1. Hadron production and QCD coherence at LEP Marco Cuffiani University of Bologna and INFN (Italy) on behalf of the OPAL Collaboration QCD coherence and correlations of particles with restricted momenta in hadronic Z decays (abstract 601) Bose-Einstein study of position-momentum correlations of charged pions in hadronic Z decays (abstract 708)

2. In a QCD cascade the presence of one gluon enhances the probability for further gluon emissions, causing positive correlations: the multiplicity distribution of partons in a jet is broader than a Poisson distribution. Due to the angular ordering induced by colour coherence, gluons produced with bounded transverse momenta p T < p T cut become, for small p T cut, independently emitted from the primary parton: the multiplicity distribution of partons becomes Poissonian. Correlations among particles may be measured in terms of the (normalized) factorial moments F q and cumulants K q of order q = 2, 3, 4...., in a region  of phase space QCD coherence and correlations of particles with restricted momenta in hadronic Z decays

3. Marco Cuffiani, EPS HEP 20073 Expectations from QCD DLLA calculations (S.Lupia, W.Ochs, J.Wosiek, Nucl.Phys. B 540 (1999) 405.) cylindrically-cut phase space (p T < p T cut ) spherically-cut phase space (p < p cut ) compare QCD predictions with data, under the hypothesis of LPHD

4. 4 Poisson limit masked by hadronization effects as p T cut Q 0 The factorial moments PYTHIA + BE 32 good agreement with data multiplicity of charged particles in a single event hemisphere

5. Marco Cuffiani, EPS HEP 20075 K 2 = F 2 – 1 (not shown) measure the genuine correlations among hadrons the strong rise of the factorial moments as p T cut 0 GeV is predominantly due to genuine correlations among particles The cumulants

6. Marco Cuffiani, EPS HEP 20076 Compare with e + p: ZEUS DIS events in the current region of the Breit frame (Phys.Lett.B 510 (2001) 36) mimic ZEUS experimental conditions exclude part of the central rapidity region select two jet events by requiring thrust > 0.96 the minimum around p T cut = 1 GeV disappears.

7. Marco Cuffiani, EPS HEP 20077 In the case of a dynamic source of pions, the expansion leads to correlations between the space-time emission points and the particle 4-momenta (position-momentum correlations). The dimensions of the regions of homogeneity for Bose-Einstein correlations depend on the momentum of the emitted particles. Study three-dimensional BE correlation functions in bins of the pair average transverse momentum k t and of the pair rapidity | Y |. Bose-Einstein study of position-momentum correlations of charged pions in hadronic Z 0 decays Two different sets of variables, components of the pair 4-momentum difference : (Q l,Q t_side,Q t_out ) and (q t,q l,q 0 )

8. 8 (Q l,Q t_side,Q t_out ) in the LCMS (the same analysis, not differential in |Y| and k t, was presented in Eur. Phys. J. C 16 (2000) 423)

9. 9 (q t,q l,q 0 ) in the CMS qlql qtqt 1 2 q 0 = E 1 – E 2 thrust axis

10. Marco Cuffiani, EPS HEP 200710 the Bertsch-Pratt with parameters: N,, R 2 long, R 2 t_side, R 2 t_out, R 2 long,t_out and the Yano-Koonin with parameters: N,, R 2 t, R 2 l, R 2 0, v  2 = 1/(1-v 2 )  Two parameterizations have been fit to the experimental correlation functions

11. Marco Cuffiani, EPS HEP 200711 Bertsch-Pratt fits

12. Marco Cuffiani, EPS HEP 200712 Yano-Koonin fits

13. Marco Cuffiani, EPS HEP 200713 The Yano-Koonin rapidity plotted as a function of the pair rapidity | Y | Y YK ≈ 0 for all | Y | in the case of a static source Y YK = | Y | for a source which expands boost- invariantly. Y YK vs |Y|

14. Marco Cuffiani, EPS HEP 200714 BP parameters may be compared with YK parameters: for a boost-invariant source,  LCMS = 0, so that:

15. Marco Cuffiani, EPS HEP 200715 longitudinal radii transverse radii “time parameters”

16. Marco Cuffiani, EPS HEP 200716 summary Large influence of the hadronization stage on the multiplicity distributions in restricted phase-space regions, inconsistent with the expectations of the LPHD hypothesis. MC models including hadronization reproduce the data qualitatively. BEC, as implemented in PYTHIA, improve significantly the agreement. BEC correlation lengths depend on k t. Y YK scales approximately with |Y|, in agreement with a nearly boost- invariant expansion of the source of pions. Similar results have been observed in pion sources created in more complex systems (pp and collisions between heavy nuclei)