Elliptic Flow Fluctuations and

1
Elliptic Flow Fluctuations and Non-flow
correlations
Paul Sorensen
Brookhaven National Laboratory
for the
collaboration
2
introduction
ambiguity arises in calculations from uncertainty
in initial conditions perfect fluid conclusion
depends on ambiguous comparison to ideal hydro
motivation to measure v2 fluct. find observable
sensitive to initial conditions

• Talk outline
• analysis procedures and changes since QM06
• non-flow ?2 and ?v2 from the q-distribution
• comparison to cumulants v2, v4
• v2 of events with a ridge and/or a jet!

See STAR Poster Navneet Kumar Pruthi
3
flow vector distribution
J.-Y. Ollitrault nucl-ex/9711003 A.M. Poskanzer
and S.A. Voloshin nucl-ex/9805001

• q-vector and v2 related by definition v2
  ?cos(2?i)? ?q2,x?/vM
• sum over particles is a random-walk ?
  central-limit-theorem
• width depends on
• non-flow broadens ?n ?cos(n(?i- ?j))?
  (2-particle corr. nonflow)
• v2 fluctuations broadens

4
flow vector distribution
from central limit theorem, q2 distribution is a
2-D Gaussian
Ollitrault nucl-ex/9711003 Poskanzer Voloshin
nucl-ex/9805001
x, y directions are unknown ? integrate over all
?? and study the length of the flow vector q2
fold v2 distributions ƒ(v2) with the q2
distribution to account for fluctuations ?v2
correction to QM06 analysis those results were
an upper limit
dynamic width dominated by non-flow and/or
fluctuations ? not determined independently
5
non-flow evident
width depends on the track sample differences
are due to more or less non-flow in various
samples smaller ?2 for like-sign (charge
ordering) larger ?2 for small ? (strong short
range correlations)
also in 2-D correlations can be fit with a ??
independent cos(2??) term non-flow structures
See STAR Talk Michael Daugherity
STAR Preliminary
N.B. relationship of measured ?2 from 2 particle
correlations and dynamic width is not trivial
depends on ZYAM and 2-component model (see backup
slides)
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dynamic width from dN/dq fit
see Miller, Snellings, nucl-ex/0312008

• includes systematic errors from comparisons to
  cumulants
• minimum ?2 derived from differences between
  subevents qq - q?q?-

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mean and width of ƒ(v2)
analysis places an upper limit on flow
fluctuations
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comparison to models
upper limit challenges models
confined quark MC treats confined constituent
quarks as the participants decreases eccentricity
fluctuations color glass MC includes effects of
saturation increases the mean eccentricity
comparison to hydro (NexSPheRio) Hama et.al.
arXiv0711.4544 eccentricity fluctuations from
CGC Drescher, Nara. Phys.Rev.C76041903,2007 ext
raction of Knudsen number Vogel, Torrieri,
Bleicher. nucl-th/0703031 fluctuating initial
conditions Broniowski, Bozek, Rybczynski.
Phys.Rev.C76054905,2007 first disagreement with
?standard and use of quark MC Miller, Snellings.
nucl-ex/0312008
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can we eliminate ?v2 0?
is there any evidence for v2 changing
event-to-event?

• consider events containing two high-pT tracks
  (pTgt2 GeV/c)
• is the average v2(pTlt2 GeV/c) still the same in
  this sample?
• or when the high pT tracks are correlated at
  large ??? or small ???
• or when the tracks are uncorrelated?

STAR Preliminary
dN/dq for low pT tracks vs ?? for the high pT
leading hadrons shape of the q-distribution for
underlying event has non-trivial dependence on ??
and ?? of the leading and next-to-leading hadron
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event classes?
characteristics of the events yielding a ridge
pair appear to be very different from those
yielding a jet pair
See STAR Poster Navneet Kumar Pruthi
jet
ridge
STAR Preliminary

• the ridge is calculated by projecting ??gt0.7
  correlation to ??lt0.7
• the jet is the remaining correlation at
  ??lt0.7 after subtracting the ridge

• inferred v2 for events associated with ridge
  pairs is large
• inferred v2 for events associated with jet
  pairs is small
• this conclusion is a direct consequence of the
  zero-yield at minimum assumption and the
  3-component model (v2 modulated background
  ridge jet)

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event classes?
events yielding a ridge-like pair have large
v2 events yielding a jet-like pair have small v2

• possible interpretations
• interactions of a jet with the medium and medium
  response to a jet (radial flow coupling to a jet
  C.Pruneau, nucl-ex/0711.1991)
• do initial state quantum fluctuations lead to
• instabilities and growth of strong color fields
  M. Strickland, hep-ph/0511212
• large q and small ?/s Majumder, Muller, Bass.
  Phys.Rev.Lett.99042301,2007
• un-quenched jets can preferentially come from
  events fluctuating towards small q and large ?/s
  (small flow)?
• strong fields lead to the ridge and large v2?
• what about jets on the periphery? and tangential
  jets? momentum conservation effects?

12
summary

• we find that the case of zero v2 fluctuations
  cannot be excluded with dN/dq without knowledge
  of non-flow, cluster flow, and non-poissonian
  multiplicity fluctuations
• analysis places stringent constraints on ?2, ?v2,
  and ?v2?
• when one parameter is specified, the others are
  fixed
• measurement challenges standard Monte-Carlo
  Glauber models
• upper limit is below standard nucleon MC Glauber
• upper limit coincides with participating nucleon
  eccentricity fluctuations
• nucleon MC Glauber leaves no room for other
  sources of fluctuations correlations
• Is there any evidence that v2 fluctuates? Not
  from untriggered dN/dq but analysis of high pT
  triggered events seems to indicate non-zero ?v2.

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the following is back-up material
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the statistical decomposition

• decomposition into events that yielded
• uncorrelated high pT pairs
• correlated and ridge-like high-pT pairs
• correlated and jet-like high-pT pairs

• each bin has a different signal to background
  ratio.
• analyze the q-distribution of events
  contributing to each bin
• algebraically solve for the q-distribution of
  signal and background separately

15
acceptance effects
about 4
acceptance effects could mimic correlations
unrelated to the event plane easy to quantify
using simulations run through a TPC
filter quantified systematics from CLT
approximation
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relationship to 2-particle corr.
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more about 2-particle correlations
simple case ?v20.00 ?2 should be the width of
the q-distribution
zyam b makes ?2 too small
vary b until ?22?v2 matches q width
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more about 2-particle correlations
add some fluctuations ?v20.010 ?2 should be
smaller
zyam b makes ?2 too small
vary b until ?22?v2 matches q width
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more about 2-particle correlations
add some fluctuations ?v20.015 ?2 should be
smaller
zyam b makes ?2 too small
vary b until ?22?v2 matches q width
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more about 2-particle correlations
add some fluctuations ?v20.020 ?2 should be
smaller
zyam b makes ?2 too small
vary b until ?22?v2 matches q width
21
more about 2-particle correlations
add some fluctuations ?v20.025 ?2 should be
smaller
zyam b makes ?2 too small
vary b until ?22?v2 matches q width
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more about 2-particle correlations
add huge fluctuations ?v20.045 ?2 should be
smaller
zyam b makes ?2 too small
vary b until ?22?v2 matches q width
v22 5.154e-02 v24 4.093e-02 ltv2gt
6.083e-02 v22 sqrt(ltv2gt2 sigv2 delta)
5.202e-02 sigv/ltv2gt 73.98
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more about 2-particle correlations
add huge fluctuations ?v20.045 ?2 is now
negative
huge ?v2 and negative ?2
the subtracted yield
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whats going on
?2 observed in two-component model depends on
jet-flow difference between simulated ?2 and
observed ?2 depends on cluster flow there are
still more variables that can come into play ?
highly probable that multiple solutions could
match the STAR data
25
compared to autocorrelation 2D fit
difference between 2-D fit and projection over
all autocorrelations ? introduces dependence on
function used to fit the data
!! words of caution about inter-analysis
comparisons !! be careful
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comparison to Estruct
lets see what happens if we take those values
for ?2
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?v2? and ?v2
caution! not necessarily a consistent picture yet
with fit to autocorrelations
STAR Preliminary
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comparison to geometric ??
fluctuations from finite bin widths have not been
removed yet likely to reduce ratio below the
model!
systematic uncertainties are still large and
under investigation
STAR Preliminary
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confined quark monte carlo
models of the initial conditions are not trivial
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introduction

• motivation for this study
• use v2 fluctuations to try to access information
  about initial geometry distinguish between
  models of initial conditions
• reduce systematic errors on v2
• results from 200 GeV AuAu collisions
• analysis procedures and change in QM06
  conclusions
• non-flow ?2 and ?v2 from the q-distribution
• comparison to cumulants v2, v4
• v2 of events with a ridge and/or a jet!

See STAR Poster Navneet Kumar Pruthi