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Leszek Zawiejski XXXIII ISMD, September 2003 1 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

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Leszek Zawiejski XXXIII ISMD, September 2003 2 Introduction DIS studies of BEC may reveal changes of the size of the source with energy scale - photon virtuality Q 2 and sensitivity BE effect to hard subprocess This talk : ZEUS results on: l Examinations of the Q 2 dependence BEC sensitive to the hard subprocesses ? l Two - dimensional analysis - the shape of the production source - for the first time in DIS, l 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.

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Leszek Zawiejski XXXIII ISMD, September 2003 3 BE effect can be expressed in terms of the two-particle correlation function ( Kopylov, Podgoretskii, Cocconi, Bowler, Andersson, Hofmann ) : (p 1,p 2 ) ( p 1 ) ( p 2 ), is replaced by 0 ( p 1,p 2 ) no BE correlation - reference sample. In use: mixed events, unlike sign particles, MC events Bose - Einstein correlation function measurement R( p 1,p 2 ) (p 1 ) (p 2 ) R is parametrised in terms of source radius r and incoherence (strength of effect) parameter. Fit to data allows to determine these values. where : p 1,p 2 are two - particles four-momenta, ( p 1,p 2 ) is two - particle probability density ( p 1 ) ( p 2 ) 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 Q 12 : Q 12 = (E 1 - E 2 ) 2 - (p 1 - p 2 ) 2 R (Q 12 ) can be measured as: R(Q 12 ) = (Q 12 ) data 0 (Q 12 ) reference and Lorentz invariant : 4 - momentum difference of the two measured particles

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Leszek Zawiejski XXXIII ISMD, September 2003 4 Correlation function - 1 D R = (1 + Q 12 )(1 + exp(-r 2 Q 2 12 )) : l - normalization factor, l (1 + Q 12 ) includes the long range correlations - slow variation of R (R) outside the interference peak l 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 l - 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 + Q 12 )(1 + exp(-rQ 12 )) : and Related to color-string fragmentation model, which predicts an exponential shape of correlation function, with r independent of energy scale of interaction. Two parametrisations were used in analysis:

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Leszek Zawiejski XXXIII ISMD, September 2003 5 BEC measurement (Q 12 ) = 1/N ev dn pairs / dQ 12 Requires calculation the normalized two-particle density (Q 12 ) pairs of charged pions l for like sign pairs ( , ) where BEC are present, l 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 (Q 12 ) = ( , ) / (+,–) 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

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Leszek Zawiejski XXXIII ISMD, September 2003 6 Results - 1D 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 Data : 1996 -2000: 121 pb -1, 0.1 < Q 2 < 8000 GeV 2 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 :

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Leszek Zawiejski XXXIII ISMD, September 2003 7 Results - 1DBEC for different Q 2 no Q 2 dependence is observed H1 and ZEUS results on radius r and incoherence are consistent average value

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Leszek Zawiejski XXXIII ISMD, September 2003 8 Results - 1DThe target and current regions of the Breit frame the significant difference in the underlying physics - but the similar independence r and on the energy scale Q 2. average value The global feature of hadronization phase? average value Target and current fragm. -

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Leszek Zawiejski XXXIII ISMD, September 2003 9 Results - 1D Comparison with other experiments pp and + p interactions e + e interactions DIS filled band - ZEUS measurement for Q 2 4 GeV 2

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Leszek Zawiejski XXXIII ISMD, September 2003 10 Correlation function - 2 D l In LCMS, for each pair of particles, the sum of two momenta p 1 + p 2 is perpendicular to the * q axis, l The three momentum difference Q = p 1 - p 2 is decomposed in the LCMS into: transverse Q T and longitudinal component Q L = | p L1 - p L2 | l 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+ T Q T + L Q L )(1+ exp( - r 2 T Q 2 T - r 2 L Q 2 L )) The radii r T and r L 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

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Leszek Zawiejski XXXIII ISMD, September 2003 11 Results - 2 D Two - dimensional correlation function R(Q L,Q T ) calculated in LCMS in analogy to 1 D analysis Projections : slices in Q L and Q T Curves : fit An example : Fit quality : 2 /ndf 1 - using two-dimensional Gaussian parametrisation

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Leszek Zawiejski XXXIII ISMD, September 2003 12 Results - 2 D Extracted radii r L, r T and i ncoherence parameter average values The different values for r L and r T 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 Q 2 (as reported previously by LEP experiments : DELPHI, L3, OPAL)

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Leszek Zawiejski XXXIII ISMD, September 2003 13 Results - 2 D :DIS and e + e – annihilation ZEUS: r T / r L = 0.62 ± 0.18 (stat) +/- 0.07/0.06 (sys.) DELPHI : r T / r L = 0.62 ± 0.02 (stat) ± 0.05 (sys.) Can we compare DIS results ( i.e. r T / r L ) with e + e – ? In e + e – studies, 3D analysis and different reference samples are often used, but for OPAL and DELPHI experiments ( at LEP1, Z 0 hadronic decay) - analysis partially similar to ZEUS: OPAL ( Eur. Phys. J, C16, 2000, 423 ) - 2 D Goldhaber like fit to correlation function in (Q T,Q L ) variables, unlike-charge reference sample, DELPHI ( Phys. Lett. B471, 2000, 460 ) - 2 D analysis in (Q T,Q L ), but mixed -events as reference sample. So try compare them with DIS results for high Q 2 : 400 Q 2 8000 GeV 2 OPAL: r T / r L = 0.735 ± 0.014 (stat.) ( estimated from reported ratio r L /r T ) DIS results compatible with e + e –

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Leszek Zawiejski XXXIII ISMD, September 2003 14 Conclusions l ZEUS supplied high precision measurements on 1D and 2D Bose - Einstein correlations. l The effect was measured as the function of the photon virtuality Q 2, in the range 0.1 - 8000 GeV 2 - in a single experiment with the same experimental procedure. l The results are comparable with e + e – experiments, but the radii are smaller than in + p and pp data. l The emitting source of identical pions has an elongated shape in LCMS consistent with the Lund model predictions. l Within the errors there is no Q 2 dependence of the BEC BE effect is insensitive to hard subprocesses and is a feature of the hadronisation phase.

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