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Open questions related to Bose-Einstein correlations in e + e _  hadrons

ISMD 2003. Open questions related to Bose-Einstein correlations in e + e _  hadrons. G. Alexander. Tel-Aviv University. OUTLINE. 1. Introduction. 5. 2-D analysis and. 2. Emitter size vs. E CM. 6. Bose condensates and BEC?. 3. Fermi-Dirac correlations. 7. Generalized BEC.

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Open questions related to Bose-Einstein correlations in e + e _  hadrons

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  1. ISMD 2003 Open questions related to Bose-Einstein correlations in e+e_ hadrons G. Alexander Tel-Aviv University OUTLINE 1. Introduction 5. 2-D analysis and 2. Emitter size vs. ECM 6. Bose condensates and BEC? 3. Fermi-Dirac correlations 7. Generalized BEC 4. Emitter size vs. mass 8. Summary and conclusions

  2. Bose-Einstein Correlation (BEC) 1-Dimension analysis Correlation function:. GGLP variable

  3. A-A Collisions Hadron emitter radius in e+e_ vs. ECM • HBT effect in the 50’s measured stellar objects dimensions. In heavy ions, an early compilation of r vs. the projectile A can be described by [Chacon, P.R. C43 (1991) 2670] AA Collisions (projectile) What about the e+e_hadrons BEC dimension vs. ECM ?

  4. r versus No. of jets and multiplicity e+e_  Z0 hadrons 3-jets 2-jets

  5. An approach to the r dependence on ECM via factorial cumulant moments and hadron sources 1. 2. Cumulant dependence on number of sources Dealt with by several authors, among them: P. Lipa & B. Bushbeck, P.L. B223 (1989) 465 B. Bushbeck, H.C. Eggers & P. Lipa, P.L. B481 (2000) 187 G. Alexander & E. Sarkisyan, P.L. B487 (2000) 215

  6. Dilution factor, Sources and Cumulants Assumption: Pion-pair correlation exist only if both of the same source Dilution factor Dq For identical sources 

  7. Emitter size vs. hadron sources Consider 2-pion BEC from S sources  • Note: in AA collisions, S vs. A is hard to estimate !

  8. r(e+e_ h) dependence on ECM Neglect for simplicity four and more jets so that: e+e_ q + q + gluon  hadrons - Take: The measured average multiplicity [Boutemeur, Fortschr. Phys. 50 (01)] The gluon energy is determined from the total averaged charge multiplicity  Estimate Dilution Factor

  9. e+e_ hadron Emitter Radius Words of warning The experiments use different methods for: * Selection of data and cuts * Choice of reference sample * Fitting procedure Source dilution approach taking λS= λ1 normalized at 40 GeV

  10. The extension to Fermi-Dirac correlation Two Methods 1. Spin-Spin Correlation Functions for e.g. ;S=S1+S2

  11. Aleph Theextension to Fermi-Dirac Correlation (cont’d) 2. The phase space density approach Like in the BEC analysis one considers the density of identical baryon pairs as Q  0 Three reference samples

  12. r(m) from BEC and FDC analyses Uncertainty relations Z0hadrons with QCD potential

  13. r(m) derived from the Heisenberg uncertainty relations [G.Alexander, I.Cohen E.Levin, Phys. Lett. B452 (99) 159] * The two bosons are at threshold in their CMS, i.e. non-relativistic * Here we assume that: essentially independent of the mass and is ~10-24 sec depends on the kinetic energy i.e. potential energy small

  14. A challenge to the Lund string model A leading model for multi-hadron production Expects in its rudimental form 1-Dimension string “Toy” model

  15. Baryon production in the Lund Model

  16. Energy density of the hadron emitter Z0 hadrons [Dashed lines for

  17. 2-Dimensional BEC analysis Longitudinal Center of Mass System 2-dimension Correlation Function: Transverse mass:

  18. rz dependence on mT in ee Zohadrons Z0 hadrons (DELPHI preliminary)

  19. Uncertainty relations applied to 1) 2) 3) G.A., P.L. B506 (2001) 45

  20. r(mT) in heavy ion collisions [U. Heinz, Ann.Rev.Nucl.Part.Sci. 49(99)529] 1. 2.

  21. Bose Condensates – Brief reminder [ A. Einstein (Sitzber. Kgl. Preuss. Akad. Wiss. 1924/5)] * In a Condensate: All atoms are in the same zero energy state *E.A.Cornell, W.Ketterle, C.E.Wieman (Nobel 2001) discovered in 1995 rubidium (Rb), sodium (Na), lithium (Li) condensates * How ? By cooling down below a TB (500nK – 2000nK) dilute bosonic atoms Any relation between Condensates and Boson produced in HE reactions ? Try: Inter-Atomic Separation and the dimension extracted from BEC

  22. Inter-Atomic separation in Bose Condensates [G.A. Phys. Lett. B506(01)45] * In Bose condensates, when T/TB<< 1, the atomic density is: * The de Broglie wave length is: *Consider two condensates with masses m1 and m2 in the same temperature T0 (<< TB1, TB2):

  23. rBEC(m) formula from Bose condensates * Inter-atomic separation: * Replace: to get * However there are obvious differences between condensates and hadrons produced in HE reactions, e.g. 1) Condensates in thermal equilibrium, hadrons in HE reactions ? 2) Condensates in coherent state, hadrons only partly Note: dBE = inter-atomic separation NOT the condensate dimension !

  24. Isospin invariance and generalized BEC (GBEC) * In analogue to the Generalized Pauli exclusion principle one may consider a Generalized BEC where I-spin is included demanding an over-all symmetric state. * This possibility was considered by several authors among them Bowler (87), Suzuki (87) and Weiner (2000). Specific GBEC relations were worked out by Alexander & Lipkin (99) in the case that the multi-hadron final states emerge from an I=0 state. * The cases where hadrons emerge from an I=0 state is quit frequent. For example, in hadronic decays of Multi-gluon decays of and into odd numbers of pions

  25. Relations between the 2-pion systems in the GBEC Conclusions (if GBEC is valid) BEC effect in the

  26. Summary and Conclusions *In spite of the fact that BEC is studied over 40 years, absent are systematic studies covering different reactions over a wide energy range *In addition, a standardization of the analysis methods and reference samples would allow more meaningful interpretation of the experimental results ____________________ *r(Ecm) is rather well described by a simple approach to hadron-jet sources *This approach however seems not to be sufficient to account for the dr/dnch seen in the Zohadrons

  27. Summary and Conclusions (cont’d) *r(m), as determined from BEC and FDC analyses on the Zo , follows roughly the expectation derived from the Heisenberg relations as well as that extracted from a QCD potential. Needs to be measured also in other reactions ! *The dependence dr/dm < 0 poses a challenge to hadron production models including the Lund one *Above all, the energy density of about 100 GeV/fm3 affixed to the baryon emitter, awakes doubt on the r interpretation as an emitter radius ____________________ *Generalized BEC has not so far been experimentally verified. If confirmed then it has a considerable effect on the analyses of resonances and on the choice of reference samples ____________________

  28. Summary and Conclusions (cont’d) * The r(mT) extracted from the 2-D BEC analysis behaves similarly to the r(m) derived from the 1-D analyses and both can be described in terms of the Heisenberg uncertainty relations *To note is that r(mT) is proportional to (mT)-1/2 in A-A reactions as is also the case in e+e- collisions even though the latter one is free of nuclear effects !! * As for Bose condensates, is the inter-atomic and NOT the Bose condensate dimension ! Final question: * Are the behavior of dr/dm, the energy density and the meaning of dBE telling us that we should re-examine what does r measure? ?

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