Transcript Anisotropic Flow @ RHIC Hiroshi Masui / Univ. of Tsukuba Mar/03/2007

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Anisotropic Flow
@ RHIC
Hiroshi Masui / Univ. of Tsukuba
Mar/03/2007
Heavy Ion Cafe
Anisotropic Flow
• What ?
Z
– Azimuthally anisotropic
emission of particles with
respect to the reaction plane
• Why ?
– The probe for early time
– Initial spatial anisotropy
(eccentricity, )
– Low pT
Y
X
Py
• Re-scattering (pressure
gradient)
Pz
– Intermediate pT
• Quark
coalescence/recombination
Px
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– High pT
H. Masui / Univ. of Tsukuba
• Jet quenching
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3
Observables
• Particle azimuthal
distributions by
Fourier expansion
• v1 = “Directed Flow”
• v2 = “Elliptic Flow”
S. Voloshin and Y. Zhang, Z. Phys. C70, 665 (1996)
A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C58, 1671 (1998)
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H. Masui / Univ. of Tsukuba
Flow analysis @ PHENIX
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PHOBOS: PRL91, 052303 (2003)
• Event plane method
– Determined at forward and backward beam counter
(BBC, || = 3.0 - 3.9)
• Correlate paticles at mid-rapidity (|| < 0.35) and
BBC event plane
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Event plane method

• “Event plane”
– Estimate of true reaction plane
• Brackets denote average over all events and all particles in a
selected rapidity window, kn is “event plane resolution”
• w (weight) is chosen to maximize the event plane resolution (ex.
pT, multiplicity etc)
– The best weight is vn itself
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Flattening correction
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• Acceptance anisotropy
should be removed
• Re-centering correction
– black -> blue
• Flattening correction
– remove remaining nonflat contributions (blue > red)
•  should be small
• Isotropic distribution ->
vanishing of k-th Forier
moment of the new
distribution ()
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Large v2 at RHIC
QM2005, H. Masui
RQMD
FOPI : Phys. Lett. B612, 713 (2005). E895 : Phys. Rev. Lett. 83, 1295 (1999)
CERES : Nucl. Phys. A698, 253c (2002). NA49 : Phys. Rev. C68, 034903 (2003)
STAR : Nucl. Phys. A715, 45c, (2003). PHENIX : Preliminary.
PHOBOS : nucl-ex/0610037 (2006)
• ~ 50 % increase from SPS to RHIC
• Hadron cascade underestimate the magnitude of v2 at
RHIC
– Due to the small transverse pressure in early times
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H. Masui / Univ. of Tsukuba
Event plane = reaction plane ?
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• We cannot determine the direction of
2nd moment BBC event plane w.r.t. the
reaction plane  sign of v2 is unknown
• 1st moment event plane give us the
reference direction
y
Py
or
x
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Px
H. Masui / Univ. of Tsukuba
Validity check (1)
• 2nd moment BBC event plane
– Same direction
– Cannot distinguish in-plane or out-of-plane
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H. Masui / Univ. of Tsukuba
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Validity check (2)
• 2nd moment Central Arm Event plane
– Same direction to BBC Event plane
– Still, sign is unknown
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H. Masui / Univ. of Tsukuba
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Validity check (3)
• 1st moment BBC and
SMD Event plane
– Back-to-back direction
for both BBC and SMD
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Validity check (4)
• BBC(1st) - SMD(1st) correlation
– Opposite direction to same side SMD
– Opposite v1 for BBC and SMD
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Validity check (5)
• BBC(2nd) - SMD(1st) correlation
– Positive correlation  v2 is in-plane !
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Outline
• Large v2 at RHIC
– v2 is in-plane ! Initial geometry origin ?!
• v2 is expected to be driven by
– initial eccentricity
– pressure (density) gradient
• Explore the origin of v2 : Several scaling
properties of v2
– Eccentricity scaling
– Transverse kinetic energy (KET) scaling + NCQ
(Number of Constituent Quark) scaling
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H. Masui / Univ. of Tsukuba
Eccentricity
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• Estimate eccentricity by Glauber
Model
• std (part) gives minimum
(maximum) eccentricity
– Since part include auto-correlation
• True  lies between std and part ?
Mar/03/2007
H. Masui / Univ. of Tsukuba
Eccentricity scaling (1)
PRL:
nucl-ex/0610037
• Scaling of v2/part in Cu+Cu
and Au+Au
• Participant eccentricity is
relevant geometric quantity
for generating elliptic flow
PRC C72, 051901R (2005)
standard
Cu+Cu
200 GeV
participant
Statistical errors only
Au+Au
200 GeV
PHOBOS Collaboration
PRL: nucl-ex/0610037
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H. Masui / Univ. of Tsukuba
Eccentricity scaling (2)
QM2006, S. A. Voloshin
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• v2{ZDC} scales std
– Insensitive the
fluctuations in the
participant eccentricity
• Linear increase of v2/
from SPS to RHIC
– Incomplete
thermalization ?
– Saturation ?
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H. Masui / Univ. of Tsukuba
Eccentricity scaling (3)
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• PHENIX uses integrated v2
as the estimate of eccentricity
– Assume  = k  v2, k = 3.1  0.2
from Glauber model
– Cancel systematic error from
event plane
• v2 scales with  and the
scaled v2 values are
independent of the system
size
– Centrality independent shape
of v2(pT)/v2
– pT does not change so much
nucl-ex/0608033
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KET scaling
nucl-ex/0608033
Baryon
Meson
•
•
PRC69, 034909 (2004)
Pressure gradient  Collective kinetic energy
Radial flow with common velocity T ~ 0.5c
– Gain more energy for heavier particles  mass ordering of v2
•
•
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KET scaling holds up to KET ~ 1 GeV
Clear meson and baryon splitting at intermediate pT
H. Masui / Univ. of Tsukuba
Centrality dependence
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• KET scaling holds for
measured centrality
range up to KET ~ 1
GeV
– Centrality dependence ?
Mar/03/2007
H. Masui / Univ. of Tsukuba
NCQ scaling of v2
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• NCQ scaling indicate
the collective flow
evolves in quark level
•
•
Number of Constituent Quark
scaling by quark coalescence /
recombination model
Assumption
– Exponential pT spectra
– Narrow momentum spread (function)
– Common v2 for light quarks (u, d,
s)
R. J. Fries, et., al, Phys. Rev. C68, 044902 (2003)
V. Greco, et., al, Phys. Rev. C68, 034904 (2003)
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 meson
•  meson v2
– Important test at
intermediate pT
• m ~ mp
• Mass (radial flow)
effect, or constituent
quarks
QM06, A. Taranenko
•  scales like a meson
– s-quark flow, not mass
effect
– Smaller radial flow
velocity also support the
partonic flow at prehadronic stage
SQM06, N. Xu
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H. Masui / Univ. of Tsukuba
Universal scaling of v2
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QM06, A. Taranenko
• Substantial elliptic flow
signals are observed for a
variety of particles species
at RHIC
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H. Masui / Univ. of Tsukuba
Universal scaling of v2
QM06, A. Taranenko
At mid-rapidity
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Summary
• Eccentricity scaling
– RHIC v2 is driven by eccentricity
• In-plane v2, and eccentricity scaling
– Participant eccentricity is relevant geometric quantity for generating
elliptic flow
• KET scaling
– KET scaling of v2 holds up to KET ~ 1 GeV
• Consistent with the flowing matter with common velocity
– At intermediate pT, NCQ scaling holds a variety of particles species
• Indication of light quark (u, d, s) collectivity at pre-hadronic stage
• Universal scaling of v2 (Eccentricity + KET + NCQ) works for a
variety of particle species and for a side range of centrality
– Need to investigate the validity range of scaling
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Back up
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BBC - SMD EP correlation
• Positive correlation, v2 > 0 at BBC
• Expected cos(2) is given by
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Differential v2, v2(pT) :
PHENIX vs STAR (Au+Au)
STAR : Phys. Rev. Lett. 93, 252301 (2004)
PHENIX : Preliminary
• Non-flow effects are under control
– v2{4}  v2{BBC} ~ v2{FTPC} < v2{2}
• Similar acceptance : BBC, FTPC
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QM2006, S. A. Voloshin
v2(pT) in Cu+Cu
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STAR preliminary (QM06, S. A. Voloshin)
PHENIX
v2{2}
v2{FTPC}
PHENIX : nucl-ex/0608033
• Larger non-flow effects in smaller system
– Dominant non-flow is ~ O(1/N)
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Clear  signal
•   K+K– Typical S/N ~ 0.3
• Centrality 20 – 60 %
Before subtraction
Signal + Background
Background
After subtraction
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– S/N is good
– Event plane resolution is
good
– Separation of v2 between
meson and baryon is good
– Magnitude of v2 do not vary
very much
H. Masui / Univ. of Tsukuba