Azimuthal correlations and anisotropic flow: trends and questions

1
Azimuthal correlations and anisotropic flow
trends and questions
Not a review, Not a presentation of STARresults
Sergei A. Voloshin

• Definitions What is flow and what is non-flow?
  Spatial asymmetry?Let us speak the same
  language!
• Continuous worry is it really collective? Has
  anything to do with the impact parameter
  orientation (real flow)? q -distributions.
  Measuring non-flow in AA and pp.
• Non-flow and many particle correlations. Mixed
  harmonics analysis.
• Many reasons for flow fluctuations. Fluctuations
  contribution to mixed harmonic analysis.
• 2-particle correlations at different angles to
  the Reaction Plane High pt, azHBT,non-identical
  particles, balance functions.
• Conclusions/Summary

2
Anisotropic flow. Definitions vs
Fourier decomposition of single particle
inclusive spectra
Anisotropic flow ? correlationswith respect to
the reaction plane
Term flow not necessarily hydro flow used
only to emphasize the collectivebehavior ??
multiparticle azimuthal correlation.
Non-zero v4 is it bad?
v2 in pp collisions is almost 100 event
anisotropy at high pt, elliptic flow at low pt
The situation is not totally clear for 2-particle
spectra. Discussed a little bit below.
3
Anisotropic flow. Definitions ?s
Other similar/same quantities Ollitrault
?s Heiselberg ? Sorge A2 Shuryak s2

• The physics is (due to Sorge) that v2 is
  proportional to any of them. Better to use the
  samedefinition to allow cross comparison (unless
  a new physics based relation established).
• (Low density limit (Heiselberg) is probably the
  best to check the meaning)
• Note
• - it is not at all trivial what should be used
  (if any) for higher harmonics (no simple form)
• - s2 parameter in the Blast Wave fit to v2(pt)
  in general is a different parameter
• -- do not confuse initial and final state
  anisotropy

4
Flow due to absorption. v2, v4 e2, e4
See also nucl-th/0310044 A. Drees, H. Feng, J.
Jia
Surface emission limit,hard sphere
V2
Such absorption corresponds to suppression for
inclusive yield in central collisionsabout
factor of 4-5
WS density,finite absorption
b/2RA
Not clear what should be used for ?4
ltcos(4?)gt would behave quite differently (sign,
etc.)
5
Looking for collectivity q-distributions
Used in the very first E877 analysis
Distribution in the magnitude of the flow vector
Non-flow contribution widening of the
distribution
Correlations due to flow shift of
the peak
Better shape description ? higher moments
(cumulant orders)? new method of Ollitrault (?)
6
v2 from q-distributions
STAR, PRC 66 (2002) 034904
-- The results are very close to those from
4-particle correlation analysis. -- Difficult to
trace the contribution of flow fluctuations.
7
Azimuthal correlation in pp collisions

• Goals (from flow point of view)
• Check if non-flow estimates/measurements reported
  for AuAu are consistentwith measurements in
  pp. (One could expect the difference of the
  order of factor of lt2. Examples Extra
  particles in jets ? non-flow ? B-to-B jet
  suppression - ?)
• Use pp data to estimate non-flow effects in AuAu
  in the regions where othermethods do not work
  well (like high pt region Kaon and Lambda ? )
• Approach/method
• Scalar product. The basic quantity in this
  approach isAdvantages simpler to work with
  and much simpler to interpret.

Flow ? ? non-flow
Subscript 2 is omitted in equations on a next
few slides.
8
?uQ? in pp and AA collisions
9
pp vs. AA
Most peripheral
Mlt10
0 pt 7 GeV
STAR Preliminary
5 central
STAR results are presented by A. Tang at this
workshop
Mgt500
The plot above, showing the rise and fall of
azimuthal correlations ( Mltuugt)can be explained
only by flow no any other known source of the
azimuthal correlation is able to give such a
dependence. The origin of such dependence M
?
10
Mixed harmonics how it works
What to do when the reaction plane is known
(AMP, SV PRC method paper)
and when it is not exactly known
Borghini, Dinh, Ollitrault
11
Non-flow and mixed harmonics
Compare to 56 ?10-3 reported.
-- Totally relies on non-flow estimates for
v2. -- Higher order cumulants do not help
12
Non-flow or Fluctuations?
Correct if v is constantin the event sample
Should be used even in a case of ?0

• Several reasons for v to fluctuate in a
  centrality bin
• Variation in impact parameter in a given exp.
  centrality bin (taken out in STAR PRC flow
  paper)
• Real flow fluctuations (due to fluctuations in
  initial conditions, in localparticle density,
  or in the system evolution)

13
Fluctuations in eccentricity ? fluctuations in v2
x,y coordinates of wounded nucleons
Calculations R. Snellings and M. Miller
v2 ? ? fluctuations in flow
14
Compare to data
R. Snellings
Fluctuations in initial geometrycould explain
the entire differencebetween v22 and v24
15
Flow fluctuations mixed harmonics
Calculations by R. Snellings. ltcos(4?s) used as e4
The effect can be as large as factor of 3
16
Where we are checking with oldstuff
S.V. RHIC Winter Workshop, Berkeley,
January 1999 http//www-rnc.lbl.gov/nxu/oldstuff/
workshop/rww99.html
17
2-particle correlations wrt RP
x azimuthal angle, transverse momentum,
rapidity, etc.
Approach - remove flow contribution-
parameterize the shape of what is left - study RP
orientation dependence of the parameters
18
STAR Results
K. Filimonov, STAR, DNP 2003
Back-to-back suppression is larger in the
out-of-plane direction
Complications particles in the trigger pt
region could have different originand
correspondingly different flow.
19
Approach Same Opposite
Work with differences ( of associated
particles in the SAME direction) - ( of
associated particle in the OPPOSITE
direction) Advantage Flow contribution cancels
out exactly.
STAR, PRL 90 (2003) 082302
Next step compare differences for 2 different
pseudorapidity windowsused to count the
associated particles ? get numbers of Same and
Opposite separately. Here one has to use one
of the assumptions - the eta distribution of
associated particles in opposite direction is
flat, or - it is the same as in pp collisions
20
Only sketch
Number ofassociatedparticles. Same
Opposite
Out-of-plane In-plane
central
peripheral
(!) Larger difference values correspond to either
larger same or smaller opposite.
21
azHBT
S.V. LBNL 1998 annual report R20http//ie.lbl.g
ov/nsd1999/rnc/RNC.htm
RQMD v 2.3, AuAu _at_ RHIC
22
azHBT-2
Should we try very low kT at RHIC?
IPES initial conditions, U. Heinz, P. Kolb PL
B542 (2002) 216
23
Non-identical particle correlations
24
Summary trends, questions

• Please avoid (unnecessary) introduction of new
  terms
• Not clear what, if any, to use instead of e2 for
  higher harmonics
• How to get rid of non-flow effects at the level
  of 0.1 level (vn)
• How to disentangle non-flow and flow fluctuations
  effects
• 2-particle correlations with respect to the RP-
  future direction?
• How to disentangle jet and soft flow at
  intermediate pt?
• Is the azHBT sensitive to the in-plane
  expansion?
• Plasma of constituent quarks?

Thanks to STAR flow group for discusion