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BEC from "inside"

BEC from "inside". O.Utyuzh. The Andrzej Sołtan Institute for Nuclear Studies (SINS) , Warsaw, Poland. * In collaboration with G.Wilk and Z.Wlodarczyk. High-Energy collisions. Quantum statistics. Quantum Correlations (QS). p 1. BE enhancement. x 1. x 2. p 2. p 2. x 2. R source

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BEC from "inside"

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  1. BEC from "inside" O.Utyuzh The Andrzej Sołtan Institute for Nuclear Studies (SINS), Warsaw, Poland * In collaboration with G.Wilk and Z.Wlodarczyk

  2. High-Energy collisions Quantum statistics O.Utyuzh/SINS

  3. Quantum Correlations (QS) p1 BE enhancement x1 x2 p2 O.Utyuzh/SINS

  4. p2 x2 R source size x1 p1 Correlationfunction (1D) – sourcesize R.Hunbury Brown and Twiss, Nature178 (1956) 1046 G.Goldhaber, S.Goldhaber, W.Lee and A.Pais, Phys.Rev120 (1960) 300 O.Utyuzh/SINS

  5. Monte-Carlo event generators (MC) Model Assumption 1 MC Assumption 2 Assumption 3 Assumption 4 O.Utyuzh/SINS

  6. Monte-Carlo event generators (MC) Model Assumption 1 MC Assumption 2 Available Phase-Space Assumption 3 Assumption 4 O.Utyuzh/SINS

  7. change MC output to simulate proper behaviour Monte-Carlo event generators (MC) O.Utyuzh/SINS

  8. Numerical modeling of BEC (a)Momenta shifting* *L.Lönblad, T.Sjöstrand, Eur.Phys.J. C2 (1998) 165 O.Utyuzh/SINS

  9. Numerical modeling of BEC (a)Momenta shifting* *L.Lönblad, T.Sjöstrand, Eur.Phys.J. C2 (1998) 165 O.Utyuzh/SINS

  10. for eachEievent one should take Ejevents Numerical modeling of BEC (b)weighting of events* j i events recounting *K.Fiałkowski,R.Wit,J.Wosiek, Phys.Rev. D57(1998) 0940013 O.Utyuzh/SINS

  11. non-identicalVSidenticalBoltzmannVSBose-Einstein Quantum statistics GEOMETRICAL symmetrization* * - E.M.Purcell, Nature174 (1956) 1449 - A. Giovannini and H.B.Nielsen, Proc. Of the IV Int. Symp. On Mult. Hadrodyn., Pavia 1973 - K.Zalewski, Nucl. Phys. Proc. Suppl. 74 (1999) 65 - S.Pratt, in “Quark-Gluon Plasma”, ed.R.C.Hwa (World Scientific Oubl. Co, Singaoure, 1999), p.700 O.Utyuzh/SINS

  12. MC particles production cellformation untilfirst failure example phasespace (1D) phasespace (1D) phasespace (1D) smearing particleenergy inthecells model (1D) O.Utyuzh/SINS

  13. output input phasespace (1D) phasespace (1D) phasespace (1D) model (1D) O.Utyuzh/SINS

  14. Clan model* Clan1 correlated Hadronic Source Clan2 correlated Independent production Clan3 correlated *L. Van Hove and A. Giovannini, XVII Int. Symp. On Mult. Dyn., ed. by M.Markitan (World Scientific, Singapore 1987), p. 561 O.Utyuzh/SINS

  15. Clan model* Clan1 correlated Hadronic Source Clan2 correlated Independent production Clan3 correlated *L. Van Hove and A. Giovannini, XVII Int. Symp. On Mult. Dyn., ed. by M.Markitan (World Scientific, Singapore 1987), p. 561 O.Utyuzh/SINS

  16. Clan model …(MD) Quantum statistics* Negative Binominal( NB ) multiplicity distribution Pólya-Aeppli ( PA ) multiplicity distribution * J.Finkelstein, Phys. Rev. D37 (1988) 2446 and Ding-wei Huang, Phys. Rev. D58 (1998) 017501 O.Utyuzh/SINS

  17. under condition model (3D) p-Space x-Space symetrization plane waves x·p-correlations 3D-model 1D-model O.Utyuzh/SINS

  18. Preliminary results O.Utyuzh/SINS

  19. W - dependence O.Utyuzh/SINS

  20. T - dependence O.Utyuzh/SINS

  21. P0 - dependence O.Utyuzh/SINS

  22.  - dependence O.Utyuzh/SINS

  23. summary • 2 steps way to model Bose-Einstein correlations: • create cells in phase space allocate particles to them (until first failure) • correlate momenta and positions of particles in the cells according to • function obtained from symmetrization procedure. • What one can get: • geometrical distribution in the cells • Negative-Binomial like • distribution in the event O.Utyuzh/SINS

  24. energy distribution has a Bose-Einstein form … to be continued … Real MC implementation O.Utyuzh/SINS

  25. Back-up Slides O.Utyuzh/SINS

  26. energy distribution has a Bose-Einstein form • - a simple way to include Final State Interaction (FSI) effects: Coulomb Final State Interaction (FSI) Correlate x·p according to instead of … to be continued … O.Utyuzh/SINS

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  29. resonances • finalstateinteractions • flows • particlesmisindification • momentum resolution • ... p2 x2 x1 p1 Correlationfunction (1D) - chaoticity chaoticity O.Utyuzh/SINS

  30. High-Energy collisions … B A O.Utyuzh/SINS

  31. Correlationfunction (1D) O.Utyuzh/SINS

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  33. O.Utyuzh/SINS

  34. ”... The correlation is determined by the size of the region from which pions are emitted with roughly the same momenta. This has the consequence that for collectively streaming matter this region is smaller than the total source due to the strong correlation between the momenta and the emission points of the particles.”- H.W.Barz, nucl-th/9808027. ”... The chaoticity of the source, i.e., the absence of initial correlations between the two emitted pions except those correlations coming from the Bose-Einstein statistics”- H.W.Barz, nucl-th/9808027. O.Utyuzh/SINS

  35. O.Utyuzh/SINS

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