1. Bose-Einstein and Fermi-Dirac Correlations at LEP and HERA Ignacio Aracena University of Bern Outline Introduction Bose-Einstein and Fermi-Dirac Correlations –One-dimensional analysis –Multidimensional analysis Bose-Einstein Correlations in hadronic WW decays Conclusions

2. 17.8.2004I. Aracena2 The reference sample : Should contain all features which are present in data, except BEC/FDC. Should not contain additional features. Is the main experimental problem. used techniques: Mixed events, unlike-sign, MC,... The reference sample : Should contain all features which are present in data, except BEC/FDC. Should not contain additional features. Is the main experimental problem. used techniques: Mixed events, unlike-sign, MC,... Introduction Bose-Einstein (Fermi-Dirac) Correlations: Enhanced (suppressed) probability for the emission of identical bosons (fermions) with similar momenta. Provides information about space-time characteristics of the particle emission region Detector inadequacies, effects introduced by the reference sample are obtained from MC without BEC/FDC: The two-particle correlation function is given by, with. : Two-particle density distribution The measured correlation function is given by:

3. 17.8.2004I. Aracena3 BEC at LEP – one-dimensional results Discrepancy between results obtained from different reference samples Gaussian does not describe data at low Q 2 BEC in K 0 K 0 pairs (submitted to Phys.Lett.B) Mixed ref. sample R = 0.57 ± 0.04(stat) ± 0.14(sys) fm χ 2 /ndf = 0.68 Standard parameterisation λ coherence strength factor. R is related to the size of the boson emission region. Why study BEC in one dimension again? During LEP1 run >~ 10 6 hadronic Z decays Statistically precise measurement and possibility to study BEC in various particle species. 0 0.2 0.4 0.6 0.8 1 1.2 Q (GeV) 2.2 2 1.8 1.6 1.4 1.2 1 0.8 1.6 1.4 1.2 1 0.8 ALEPH BEC in ) ( 2 Q C mix ) ( 2 Q C   MC reference sample main contribution to systematic error λ = 0.438±0.001(stat) R = 0.777±0.007(stat) fm χ 2 /ndf = 432 / 72 λ = 0.362±0.001(stat) R = 0.528±0.006(stat) fm χ 2 /ndf = 513 / 94 Unlike-signMixed events ALEPH – BEC in pairs: Eur. Phys. J. C36: 2004, 147 BEC in pairs 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Q (GeV) 2 1.8 1.6 1.4 1.2 1 0.8 ALEPH

4. 17.8.2004I. Aracena4 OPAL Coll. Phys. Lett. B568 (2003) 181 BEC in pairs mixed reference sample OPAL Coll. Phys. Lett. B568 (2003) 181 BEC in pairs mixed reference sample BEC at LEP – one-dimensional results Fragmentation models currently used: Lund string model Lund string model: A larger BEC strength and a smaller effective radius of the source for compared to. Cluster fragmentation model Cluster fragmentation model: No difference between BEC in and pairs. 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 Q (GeV) 2 1.5 1 0.5 ) ( 2 Q C BEC in pairs: Opal Eur. Phys. J. C16 (2000) 423 unlike-sign reference sample R = (1.002 ± 0.016(stat) +0.023/−0.096(sys)) fm BEC in pairs: Opal Eur. Phys. J. C16 (2000) 423 unlike-sign reference sample R = (1.002 ± 0.016(stat) +0.023/−0.096(sys)) fm λ = 0.55 ± 0.10(stat) ± 0.10(sys) R = (0.59 ± 0.08(stat) ± 0.05(sys)) fm λ = 0.55 ± 0.10(stat) ± 0.10(sys) R = (0.59 ± 0.08(stat) ± 0.05(sys)) fm No sensitivity to from string Cannot test hadronisation model predictions. BEC exist in pairs in which each is a decay product of a different hadron. Comparison with previous results difficult due to different reference sample and selection cuts.

5. 17.8.2004I. Aracena5 Fermi-Dirac Correlations at LEP Parameterisation of the FD correlation function: The λ parameter contains information about the incoherence of the source and the spin composition of the pair. 0.11±0.01(stat)±0.01(sys) 0.16±0.04(stat)±0.03(sys) R (fm)λ 0.49±0.04(stat)±0.08(sys) 0.67+0.19/−0.17(stat)±0.18(sys) ALEPH DELPHI p 1.2 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 9 10 Q (GeV) χ 2 /ndf = 0.40 ALEPH ALEPH (sub. to Phys.Lett. B): FDC in pp and pairs 3526 pp, pairs in the region 0 < Q < 10 GeV 74% of pairs from the primary vertex for Q < 5 GeV 65% of pairs for Q < 10 GeV pp pp pp pp pp χ 2 /ndf = 18/23 DELPHI Q (GeV) DELPHI: FDC in pairs 955 pairs 70% purity for pairs pp pp pp pp

6. 17.8.2004I. Aracena6 Results indicate a smaller correlation radius for baryons than for mesons: Correlation radius is a function of the particle mass, R(m). One-dimensional BEC and FDC at LEP BEC and FDC have been studied at LEP1 in a large variety of particle species: K pΛ π Mixed ref. sample Unlike-sign ref. sample MC ref. sample

7. 17.8.2004I. Aracena7 BEC in ep neutral current DIS at HERA Motivation : In DIS the production volume may depend on the virtuality of the exchanged photon. Study differences of BEC between the current and the target regions. Studies performed in the Breit frame: momentum of the exchanged photon q = (0,0,0,−Q γ = −2xP Breit ) Allows separation of outgoing struck quark from the proton remnant No significant difference between the BE effects in the current and the target regions. HERA results are compatible with LEP results. λ = 0.475±0.007+0.011/− 0.003 R = 0.666±0.009+0.022/ − 0.036 fm λ = 0.475±0.007+0.011/− 0.003 R = 0.666±0.009+0.022/ − 0.036 fm ZEUS: Phys.Lett.B583:2004, 231 0.1 < < 8000 GeV 2 121 pb -1 assume particles are charged pions unlike-sign reference sample BEC studied in current and target region The BEC function measured at HERA shows no dependence on the virtuality of the exchanged photon.

8. 17.8.2004I. Aracena8 Multidimensional BEC analyses The standard parameterisation of the three-dimensional BEC function is: Longitudinal Centre-Of-Mass System (LCMS): Is defined as the coordinate system in which the momentum sum of the two particles is perpendicular to the event axis. Is the coordinate system used in multidimensional BEC studies. Motivation Test predictions of the Lund string model (M. Ringner, B. Andersson, Phys. Lett. B421: 1998, 283): The longitudinal size of the boson source is bigger than the transverse one in the string fragmentation model

9. 17.8.2004I. Aracena9 Multidimensional BEC analyses – LEP results Multidimensional BEC analyses in charged pion pairs in hadronic Z decays by the four LEP collaborations ALEPH : Two-dimensional analysis Using mixed and unlike-sign reference samples Eur. Phys. J. C36: 2004, 147. DELPHI : Two- and three-dimensional analysis Using mixed reference sample Phys. Lett. B471: 2000, 460. L3 : Two- and three-dimensional analysis Using mixed reference sample Phys. Lett. B458: 1999, 517. OPAL : Three-dimensional analysis Using mixed reference sample Eur. Phys. J. C16: 2000, 423. ALEPH

10. 17.8.2004I. Aracena10 Two-dimensional BEC analysis by the ZEUS collaboration: Phys. Lett. B583:2004, 231 Data taking period: 1996 – 2000 (121pb −1 ) 0.1 < < 8000 GeV 2 unlike-sign reference sample assume particles are charged pions Multidimensional BEC in DIS at HERA Multidimensional analysis in neutral current DIS: Does the difference between the transverse and longitudinal dimensions of the boson source depend on the virtuality of the exchanged photon ? 4 < < 8000 GeV 2 R T = 0.69 ± 0.01(stat)+0.01/−0.06(sys) fm R L = 0.95 ± 0.03+0.03(stat)/−0.08(sys) fm R T /R L = 0.72 ± 0.03(stat)+0.04/−0.03(sys) 4 < < 8000 GeV 2 R T = 0.69 ± 0.01(stat)+0.01/−0.06(sys) fm R L = 0.95 ± 0.03+0.03(stat)/−0.08(sys) fm R T /R L = 0.72 ± 0.03(stat)+0.04/−0.03(sys) Elongated boson source shape measured at HERA. Difference between longitudinal and transverse correlation length shows no dependence on the virtuality of the exchanged photon.

11. 17.8.2004I. Aracena11 Multidimensional BEC analyses – LEP results R T /R L < 1 measured at the LEP and HERA experiments Indication for elongated pion source. Quantitative comparison of results from different experiments is not straightforward The results depend on the choice of the reference sample. Experiments use different selection criteria. ALEPH DELPHI L3 ALEPH OPAL ZEUS

12. 17.8.2004I. Aracena12 BEC in hadronic WW decays at LEP2 Do BEC exist between bosons from different W decays in e + e − W + W − q 1 q 2 q 3 q 4 events? At LEP2: Overlap between the two production regions Hadronisation region >~0.5 fm Separation of W-pair ~ 0.1 fm Two observables: Measurement of inter-W BEC signal Mixed method: Genuine inter-W correlation function: Indication for inter-W BEC: At LEP2 inter-W BEC cannot be excluded a priori Important for the measured M W

13. 17.8.2004I. Aracena13 Inter-W BEC at LEP2 DELPHI: Final paper in preparation Fit to the δ I (Q) distribution: Λ = 0.82 ± 0.29(stat) ± 0.17(sys) 2.0σ below the model predictions. Indication for inter-W BEC at the 2.4σ level. OPAL: Accepted for publication in Eur. Phys. J. C (i)Fit to the D(Q) distribution: Λ = 0.063 ± 0.036(stat) ± 0.038(sys); 1.5σ below the LUBOEI prediction (ii) I(Δρ) = 0.17 ± 0.26(stat) ± 0.23(sys); 2.2σ from LUBOEI prediction No indication for inter-W BEC. ! Take estimator values, obtained from the different distributions (D(Q), Δρ, δI(Q), …) from data from MC with Inter-W BEC simulated (LUBOEI BE32) Comparison across experiments might be misleading. Compare deviation from model instead. ALEPH: Final paper in preparation (i)Fit D’(Q): λ = −0.003 ± 0.010(stat) ± 0.014(sys) data 4.4σ below LUBOEI prediction. (ii) I(Δρ’) = −0.134 ± 0.166(stat) ± 0.196(sys) 3.3σ below LUBOEI prediction. (iii) Weak signal from I(D’) at the 1.7σ level. No indication for inter-W BEC. L3: Phys. Lett. B 547(2002) 139 (i)Fit D’(Q): Λ = 0.008 ± 0.018(stat) ± 0.012(sys) 3.8σ below LUBOEI prediction. ( ii ) I (Δρ) = 0.03 ± 0.33(stat) ± 0.15(sys); 3.6σ below LUBOEI prediction. No indication for inter-W BEC.

14. 17.8.2004I. Aracena14 Conclusions BEC and FDC have been studied in various particle species at LEP and HERA. BEC and FDC have been studied in various particle species at LEP and HERA. ♦The measured correlation radius depends on the mass of the particle. It turns out the correlation radius measured in baryon pairs is smaller than the correlation radius measured in meson pairs. ♦In DIS the BEC parameters are the same in the current and target region and they are insensitive to. Multidimensional analyses of BEC in charged pion pairs have been published by the four LEP experiments and the ZEUS collaboration at HERA. Multidimensional analyses of BEC in charged pion pairs have been published by the four LEP experiments and the ZEUS collaboration at HERA. ♦An elongation, R T /R L <1, as predicted by the Lund string model, is measured by all collaborations. ♦The measured elongation depends on the choice of the reference sample. ♦The correlation radii measured at HERA are independent of the virtuality of the exchanged photon,, in the range 0.1< <8000GeV 2. Correlations between particles from hadronic WW decays have been measured by the four LEP experiments. Correlations between particles from hadronic WW decays have been measured by the four LEP experiments. ♦DELPHI finds a signal for inter-W BEC at the 2.4σ level. The other three experiments find no indication for inter-W BEC.

15. 17.8.2004I. Aracena15 BEC and FDC at LEP1 - Summary Measured correlation radius indicates a smaller correlation radius for baryons than for mesons: Correlation radius is a function of the particle mass R(m). BE and FD correlations have been studied at LEP1 in a large variety of particle species:

16. 17.8.2004I. Aracena16 Multidimensional BEC analyses – LEP results ALEPH Fit range:0.04 < Q T < 1.2 GeV −1.2 < Q L < 1.2 GeV Mixed ref. sample R T (fm) R L (fm) R T /R L χ 2 /ndf 0.470 ± 0.007 0.767 ± 0.011 0.612 ± 0.010 2297/1792 unlike-sign ref. sample R T (fm) R L (fm) R T /R L χ 2 /ndf 0.788 ± 0.002 0.870 ± 0.019 0.906 ± 0.020 1810/1158 Discrepancy between results obtained with the two methods. Data not well described by the standard parameterisation.

17. 17.8.2004I. Aracena17 Multidimensional BEC analyses – LEP results Study correlation radii values as a function of the two-jet purity T > T cut Correlation radii depend on the two-jet purity Behaviour of correlation radii different for mix and unlike-sign reference sample Similar study by OPAL (Eur. Phys. J. C16 423, 2000) using unlike-sign ref. sample:  0.01 < y cut < 0.06 R T, R L independent of y cut.

18. 17.8.2004I. Aracena18 Multidimensional BEC in DIS at HERA ZEUS results (stat. error only) 4 < Q 2 < 8000 GeV 2 R T = 0.69 ± 0.01 fm R L = 0.95 ± 0.03 fm R T /R L = 0.72 ± 0.03 100 < Q 2 < 8000 GeV 2 R T = 0.62 ± 0.04 fm R L = 0.88 ± 0.08 fm R T /R L = 0.70 ± 0.08 Elongated boson source shape measured at HERA, compatible with LEP results Difference between longitudinal and transverse correlation length shows no dependence on the four-momentum Q 2 of the exchanged photon. Multidimensional analysis in neutral current DIS : Does the difference between the transverse and longitudinal dimensions of the boson source depend on the virtuality of the exchanged photon Q 2 ? Two-dimensional BEC analysis by the ZEUS collaboration: Published in Phys. Lett. B583:2004, 231 Data taking period: 1996 – 2000 (121pb −1 ) 0.1 < Q 2 < 8000 GeV 2 mixed reference sample assume particles are charged pions

19. 17.8.2004I. Aracena19 Multidimensional BEC analyses – LEP results Correlation radii values published by the four LEP collaborations Reference sampleR T (fm)R L (fm)RT/RLRT/RL ALEPHMix0.47±0.01±0.020.77±0.01±0.010.61±0.01±0.01 Unlike-sign0.79±0.01±0.020.87±0.02±0.050.91±0.02±0.04 DELPHIMix0.53±0.02±0.070.85±0.02±0.070.62±0.02±0.05 L3Mix0.58±0.01+0.04/−0.090.79±0.02+0.04/−0.050.73±0.02+0.03/−0.10 OPALUnlike-sign0.81±0.01+0.02/−0.030.99±0.01+0.03/−0.020.82±0.04+0.08/−0.01 R T /R L < 1 measured by the four LEP experiments Indication for elongated pion source Analysis method is not standardised Quantitative comparison of results from different experiments is not straightforward. ALEPHDELPHIL3OPAL T > 0.95 p < 5 GeV T > 0.95 p < 4.5 GeV T cut variation included in systematic error No two-jet selection p < 40 GeV Durham y cut = 0.04 p < 40 GeV R T ≡ R t,side

20. 17.8.2004I. Aracena20 21 43 lqqWW    qqlWW    4321 qqqqWW    Mixed method: BEC in hadronic WW decays at LEP2 Two observables: Compute distortions introduced by the event mixing technique and detector effects with MC simulated with BEC only inside a single W (BEI): Hadronisation region >~0.5 fm Separation of W-pair ~ 0.1 fm BEC between bosons from different W’s (inter-W BEC)? Indication for inter-W BEC: Genuine inter-W correlation function: Indication for inter-W BEC: Genuine inter-W correlation function: Overlap between the two production regions Potential bias of measured M W Measurement of inter-W BEC signal

21. 17.8.2004I. Aracena21 Inter-W BEC Distributions analysed by the LEP collaborations