Hongbo Liao, Phys. Rev. E71,
017103(2005).
m the sequence number of bins nm the
multiplicity in the mth angular bin

Its a good observable for tracing the
interaction among different azimuthal directions
in relativistic heavy ion collision.
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2. Corr. pattern in transport models
Transport models

• RQMD with hadron rescattering

a hadron-based transport model where v2 is
smaller than the data at RHIC.
H. Sorge, Phys. Rev. C52, 3291 (1995) Y. Lu et
al. nucl-th/0602009

• AMPT with string melting

a multi-phase transport model, where parton
cascade hadron rescattering are both included.
This model can reproduce v2 (pt) data at RHIC.
Zi-Wei Lin, Che Ming Ko, Bao-An Li, Bin Zhang
and Subrata Pal, Phys. Rev. C72, 064901
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2. Corr. pattern in transport model
In Fig.(a) Corr. patterns from two models are
cos2F like, opposite to
the well-known cos2F like azimuthal distribution.

In Fig.(b)Fig.(c) two opposite trends
dominate in peripheral and near-central
collisions, which can be called as in-plane and
out-of-plane corr. pattern respectively. In the
mid-central collisions, the two trends turn to
balance.
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2. Corr. pattern in transport model
What is the physical origin of the two opposite
trends ?
? In-plane corr. pattern
It is the same as in-plane flow, which is caused
by anisotropic expansion in non-central
collisions.
?Out-of-plane corr. pattern

• the anisotropic expansion and the late
  hadronization are impossible
• to produce strong correlations in
  out-of-plane directions.

• Only the initial source anisotropy is
  preferential in these directions.

A larger initial number of participant nucleons
in the out-of-plane directions, which in turn
generates stronger interaction in these
directions.
?
What is the physical origin of the two opposite
trends
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2. Corr. pattern in transport model
? Why the out-of-plane corr. patterns appear at
near-central coll.?
In peripheral collisions
The overlap zone is small, and so is the no.
of participants the diff. between two axes
of overlap zone is large, and so is the
difference of pressure gradient.
The anisotropic expansion dominates the final
observable,the effects of initial interaction in
corr. patterns are hidden.
In near-central collisions
The overlap zone becomes large, and the diff.
between two axes of overlap zone is small.
The initial interactions are strong enough to
show themselves up!
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2. Corr. pattern in transport models

• If there is hydrodynamic flow, the system should
  be well thermalized and reach thermal
  equilibrium. Then all other interaction before
  anisotropic expansion should be forgotten!

• The out-of-plane corr. pattern is observed as
  the result of initial interaction
• before anisotropic expansion, i.e, a larger
  initial number of participant nucleons
• in the out-of-plane directions. This is out of
  the hydrodynamic expectation!

Measuring the corr. pattern by the data of RHIC
and LHC is looking forward to!
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3. Anisotropic correlation coefficient
The correlation patterns are typical periodic
function of azimuthal angle in periph.and
central collisions, so it can be expanded by
Fourier series
1) ?r is the direction of reaction plane, and is
zero in model analysis, while in real exp. data
analysis, it has to be determined event-by-event.
2) The main contribution in the expansion series
comes from cos2(F-?r). 3) The coefficient u2
provides the preferential direction and strength
of anisotropic correlation pattern. We specify it
as anisotropic correlation coefficient (ACC).
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3. The rapidity dependence of ACC
(1, 5-5,-1) -1,1 are chosen ,which
correspond to forward, backward and central
rapidity region.
ACC is independent of the choice of rapidity
and similar to that in whole rapidity space.
So in finite rapidity range of current
relativistic heavy ion exp., studying the corr.
pattern and ACC is expectable.
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4. Summary

• A spatially-dependent azimuthal multiplicity
  corr. pattern is suggested! There are two kinds
  of interactions at early stage of Au Au
  collisions at vsNN 200GeV generated by the two
  models.

• The out-of-plane corr. pattern is observed as
  the result of initial interaction
• before anisotropic expansion. This is out
  of the hydrodynamic expectation!

• Studying the corr. pattern of data of RHIC
  and LHC is looking forward to!
• i.e, ACC is independent of rapidity
  range, it is measurable in finite rapidity
• range of current relativistic heavy ion
  exp..

Thanks!