1. 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

2. 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.

3. 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

4. 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:

5. 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

6. 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 :

7. 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

8. 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. -

9. 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

10. 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

11. 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

12. 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)

13. 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 –

14. 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.