Momentum%20Anisotropies%20--%20Probing%20the%20detailed%20Dynamics

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Momentum Anisotropies --Probing the detailed
Dynamics
Peter F. Kolb
Department of Physics and Astronomy State
University of New York Stony Brook, NY
11794 with support from the Alexander von
Humboldt Foundation

• Brookhaven National LaboratoryFlow and QGP
  Workshop
• November 18, 2003

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Non-Central Collisions Feature Broken Symmetry
Characterize azimuthal dependence of the
resulting observables by their Fourier expansion
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Elliptic Flow - A Prominent Observable
reaching the hydrodynamic limit
on a timescale lt 1 fm/c
indicating a soft transition region
common partonic flow
heavier particles pick up larger ltpTgt in the
common flow field
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Elliptic Flow at Large Pt is HUGE !
PHENIX Collaboration, nucl-ex/0305013
v2 0.25 means that there are 3 times as many
particles emitted into the reaction plane than
out of the reaction plane!Furthermore the
distribution is not elliptic any longer!
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Higher order term to Counteract ?
develops a minimum in cartesian coordinates at
x0 for v2 gt 0.1
To balance the minimum a v4 gt (10v2-1)/34 is
required (this brings the second derivative of
y(x) at x0 to vanish).
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Differential Expectations on Higher vs
From a recent hydrodynamic calculation to
describe collisions at 200 GeV
PFK, and R. Rapp, PRC 67 (2003) 044903
It is however not sufficient to balance the
peanut shape
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Geometric Anisotropy is Rapidly Converted to
Momentum Space
quantify anisotropies
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A short Digression on Fourier Coefficients
Distribution within the reaction plane
Distribution out of the reaction plane
for a delta-function like distribution
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Geometric Anisotropy is Rapdily Converted to
Momentum Space
quantify anisotropies
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Elliptic Flow in the Blast Wave
Blast wave parametrization for non-central
collisions
Huovinen, PFK, Heinz, Ruuskanen, Voloshin, PLB
503 (01) 58
Radial rapidity-field with angular modulation
Freeze-out on azimuthally symmetric hypersurface
of temperature T
Collapse of the radial integration onto shell
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Elliptic Flow in the Blast Wave
Reproduces momentum - and mass
dependenceof elliptic anisotropy

• Tdec 140 MeV
• r0 0.58
• f2 7.7

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Anisotropic Flow in the Blast Wave
Blast wave parametrization for non-central
collisions
Huovinen, PFK, Heinz, Ruuskanen, Voloshin, PLB
503 (01) 58
Radial rapidity-field with angular modulation
Freeze-out on azimuthally symmetric hypersurface
of temperature T
Collapse of the radial integration onto shell
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Blast Wave - Influence of f4
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Blast Wave - Influence of f6
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Sensitivity on f2 and f4
at some fixed transverse momentum (here pT 2 GeV)
an additional small quadropoledistortion in
the flow field yieldsa large quadrupole moment
inthe particle distribution
A purely elliptic flow anisotropyproduces a
small quadrupolemoment after folding with the
thermal distribution
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Anisotropies from a Black Lense
Carry the idea of Shuryak and Voloshin to higher
levels (higher orders)
PRC 66 (2002) 027902
NPA 715 (2003) 379
pure surface emission in the high pT limit (i.e.
from extreme jet-quenching)
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Limiting Anisotropies versus Centrality
Extremely interesting centrality dependence
This picture predicts a peanut like distribution
as well!
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One Thought on Coalescence
assume there are no higher order anisotropies on
the quark level
See talk by Art Poskanzer for experimental
results!
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Summary Why Study Higher Harmonics ?
Get a full picture of the transverse momentum
spectrum