Prezentacja programu PowerPoint

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Bose Einstein Correlations in DIS at
HERA
XXXIII International Symposium on
Multiparticle Dynamics, Cracow, September 5 -
11, 2003
Leszek Zawiejski, Institute of Nuclear Physics,
Cracow

• Introduction
• Correlation function measurement
• One and two - dimensional BEC results
  from ZEUS
• Conclusions

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Introduction
In Bose - Einstein correlations (BEC) studies
an enhancement in the number of identical
bosons produced with similar energy-momenta is
observed. This effect arises due to
symmetrization of the two-boson wave function.
BEC can be used to investigate the space-time
structure of particle production in different
particle interactions.
DIS studies of BEC may reveal changes of
the size of the source with energy scale -
photon virtuality Q2 and sensitivity BE effect
to hard subprocess
To check these expectations the DIS
measurements were done in the Breit frame for
one and two dimensions.

• This talk ZEUS results on
• Examinations of the Q2 dependence ? BEC
  sensitive to the hard subprocesses ?
• Two - dimensional analysis - the shape of the
  production source - for the first time in DIS,
• Comparison with other experiments.

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Bose - Einstein correlation function measurement
In theory
BE effect can be expressed in terms of the
two-particle correlation function (Kopylov,
Podgoretskii, Cocconi, Bowler, Andersson,
Hofmann)
?(p1,p2)
R(p1,p2) ?
p1,p2 are two - particles four-momenta,
where
?(p1)?(p2)
?(p1)?(p2) is product of single particle
probability densities
?(p1,p2) is two - particle probability
density
and
R - 1 is related to the space-time density
distribution of emisssion sources through a
Fourier transform.
In experiment

?(p1)?(p2), is replaced by ?0(p1,p2) ? no
BE correlation - reference sample.
In use mixed events, unlike sign
particles, MC events
By choosing the appropriate variable like
Q12
Q12 ? (E1 - E2)2 - (p1 - p2)2
R (Q12) can be measured as
Lorentz invariant 4 - momentum difference
of the two measured particles
R(Q12) ?(Q12)data ? ?0(Q12)reference
R is parametrised in terms of source radius r
and incoherence (strength of effect)
parameter ? . Fit to data allows to determine
these values.
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Correlation function - 1 D
Two parametrisations were used in analysis
R ?(1 ?Q12)(1 ? exp(-r2Q212))
Well describes the BE correlations - based on
assumption that the distribution of
emitters is Gaussian in space - static sphere
of emitters.
and
R ?(1 ?Q12)(1 ? exp(-rQ12))
Related to color-string fragmentation model,
which predicts an exponential shape of
correlation function, with r independent of
energy scale of interaction.

• ? - normalization factor,
• (1 ??Q12) includes the long range
  correlations - slow variation of R (R)
  outside
• the interference peak
• radius r - an average over the spatial and
  temporal source dimensions,
• r is related to the space-time
  separation of the productions points -
• string tension in
  color-string model
• ? - degree of incoherence 0 -
  completely coherent, 1 - total incoherent

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BEC measurement
Requires calculation the normalized
two-particle density ? (Q12) pairs of charged
pions
?(Q12) 1/Nev dnpairs / dQ12

• for like sign pairs (?, ?) where BEC are
  present,
• and for unlike pairs (,) where no BEC are
  expected but short range correlations
• mainly due to resonance decays will be
  present - reference sample

Look at the ratio
This ratio can be affected by
reconstruction efficiency particle
misidentification momentum smearing
?data(Q12) ?(?, ?) / ?(,)
and remove the most of the background but no
BEC using Monte Carlo without BEC
?MC,no BEC .
?data
Find as the best estimation of the measured
correlation function
R
?MC,no BEC
Detector acceptance correction, C is
calculated as
C (?(?, ?)/?(,))gen / (?(?, ?)/?(,))det
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Results - 1D
Data 1996 -2000
121 pb-1,
0.1 lt Q2 lt 8000 GeV2 Monte Carlo
ARIADNE with/without BEC,
HERWIG for systematic study.
An example
The fit - parameters
Values obtained for radius of source r and
incoherent parameter ? from Gaussian (? 2 /
ndf 148/35) r 0.666 0.009 (stat.) /-
0.023/0.036(syst.) ? 0.475 0.007 (stat.)
/- 0.021/0.003 (syst.) and exponential
(?2 / ndf 225/35) r 0.928 0.023 (stat.)
/- 0.015/0.094 (syst.) ? 0.913 0.015
(stat.) /- 0.104/0.005 (syst.) like
parametrization of R
Fit to the spherical Gaussian density
distribution of emitters - more convincing and
was used mainly in the analysis
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Results - 1D
BEC for different Q2
average value
H1 and ZEUS results on radius r and
incoherence ? are consistent
average value
no Q2 dependence is observed
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Results - 1D
The target and current regions of the Breit
frame
average value
Target and current fragm. -
the significant difference in the underlying
physics - but the similar independence r and
? on the energy scale Q2.
The global feature of hadronization phase?
average value
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Results - 1D
Comparison with other experiments
pp and ? p interactions
e e? interactions
DIS
filled band - ZEUS measurement for Q2 ? 4
GeV2
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Correlation function - 2 D
To probe the shape of the pions (bosons)
source
In DIS ( Breit frame), the LCMS is defined as
The Longitudinally Co-Moving System (LCMS) was
used.

The physical axis was chosen as the virtual
photon (quark) axis

• In LCMS , for each pair of particles, the sum
  of two momenta p1 p2 is
• perpendicular to the ? q axis,
• The three momentum difference Q p1 - p2 is
  decomposed in the LCMS into
• transverse QT and longitudinal component
  QL pL1 - pL2
• The longitudinal direction is aligned with
  the direction of motion of the initial quark
• (in the string model LCMS - local rest
  frame of a string)

Parametrisation - in analogy to 1 D
R ?(1 ?TQT ?LQL)(1? exp( - r2TQ2T - r2LQ2L
))
The radii rT and rL reflect the transverse and
longitudinal extent of the pion source
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Results - 2 D
An example
Two - dimensional correlation function R(Q
L,QT) calculated in LCMS in analogy to 1 D
analysis
Curves fit
- using two-dimensional Gaussian
parametrisation
Projections slices in QL and QT
Fit quality
?2/ndf ? 1
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Results - 2 D
Extracted radii rL, rT and incoherence
parameter ?
The different values for rL and rT
The source is elongated in the
longitudinal direction
(as reported previously by LEP experiments
DELPHI, L3, OPAL)
average values
The results confirm the string model
predictions the transverse correlation
length showed be smaller than the
longitudinal one.
No significant dependence of elongation
on Q2
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Results - 2 D
DIS and ee annihilation
Can we compare DIS results (
i.e. rT / rL) with ee ? In ee
studies, 3D analysis and different reference
samples are often used, but for OPAL and
DELPHI experiments (at LEP1, Z0 hadronic decay)
- analysis partially similar to ZEUS OPAL
(Eur. Phys. J, C16, 2000, 423 ) - 2 D Goldhaber
like fit to correlation function in (QT,QL)
variables, unlike-charge reference sample, DELPHI
(Phys. Lett. B471, 2000, 460) - 2 D analysis in
(QT,QL), but mixed -events as reference
sample. So try compare them with DIS
results for high Q2 400 ? Q2 ?
8000 GeV2

ZEUS rT / rL 0.62 0.18 (stat) /-
0.07/0.06 (sys.)
OPAL rT / rL 0.735 0.014 (stat.)
( estimated from reported ratio rL/rT )
DELPHI rT / rL 0.62 0.02 (stat) 0.05
(sys.)
DIS results compatible with ee
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Conclusions

• ZEUS supplied high precision measurements
  on 1D and 2D
• Bose - Einstein correlations.
• The effect was measured as the function of
  the photon virtuality Q2,
• in the range 0.1 - 8000 GeV2 - in a
  single experiment
• with the same experimental procedure.
• The results are comparable with e e
  experiments, but
• the radii are smaller than in ? p
  and pp data.
• The emitting source of identical pions
  has an elongated shape
• in LCMS ? consistent with the Lund
  model predictions.
• Within the errors there is no Q2
  dependence of the BEC ?
• BE effect is insensitive to hard
  subprocesses and is a feature
• of the hadronisation phase.