Elliptic Flow Fluctuations and

1
Elliptic Flow Fluctuations and Non-flow
correlations
Paul Sorensen
Brookhaven National Laboratory
Thank you to the Tata Institute for Fundamental
Research and the organizers
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 fluctuations find
an observable sensitive to initial conditions

• analysis of the distribution of the length of
  the flow vector
• non-flow ?2 and ?v2 from the q-distribution
• comparison to cumulants v2, v4
• relationship to 2 particle correlations
• v2 of events with a ridge and/or a jet!
• See STAR Poster at QM08 Navneet Kumar Pruthi

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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

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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
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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 at QM08 Michael Daugherity
STAR Preliminary
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dynamic width from dN/dq fit
see Miller, Snellings, nucl-ex/0312008
Caution! relationship of measured ?2 from 2
particle correlations and dynamic width is not
trivial depends on ZYAM and 2-component model
(see following slides)

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

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relationship to 2-particle corr.
ZYAM assumption that theres zero yield at the
minumum of the correlation function
above quantities are related to the width of the
q-distribution
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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
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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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compared to correlation 2D fit
difference between 2-D fit and projection over
all correlations ? introduces dependence on
uncontrolled assumptions
!! words of caution about inter-analysis
comparisons !! be careful
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?v2? and ?v2
consistency of this picture requires a
contribution of non-poissonian fluctuations that
breaks ZYAM
with fit to autocorrelations
STAR Preliminary
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comparison to geometric ??
result is not unique only the width ?dyn2
?22?v22 is uniquely determined multiple models
may find consistency with the data
systematic uncertainties are still under
investigation
STAR Preliminary
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comparison to models
upper limit using ?2gt0 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)
• is this evidence that 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?

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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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mean and width of ƒ(v2)
assuming ?2gt0 analysis places an upper limit on
flow fluctuations
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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

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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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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 data
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comparison to 2 part. correlations
lets see what happens if we take those values
for ?2
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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