Anisotropic Flow RHIC

1
Anisotropic Flow_at_ RHIC

• Hiroshi Masui / Univ. of Tsukuba
• Mar/03/2007
• Heavy Ion Cafe

2
Anisotropic Flow

• What ?
• Azimuthally anisotropic emission of particles
  with respect to the reaction plane
• Why ?
• The probe for early time
• Initial spatial anisotropy (eccentricity, ?)
• Low pT
• Re-scattering (pressure gradient)
• Intermediate pT
• Quark coalescence/recombination
• High pT
• Jet quenching

Z
Reaction plane
Y
X
Pz
Py
Px
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)
4
Flow analysis _at_ PHENIX
PHOBOS PRL91, 052303 (2003)

• Event plane method
• Determined at forward and backward beam counter
  (BBC, ? 3.0 - 3.9)
• Correlate paticles at mid-rapidity (? lt 0.35)
  and BBC event plane

5
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

6
Flattening correction

• Acceptance anisotropy should be removed
• Re-centering correction
• black -gt blue
• Flattening correction
• remove remaining non-flat contributions (blue -gt
  red)
• ?? should be small
• Isotropic distribution -gt vanishing of k-th
  Forier moment of the new distribution (?)

7
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

8
Event plane reaction plane ?

• 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

Py
y
or
x
Px
9
Validity check (1)

• 2nd moment BBC event plane
• Same direction
• Cannot distinguish in-plane or out-of-plane

10
Validity check (2)

• 2nd moment Central Arm Event plane
• Same direction to BBC Event plane
• Still, sign is unknown

11
Validity check (3)

• 1st moment BBC and SMD Event plane
• Back-to-back direction for both BBC and SMD

12
Validity check (4)

• BBC(1st) - SMD(1st) correlation
• Opposite direction to same side SMD
• Opposite v1 for BBC and SMD

13
Validity check (5)

• BBC(2nd) - SMD(1st) correlation
• Positive correlation ? v2 is in-plane !

14
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

15
Eccentricity

• Estimate eccentricity by Glauber Model
• ?std (?part) gives minimum (maximum) eccentricity
• Since ?part include auto-correlation
• True ? lies between ?std and ?part ?

16
Eccentricity scaling (1)

• Scaling of v2/??part? in CuCu and AuAu
• Participant eccentricity is relevant geometric
  quantity for generating elliptic flow

PRL nucl-ex/0610037
PRC C72, 051901R (2005)
standard
participant
CuCu 200 GeV
Statistical errors only
AuAu 200 GeV
PHOBOS CollaborationPRL nucl-ex/0610037
17
Eccentricity scaling (2)
QM2006, S. A. Voloshin

• v2ZDC scales ?std
• Insensitive the fluctuations in the participant
  eccentricity
• Linear increase of v2/? from SPS to RHIC
• Incomplete thermalization ?
• Saturation ?

18
Eccentricity scaling (3)

• 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
19
KET scaling
Baryon
nucl-ex/0608033
PRC69, 034909 (2004)
Meson

• Pressure gradient ? Collective kinetic energy
• Radial flow with common velocity ??T? 0.5c
• Gain more energy for heavier particles ? mass
  ordering of v2
• KET scaling holds up to KET 1 GeV
• Clear meson and baryon splitting at intermediate
  pT

20
Centrality dependence

• KET scaling holds for measured centrality range
  up to KET 1 GeV
• Centrality dependence ?

21
NCQ scaling of v2

• 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)
22
? meson

• ? meson v2
• Important test at intermediate pT
• m? mp
• Mass (radial flow) effect, or constituent quarks
• ? scales like a meson
• s-quark flow, not mass effect
• Smaller radial flow velocity also support the
  partonic flow at pre-hadronic stage

QM06, A. Taranenko
SQM06, N. Xu
23
Universal scaling of v2
QM06, A. Taranenko

• Substantial elliptic flow signals are observed
  for a variety of particles species at RHIC

24
Universal scaling of v2
QM06, A. Taranenko

• At mid-rapidity

25
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

26
Back up
27
BBC - SMD EP correlation

• Positive correlation, v2 gt 0 at BBC
• Expected ?cos(2??)? is given by

28
Differential v2, v2(pT) PHENIX vs STAR (AuAu)
STAR Phys. Rev. Lett. 93, 252301 (2004) PHENIX
Preliminary
QM2006, S. A. Voloshin

• Non-flow effects are under control
• v24 ? v2BBC v2FTPC lt v22
• Similar acceptance BBC, FTPC

29
v2(pT) in CuCu
STAR preliminary (QM06, S. A. Voloshin)
PHENIX
v22
v2FTPC
PHENIX nucl-ex/0608033

• Larger non-flow effects in smaller system
• Dominant non-flow is O(1/N)

30
Clear ? signal

• ? ? KK-
• Typical S/N 0.3
• Centrality 20 60
• 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

Before subtraction
Signal Background
Background
After subtraction