Leszek Zawiejski XXXIII ISMD, September 2003

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Bose – Einstein Correlations in DIS at HERA

XXXIII International Symposium on Multiparticle Dynamics, Cracow, September 5 - 11, 2003

Introduction

Correlation function measurement

One and two - dimensional BEC results from ZEUS

Conclusions

Leszek Zawiejski,Institute of Nuclear Physics, Cracow

Leszek Zawiejski XXXIII ISMD, September 2003

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Introduction

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

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.

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.

To check these expectations the DIS measurements were done in the Breit frame for one and two dimensions.

Leszek Zawiejski XXXIII ISMD, September 2003

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BE effect can be expressed in terms of the two-particle correlation function(Kopylov, Podgoretskii, Cocconi, Bowler, Andersson, Hofmann) :

(p1,p2)

(p1)(p2), is replaced by 0(p1,p2) no BE correlation - reference sample. In use: mixed events, unlike sign particles, MC events

Bose - Einstein correlation function measurement

R(p1,p2) (p1)(p2)

R is parametrised in terms of source radius r and incoherence (strength of effect) parameter . Fit to data allows to determine these values.

where : p1,p2 are two - particles four-momenta,

(p1,p2) is two - particle probability

density

(p1)(p2) is product of single particle

probability densities

In theory

R - 1 is related to the space-time density distribution of emisssion sources through a Fourier transform.

In experiment

By choosing the appropriate variable like Q12 : Q12 = (E1 - E2)2 - (p1 - p2)2

R (Q12) can be measured as:

R(Q12) = (Q12)data 0(Q12)reference

and

Lorentz invariant : 4 - momentum difference of the two measured particles

Leszek Zawiejski XXXIII ISMD, September 2003

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Correlation function - 1 D

R = (1 + Q12)(1 + exp(-r2Q212)) :

- 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

Well describes the BE correlations - based on assumption that the distribution of emitters is Gaussian in space -static sphere of emitters.

R = (1 + Q12)(1 + exp(-rQ12)) :

and

Related to color-string fragmentation model, which predictsan exponential shape of correlation function, with r independent of energy scale of interaction.

Two parametrisations were used in analysis:

Leszek Zawiejski XXXIII ISMD, September 2003

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BEC measurement

(Q12) = 1/Nev dnpairs / dQ12

Requires calculation the normalized two-particle density (Q12) pairs of charged pions

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:

data(Q12) = (, ) / (+,–)

and remove the most of the background but no BEC using Monte Carlo without BEC : MC,no BEC .

R = data

MC,no BEC

This ratio can be affected by : – reconstruction efficiency – particle misidentification – momentum smearing

Detector acceptance correction, C is calculated as : C = ((, )/(+,–))gen / ((, )/(+,–))det

Find as the best estimation of the measured correlation function

Leszek Zawiejski XXXIII ISMD, September 2003

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Results - 1D

Values obtained for radius of source r and incoherent parameter fromGaussian ( 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

Data : 1996 -2000: 121 pb-1,

0.1 < Q2 < 8000 GeV2 Monte Carlo: ARIADNE with/without BEC, HERWIG for systematic study.

The fit - parameters :

Fit to the spherical Gaussian density distribution of emitters -more convincing and was used mainly in the analysis

An example :

Leszek Zawiejski XXXIII ISMD, September 2003

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Results - 1D BEC for different Q2

no Q2 dependence is observed

H1 and ZEUS results

on radius r and incoherence are consistent

average value

average value

Leszek Zawiejski XXXIII ISMD, September 2003

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Results - 1D The target and current regions of the Breit frame

the significant differencein the underlying physics -

but the similar independence r and on the energy scale Q2.

average value

The global feature of hadronization phase?

average value

Target and current fragm. -

Leszek Zawiejski XXXIII ISMD, September 2003

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Results - 1D Comparison with other experiments

pp and + pinteractions

e+ e interactions

DISfilled band -

ZEUS measurementfor Q2 4 GeV2

Leszek Zawiejski XXXIII ISMD, September 2003

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Correlation function - 2 D

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)

In DIS ( Breit frame), the LCMS is defined as :

Parametrisation - in analogy to 1 D: R = (1+ TQT + LQL)(1+ exp( - r2

TQ2T - r2

LQ2L ))

The radii rT and rL reflect the transverse and longitudinal extent of the pion source

To probe the shape of the pions (bosons) source

The Longitudinally Co-Moving System (LCMS) was used.

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

Leszek Zawiejski XXXIII ISMD, September 2003

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Results - 2 D

Two - dimensional correlation function R(Q L,QT) calculated in LCMSin analogy to 1 D analysis

Projections :slices in QL and QT

Curves : fit

An example :

Fit quality : 2/ndf 1

- using two-dimensional Gaussian parametrisation

Leszek Zawiejski XXXIII ISMD, September 2003

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Results - 2 DExtracted radii rL, rT and incoherence parameter

average values

The different values for rL and rT

The source is elongated in the longitudinal direction

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

(as reported previously by LEP experiments : DELPHI, L3, OPAL)

Leszek Zawiejski XXXIII ISMD, September 2003

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Results - 2 D : DIS and e+e– annihilation

ZEUS: rT / rL = 0.62 ± 0.18 (stat) +/- 0.07/0.06 (sys.)

DELPHI : rT / rL = 0.62 ± 0.02 (stat) ± 0.05 (sys.)

Can we compare DIS results ( i.e. rT / rL) with e+e– ?

In e+e– studies, 3D analysis and different reference samples are often used, but for OPAL and DELPHI experiments (at LEP1, Z0 hadronic decay) - analysispartially 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

OPAL: rT / rL = 0.735 ± 0.014 (stat.) ( estimated from reported ratio rL/rT )

DIS results compatible with e+e–

Leszek Zawiejski XXXIII ISMD, September 2003

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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.