Angular Correlations in STAR

1
Angular Correlations in STAR
Michael Daugherity for the STAR
Collaboration Graduate Student - University of
Texas
Fluctuations and Correlations Workshop Firenze,
July 2006
2
Outline

• Relating fluctuations and correlations
• Making a correlation measure from scratch
• Angular correlations in STAR
• Charge-dependent angular correlations

3
Event-by-Event Fluctuations
It all started by looking at event-wise mean pt
looking for anomalous events

• Distribution is smooth, contrary to some
  phase-transition model predictions...
• but its broader than expected.
• A measurement of non-statistical fluctuations

Data
mixed event reference
But what causes fluctuations? How do we quantify
and interpret the result?
14 increase
it turns out that measuring pt fluctuations is
fairly difficult
similar to z-score in statistics, counts number
of ss away from mean
4
Fluctuation Measures
A large number of multiplicity, net charge, and
transverse momentum fluctuation measures have
been used at SPS at RHIC ?-,dyn, ?(Q), Fq, D,
?s2nch, ?s2q, Fpt, Spt, Fpt, s2pt,dyn, ?sptn,
etc. Not much agreement on how to quantify
fluctuations, but the essential common feature is
an integral of a covariance
Cov ltxygt - ltxgtltygt mean of products -
product of means object -
reference
Zero covariance means ltxygt ltxgtltygt, thus ltxgtltygt
is our uncorrelated reference

• We can understand fluctuations by measuring
  2-particle correlations
• Easier to interpret and relate to physical
  processes
• Must use all pairs equally, no high-pt trigger
  requirement

5
The Big Picture
STAR Preliminary
A formal relationship between fluctuation,
covariance, and correlation
Defined as variance - reference
PRC 71, 064906
More on fluctuations and inversion this afternoon
Written as covariance between bins a and b
fluctuation
hep-ph/0506173
Integral of correlation
J Phys G 31 809-824
sum over bins
correlation
2D binning function
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Correlation Measures
Number Correlations
Covariance ?? object - reference
Or, defining ?? as a histogram, bin (a,b) can be
written as
e bin width, converts density to bin counts
is a per-particle measure
Normalize
This measure comes from a direct application of
the standard correlation function, and all we
have to do is count pairs
We calculate this as a function of (?? ?1
?2, F? F1 F2), separation in pseudorapidity
and azimuth (axial momentum space)
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Correlation Measures
?sib
dominated by ?? acceptance permil corr signal
??
F?

• The terminology
• correlation measured as a function of variable
  x for each particle, e.g. (x1,x2)
• autocorrelation transformed to relative
  variable x? x1 x2 by averaging along xS x1
  x2, requires stationarity along xS
• joint autocorrelation autocorrelation as
  function of two different relative variables,
  e.g. (x?,y?)
• The joint autocorrelation (?? ?1 ?2, F? F1
  F2) compactly represents the entire axial space

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Correlation Analysis

• A quick recap before moving on
• Fluctuation measures all depend in some way on
  covariance (correlations) of particles, but no
  agreement on normalization and other factors
• Relating fluctuation to correlations places the
  results in a larger context
• Correlations can be defined with straightforward
  statistics, and have a direct physics
  interpretation
• By looking at all possible pairs we measure
  correlations that are minimum-bias,
  model-independent, and require no high-pt trigger

• Next up, two examples of correlation analysis
• Proton-Proton
• the essential reference before tackling Au-Au
• well known and described physics in terms of
  soft transverse strings and semi-hard scattering
• Hijing
• what changes from p-p to Au-Au, and what changes
  with centrality?
• does quenching describe the data well?

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Proton-Proton
minimum-bias i.e. no high-pt trigger
We expect to see STRINGS (soft, Lund-model) and
MINIJETS (semi-hard, back-to-back scattering)
proton-proton 200 GeV axial
STAR Preliminary
STRING
1D Gaussian
away-side ridge
MINIJET
same-side jet cone
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Proton-Proton
hep-ph/0506172
away-side F? p
MINIJETS
same-side small opening angle
yt2

• This is a minimum-bias jet, no trigger particle
  required
• we can see jets down to 0.5 GeV

STAR Preliminary
yt1
STRINGS
HBT
string fragments 1D Gaussian on ??
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HIJING
proton-proton
Au-Au 200 GeV
Quench Off
peripheral (70-80)
mid (40-50)
central (0-5)

• We can do the same soft/hard cuts and see the
  same string and minijet components as in p-p
• Hijing predicts very little change with
  centrality, soft component a bit smaller in
  central, but no major modifications
• The jet quenching does reduce the hard
  component, but again no modifications to
  correlation structures

central quench on
http//www.rhip.utexas.edu/daugherity/analysis/hi
jing/index.html
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Au-Au 130 GeV
300k events 0.15 lt ptlt2 GeV/c hlt1.3, full
f2p merging HBT cuts applied
PRC, in press (nucl-ex/0411003)
Features peak at small relative angles
cos(fD) - momentum conservation at low pt
cos(2fD) - elliptic anisotropy
Now remove the (??-independent) sinusoids to
isolate the small-angle peak
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Au-Au 130 GeV
sinusoids removed
Widths
p-p
130 GeV Au-Au mid-central
s?
sF
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Au-Au 62 GeV
proton-proton

• Correlation structure evolves smoothly from p-p
  to central Au-Au
• We see strings disappearing and minimum-bias
  jets being modified

80-90
70-80
60-70
50-60
90-100
F?
??
STAR Preliminary
30-40
20-30
10-20
5-10
0-5
F?
??
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Au-Au 200 GeV
Similar to 62 GeV, but strings damp out more
quickly, and broadening along ?? is more dramatic
80-90
70-80
60-70
50-60
90-100
F?
??
STAR Preliminary
30-40
20-30
10-20
5-10
0-5
F?
??
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Possible interpretation
Interaction with longitudinally expanding medium
carries radiated gluons and hadron fragments
along pseudorapidity
Fragmentation asymmetry reverses from p-p to
Au-Au
dramatic evolution with centrality
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Axial Correlations Recap

• The dominant feature is a jet-like correlation
  that broadens with centrality
• consistent with coupling to longitudinally
  expanding medium
• Minimum-bias correlations reveal dynamics of
  low-Q2 partons
• new access to non-perturbative interactions
• These correlations have significant energy and
  centrality dependence
• This rich structure drives observed multiplicity
  fluctuations
• Measuring the correlations directly gives new
  insight into the physics behind the fluctuations

Up Next measuring charge-dependent correlations
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Charge-Dependent Correlations

• We can access additional dynamics by considering
  the relative charge of particle pairs
• Like Sign (LS and --) pairs include quantum
  interference correlations and boson enhancement
  from identical particles
• Unlike Sign (US - or -) pairs are produced
  nearby from quark-antiquark pairs and resonance
  decays
• We expect to see a short-range enhancement of US
  pairs.

Charge-ordering
In string fragmentation models, the
charge-ordered particles are also ordered in ?
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CD References
CI
Proton-Proton
STAR Preliminary

CD
US
LS
No structure on F?
Gaussian on ??
HIJING

• p-p shows charge-ordering signal as Gaussian on
  ?? with no structure on F?
• Hijing also shows charge-ordering along ?? and
  no change with centrality

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STAR 130 GeV Charge-Dependent
PLB 634 347
Same plots viewed from above
The 130 GeV data show changes in structure with
centrality, need finer centrality bins to see
more
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Au-Au 62 GeV
proton-proton

• Good agreement between p-p and peripheral bin
• Smooth evolution to symmetric exponential signal

80-90
70-80
60-70
50-60
90-100
F?
??
STAR Preliminary
30-40
20-30
10-20
5-10
0-5
F?
??
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Au-Au 200 GeV

• Similar to 62 GeV results
• 1-D Gaussian on ?? disappears more quickly

80-90
70-80
60-70
50-60
90-100
F?
??
STAR Preliminary
30-40
20-30
10-20
5-10
0-5
F?
??
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Charge-Dependent Summary

• The largest correlation amplitude observed at
  RHIC

• Smooth evolution all the way from proton-proton
  to central Au-Au

peripheral Au-Au
mid Au-Au
proton-proton
central Au-Au

• Evidence for charge-ordering moving from
  one-dimensional string to a surface
• The 1-D signal becomes symmetric on ?? and F? in
  central Au-Au
• Inconsistent with resonance gas or string
  fragments

• Evidence for attenuation through an opaque
  medium
• The change from Gaussian to exponential implies
  pair loss increasing with opening angle,
  consistent with attenuation through a medium

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Summary Angular Correlations
Au-Au 200 GeV
p-p 200 GeV
minijet
pt gt 0.5 GeV
minijet correlations
peripheral
central
no pt cut
pt lt 0.5 GeV
elongation
string
net-charge correlations
charge-ordering
peripheral
central
1D
2D
LS - US
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Conclusions

• Fluctuations and correlations provide different
  manifestations of underlying dynamics
  correlations are more readily interpreted.
• Correlations show that multiplicity and ltptgt
  fluctuations at RHIC are driven by minijets,
  while net-charge fluctuations are related to
  charge-ordering
• String fragmentation and minimum-bias jet
  correlations smoothly and dramatically evolve
  from p-p to central Au-Au.
• Our observations are consistent with the
  following interpretation
• semi-hard processes measured in p-p are embedded
  in an increasingly dense and thick longitudinally
  expanding medium in Au-Au.
• hadronization via longitudinal strings in p-p
  becomes insignificant in Au-Au where the bulk
  medium hadronizes isotropically along the axial
  surface.

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The Big Picture

• We have developed a general and powerful method
  for measuring two-particle correlations
• These number correlations were found by counting
  pairs, but covariance derivation allows for easy
  extension to any arbitrary function
• so we can directly measure the correlations
  relating to any non-statistical fluctuation
• Results are model independent and minimum-bias,
  includes important measurements of low-Q2
  dynamics
• other correlation measurements done at RHIC
  require jet hypothesis and trigger bias or are
  limited in phase-space
• The Bottom Line A lot of work has been invested
  on integral measures of fluctuations, but
  differential measures of correlations show
  dramatic novel behavior and access new physics