Transcript Event-by-event Fluctuations of the Particle Ratios

Event-by-event Fluctuations of
the Particle Ratios
D.Kresan, O.Bezshyyko, I.Kadenko, V.Shevchenko, V.Pluyko
Taras Shevchenko National University of Kyiv
Ukraine
CBM Collaboration Meeting
October 6 – 8 2004
Motivation
• Signal for the critical point
• Fluctuations carry the information about the
nature and order of the phase transition
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pt (GeV/c)
Acceptance
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rapidity
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pt (GeV/c)
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rapidity
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Inclusive analysis
Squared mass measured with TOF
1. UrQMD central Au + Au
at 25 AGeV
2. symmetrical field map
3. full geometry setup
4. time resolution 80 ps
Unfolding of inclusive squared
mass distribution in 2D binning
variable
range
bin size
p
1
10
0.1 (GeV/c)
m2
-0.5
2.0
0.005 (GeV2/c4)
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Inclusive analysis (2)
Unfolded m2 distribution
p = 6 GeV/c
Squared mass resolution goes
with squared momentum
m2K -mp2
•
•
•
the width of distributions is the same
mean values are known
relative normalisations are free
parameters
2D probability density function
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(each
specie
normalized to 1)
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Meeting is
2004
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Pt-y distributions of identified hadrons
Using the values of p and m2 of a particle the probabilities to be , K
or p are given by the 2D probability density function
8 GeV/c
7 GeV/c
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Momentum spectra of identified hadrons
The method allows to identify K up to 7 GeV/c
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Single event analysis
Problem: fitting will fail due to low number
of entries in the single event distribution
Using the maximum likelihood method,
the relative particle yields can be
estimated
L   PDF ( pi , m ; )
2
i
i
Minuit package was used to minimize the function
And since the PDF was represented not
analytically but as the look-up table :
The performance and accuracy of the method
are to be improved
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Event-by-event ratio
Measure the relative
width of the distribution
/mean * 100%
50k events
time resolution 80 ps
Event statistics:
 : 694 : 337
K : 54 : 22
P : 161 : 101
4
acceptance
PID
K/  14.2  0.05 18.4  0.06
p/ 
7.8  0.03
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11.2  0.04
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Estimation of the background
Event mixing was used
Constructing of new events from tracks from different data events
Tracks selection : primary hadrons
Requirements for the event mixer:
1. In order to destroy correlations inside one event
One real event is used only once to construct current mixed event
Limitation on the track pool size (at least 1k events)
2. In order to reproduce the phase space population
Each track is used only once
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Dynamical fluctuations
 dyn  
2
data

2
mixed
data
mixed events
Positive for K/  ratio
Negative for p/  ratio
Results of background subtraction:
4
acceptance
PID
K/ 
3.2  0.3
2.6  0.6
p/ 
-5.3  0.07
-5.9  0.1
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Improvement with large statistics
The error is decreasing with increasing of number of events
K/
p/
 1/ N
Reasonable range is found to be 130k – 150k
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p and  from resonance decays
50k events generated with
100 p– pairs per event
Only resonance decays
data
mixed events
 dyn   mixed 
 13.1  0.04  %
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Conclusions and next steps
• Measurement of fluctuations of particle
ratios with TOF is feasible
• Test the sensitivity of method to different
signal values
• Study the mean pt fluctuations
• …
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