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Bose – Einstein Correlations in DIS at HERA

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

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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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