BoseEinstein Correlations

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Bose-Einstein Correlations

• T. Csörgo
• with W. Metzger, T. Novák and W. Kittel
• for the L3 Collaboration
• Department of Physics, Harvard University,
  Cambridge, MA
• MTA KFKI RMKI, Budapest, Hungary

Reconstruction of the Source Function in Hadronic
Z-Boson Decays
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Motivation

• Bose-Einstein Correlations, HBT, femtoscopy
• 1) Tools to measure Sizes, lifetimes, shapes
  snapshot pictures or even
• a video of particle emission (in ee-
  annihilation only, for now).
• 2) Reflect both geometrical and dynamical
  properties
• In ee- annihilation a) dependence on Q, which
  is different from hp,pp AB, b) small
  paradigm shift R(Q) ?1 positive definite
  form c) mt dependence similar decrease in
  ee-, pp, dA AB d) elongation source is
  not spherically symmetric in ee (when studied
  in LCMS by ALPEH, DELPHI, L3, OPAL)?
• ?-model described with CL gt 4 properties a), b)
  and c)
• For ISMD 2009 test of ?-model on d)
  elongation in 2-jet

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Large Electron Positron (LEP) collider
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The L3 detector
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Two particle Interferometry
for non-interacting identical bosons
emission function
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Correlations for various collisions
STAR prel. data
C2(Qinv)?
Qinv (GeV/c)?
Correlations have detailed size shape info (3d
shape analysis)? Depending on the geometry and
the dynamics of the source
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Bose-Einstein Correlation
In practice
Two particle number density (Data)?
Two particle density without BEC (Reference
sample)?
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Data Sample

• 36 M like-sign pairs
• vs 91.2 GeV
• 0.8 M hadronic Z0 decays
• Events classified as two or three() jet events
  Durham jet algorithm, with ycut 0.006 450
  k two jet events 350 k three jet
  events (few events with more than
  3 jets included to 3-jet)?
• Track selection and quality cuts varied to obtain
  syst errors

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Puzzles in the late 80s
First, the measured correlation functions are
consistent with the invariant Q dependence.
(the statistics were not large enough)?
Second, the correlation function is more peaked
than a Gaussian.
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Demonstrating Q dependence in ee-
BEC is maximal, when the invariant Q v-(p1-p2)2
is small, although any of the components of Q can
be large !
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Demonstrating Q dependence in ee-
BEC is maximal, when the invariant Q v-(p1-p2)2
is small, although any of the components of Q can
be large !
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Q dependence not present in hp
In NA22 data, BEC is NOT maximal, when the
invariant Q v-(p1-p2)2 is small, but one the
components of Q is large !
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Examples with Q dependence
The correlation function will be investigated as
a function of Q, the invariant four-momentum
difference. (See later)?
Source function
Correlation function
Gaussian
Intercept parameter
Edgeworth expansion
Symmetric Lévy stable
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Beyond the Gaussian
Far from Gaussian
Poor CLs. Edgeworth and Lévy better than Gaussian.
Note that data dip in the region 0,6 lt Q lt 1,5
GeV.
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The t-model
Assume that the average production point of
particles and the four momentum are strongly
correlated.
This correlation is much narrower than the
proper-time distribution.
In the plane-wave approxiamtion, using the
Yano-Koonin formula, one gets for two-jet events
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Further assumptions
Assume a Lévy distribution for H(t).
Since no particle production before the
interaction, H(t) is one-sided.
Then
a is the index of stability
where
t0 is the proper time of the onset of particle
production
?t is a measure of the width of the dist.
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Results for 2-jet events
CLs are good. Parameters are approx. independent
of mt.
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Results for 2-jet events
t-model passes test on Q dependence, and fits in
R(Q) lt 1 too
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Tests for mt dependence
Parameters of t-model are independent of mt - l
is mt dependent
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What about elongation?
Elongation Rlong gt Rside, Rout is seen by all
LEP experiments
We confirm this earlier result with the present
analysis too.
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Tests allowing for elong. in t-model
Elongation is needed to describe L3 data, fit
w/o elongation fails
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Tests allowing for elong. in t-model
Elongation is needed to describe L3 data, fit
w/o elongation fails
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The shortest movie -w/o elongation
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Summary
Analysis of L3 data for 2-jet events using
t-model finds Q-dependence mt-dependence R(Q) ?1
pos. definit form but elongation not
described t-model has to be generalized for
elongation
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