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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

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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

Leszek Zawiejski XXXIII ISMD, September 2003


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 Q2and 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.

Leszek Zawiejski XXXIII ISMD, September 2003


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,p2aretwo - particles four-momenta,

where :

(p1)(p2)

(p1)(p2)is product of single particle

probability densities

(p1,p2) is two - particle probability

density

and

R - 1is 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.

Leszek Zawiejski XXXIII ISMD, September 2003


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 tocolor-string fragmentationmodel,which predicts

an exponential shapeof correlation function,withrindependent 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

Leszek Zawiejski XXXIII ISMD, September 2003


BEC measurement

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

(Q12) = 1/Nev dnpairs / dQ12

  • for like sign pairs(, )where BECare present,

  • and for unlike pairs(+,–)whereno 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, Cis calculated as :

C= ((, )/(+,–))gen / ((, )/(+,–))det

Leszek Zawiejski XXXIII ISMD, September 2003


Results - 1D

Data : 1996 -2000:

121 pb-1,

0.1 < Q2 < 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

Leszek Zawiejski XXXIII ISMD, September 2003


Results - 1D

BECfor different Q2

average value

H1 andZEUS

results

on radiusr

and incoherence

are consistent

average value

no Q2 dependence is observed

Leszek Zawiejski XXXIII ISMD, September 2003


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.

average value

The global feature of

hadronization phase?

Leszek Zawiejski XXXIII ISMD, September 2003


Results - 1D

Comparison with other experiments

pp and + p

interactions

e+ e

interactions

DIS

filled band -

ZEUS measurement

for Q2  4 GeV2

Leszek Zawiejski XXXIII ISMD, September 2003


Correlation function - 2 D

To probe the shape of the pions (bosons) source

The Longitudinally

Co-Moving System (LCMS)

was used.

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

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 differenceQ = p1 - p2is decomposed in the LCMS into:

  • transverse QTand longitudinal componentQL = | 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 radiirTand rLreflect the transverse and longitudinal extent of the pion source

Leszek Zawiejski XXXIII ISMD, September 2003


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

Leszek Zawiejski XXXIII ISMD, September 2003


Results - 2 D

Extracted radiirL, rT and incoherence parameter 

The different values

for rLandrT

The source is elongated

in thelongitudinal 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

Leszek Zawiejski XXXIII ISMD, September 2003


Results - 2 D :

DIS ande+e– annihilation

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) - 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 e+e–

Leszek Zawiejski XXXIII ISMD, September 2003


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.

Leszek Zawiejski XXXIII ISMD, September 2003


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