Twoparticle number and transverse momentum correlations in AuAu collisions at RHIC

1
Two-particle number and transverse momentum
correlations in Au-Au collisions at RHIC
Michael Daugherity Graduate Student - University
of Texas

• APRIL APS Meeting
• Dallas, TX 2006

2
Outline

• Relating fluctuations and correlations
• Constructing correlation measures
• Correlation measurements in Au-Au collisions at
  RHIC

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
pretty hard
similar to z-score in statistics, counts number
of ss away from mean
4
Fluctuation Measures
Transverse momentum fluctuation measures from SPS
and RHIC include Fpt , Spt , Fpt , s2pt,dyn ,
?sptn Not much agreement on how to quantify ltptgt
fluctuations, but they are all integrals of a
covariance
Cov ltxygt - ltxgtltygt mean of products -
product of means object -
reference
Now we can take Pearsons Correlation
Coefficient
the gold-standard correlation measure for the
last 100 years.

• 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
ltptgt at full STAR acceptance
Correlation
invert
integrate
Scale (bin size) dependence
Defined as variance - reference
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
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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Transverse Momentum Correlations
Using the covariance notation, we can generalize
the correlation measure
NUMBER
How not to do it
We cant use event-wise mean pt
Ratio of fluctuating quantities, high systematic
error
We also want to separate out multiplicity
fluctuation dependence
want to avoid this
This is why the fluctuation measure is defined as
when we invert this, we get pt (not number)
correlations
8
Proton-Proton
hep-ph/0506172

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

soft/hard components decomposed by cuts on
transverse rapidity correlations
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proton-proton

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

STAR Au-Au 62 GeV Number Correlations
Peripheral
F?
??
STAR Preliminary
Central
F?
??
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Au-Au Number Correlations

• the soft, longitudinal component disappears and
  the jets are modified

STAR Au-Au 200 GeV Number Correlations
Peripheral
F?
??
STAR Preliminary
Central
F?
??
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Comparing Correlation Measures
nucl-ex/0411003
Number
subtract cos(F?) and cos(2F?) components to
compare peaks
nucl-ex/050903
pt
Several new features
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Overview

• Fluctuations may be expressed as integrals of
  correlations
• The correlations seen in p-p are well described
  by jets and soft, longitudinal scattering
• Peripheral A-A is very similar to p-p, but the
  features are strongly modified in central
  collisions, even more so at higher energies
• The correlation features evolve smoothly with
  centrality and energy and are dominated by
  jet-like correlations

?s2
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Conclusions

• Correlations provide insight into the sources of
  fluctuations
• Minimum-bias two-particle correlations give
  unique access for studying HI collisions
• More applications of correlation measurements and
  interpretations in the next talk

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Extra Slides
15
Separating soft from hard
Spectrum on transverse rapidity yt using
two-component model
Correlation on yt
hard
soft
peak 2.7
peak 2.7
cut region
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Proton-Proton
see tutorials at http//www.star.bnl.gov/STAR/estr
uct/tutorial/ for more explanation of these
correlation structures
hep-ph/0506172
away-side F? p
JETS
same-side small opening angle
yt2
An open question are Lund-model strings viable
in central Au-Au collisions?
yt1
STRINGS
HBT
string fragments 1D Gaussian on ??
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pt Correlations
20-30
3 Gaussian model
70-80
fit
data
fit peak
20-30
data - fit peak
fit residuals
0-5
18
plotted in cylindrical coordinates
data - fit peak
Why does the jet cone sit inside a negative peak?
Medium recoil? Momentum red-shift?
The jet punches the medium
freeze-out
The medium responds
The number of particles doesnt change, but their
momenta do