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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

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 by0(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

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

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

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

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

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

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

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

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

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

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

- 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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