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

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

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 ISMD'2005, KromerizO.Utyuzh/SINS2 High-Energy collisions Quantum statistics

3 ISMD'2005, KromerizO.Utyuzh/SINS3 Quantum Correlations (QS) x1x1 x2x2 p1p1 p2p2 BE enhancement

4 ISMD'2005, KromerizO.Utyuzh/SINS4 Correlation function (1D) – source size x1x1 x2x2 p1p1 p2p2 R source size R.Hunbury Brown and Twiss, Nature 178 (1956) 1046 G.Goldhaber, S.Goldhaber, W.Lee and A.Pais, Phys.Rev 120 (1960) 300

5 ISMD'2005, KromerizO.Utyuzh/SINS5 Model Monte-Carlo event generators (MC) Assumption 1 Assumption 2 Assumption 4 Assumption 3 MC

6 ISMD'2005, KromerizO.Utyuzh/SINS6 Model Monte-Carlo event generators (MC) Assumption 1 Assumption 2 Assumption 4 Assumption 3 MC Available Phase-Space

7 ISMD'2005, KromerizO.Utyuzh/SINS7 Monte-Carlo event generators (MC) change MC output to simulate proper behaviour

8 ISMD'2005, KromerizO.Utyuzh/SINS8 Numerical modeling of BEC * L.Lönblad, T.Sjöstrand, Eur.Phys.J. C2 (1998) 165 Momenta shifting * (a) Momenta shifting *

9 ISMD'2005, KromerizO.Utyuzh/SINS9 Momenta shifting * (a) Momenta shifting * Numerical modeling of BEC * L.Lönblad, T.Sjöstrand, Eur.Phys.J. C2 (1998) 165

10 ISMD'2005, KromerizO.Utyuzh/SINS10 Numerical modeling of BEC * K.Fiałkowski,R.Wit,J.Wosiek, Phys.Rev. D57 (1998) 0940013 weighting of events * (b) weighting of events * i j events recounting E i for each E i event one should take E j E j events

11 ISMD'2005, KromerizO.Utyuzh/SINS11 symmetrization * non-identical VS identical Boltzmann VS Bose-Einstein QuantumstatisticsQuantumstatistics - K.Zalewski, Nucl. Phys. Proc. Suppl. 74 (1999) 65 - A. Giovannini and H.B.Nielsen, Proc. Of the IV Int. Symp. On Mult. Hadrodyn., Pavia 1973 - S.Pratt, in “Quark-Gluon Plasma”, ed.R.C.Hwa (World Scientific Oubl. Co, Singaoure, 1999), p.700 * - E.M.Purcell, Nature 174 (1956) 1449 GEOMETRICAL

12 ISMD'2005, KromerizO.Utyuzh/SINS12 cell formation until first failure smearing particle energy in the cells MC particles production example model (1D) phase space (1D)

13 ISMD'2005, KromerizO.Utyuzh/SINS13 model (1D) phase space (1D) inputinput output

14 ISMD'2005, KromerizO.Utyuzh/SINS14 Clan model* Hadronic Source Clan 1 Clan 2 Clan 3 Independent production correlated correlated correlated * L. Van Hove and A. Giovannini, XVII Int. Symp. On Mult. Dyn., ed. by M.Markitan (World Scientific, Singapore 1987), p. 561

15 ISMD'2005, KromerizO.Utyuzh/SINS15 Clan 2 Clan model* Hadronic Source Clan 1 Clan 3 Independent production correlated correlated correlated * L. Van Hove and A. Giovannini, XVII Int. Symp. On Mult. Dyn., ed. by M.Markitan (World Scientific, Singapore 1987), p. 561

16 ISMD'2005, KromerizO.Utyuzh/SINS16 Clan model … (MD)  Pólya-Aeppli ( PA ) multiplicity distribution  Negative Binominal ( NB ) multiplicity distribution Quantum statistics * * J.Finkelstein, Phys. Rev. D37 (1988) 2446 and Ding-wei Huang, Phys. Rev. D58 (1998) 017501

17 ISMD'2005, KromerizO.Utyuzh/SINS17 model (3D) p-Spacex-Space  x·  p-correlations symetrization 1D-model 3D-model under condition plane waves

18 ISMD'2005, KromerizO.Utyuzh/SINS18 Preliminary results

19 ISMD'2005, KromerizO.Utyuzh/SINS19 WT  T P0P0 σnσn 45.63.50.31.050.710.834.2921.54/1.023.23/1.61 91.23.50.31.050.720.886.3701.55/1.056.31/2.39 182.43.50.31.050.741.978.9851.57/1.0812.60/3.29 W - dependence

20 ISMD'2005, KromerizO.Utyuzh/SINS20 T  T P0P0 σnσn 3.10.30.930.723.346.6961.56/1.047.12/2.50 3.50.31.050.720.886.3701.55/1.056.31/2.39 3.90.31.170.718.866.0751.57/1.075.72/2.42 T - dependence

21 ISMD'2005, KromerizO.Utyuzh/SINS21 T  T P0P0 σnσn 3.50.31.050.619.915.7141.41/0.706.74/2.46 3.50.31.050.720.886.3701.55/1.056.31/2.39 3.50.31.050.822.157.3011.79/1.555.89/2.26 P 0 - dependence

22 ISMD'2005, KromerizO.Utyuzh/SINS22  - dependence T  T P0P0 σnσn 3.50.10.350.721.846.9271.57/1.076.62/2.44 3.50.31.050.720.886.3701.55/1.056.31/2.39 3.50.51.750.719.655.8161.56/1.045.99/2.29

23 ISMD'2005, KromerizO.Utyuzh/SINS23 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

24 ISMD'2005, KromerizO.Utyuzh/SINS24 - energy distribution has a Bose-Einstein form … to be continued … Real MC implementation

25 ISMD'2005, KromerizO.Utyuzh/SINS25 Back-up Slides

26 ISMD'2005, KromerizO.Utyuzh/SINS26 - 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 …

27 ISMD'2005, KromerizO.Utyuzh/SINS27 WT  T P0P0 1/2 91.23.50.00.00.722.037.0811.57/1.076.69/2.46 91.23.50.31.050.720.886.3701.55/1.056.31/2.39

28 ISMD'2005, KromerizO.Utyuzh/SINS28

29 ISMD'2005, KromerizO.Utyuzh/SINS29 Correlation function (1D) - chaoticity x1x1 x2x2 p1p1 p2p2chaoticity resonances final state interactions final state interactions flows particles misindification particles misindification momentum resolution momentum resolution......

30 ISMD'2005, KromerizO.Utyuzh/SINS30 High-Energy collisions … A B

31 ISMD'2005, KromerizO.Utyuzh/SINS31 Correlation function (1D)

32 ISMD'2005, KromerizO.Utyuzh/SINS32

33 ISMD'2005, KromerizO.Utyuzh/SINS33

34 ISMD'2005, KromerizO.Utyuzh/SINS34 ”... 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.

35 ISMD'2005, KromerizO.Utyuzh/SINS35

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