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Coulomb final state interactions and modelling B-E correlations

Coulomb final state interactions and modelling B-E correlations. O.Utyuzh. The Andrzej Sołtan Institute for Nuclear Studies (SINS) , Warsaw, Poland. Correlation s: quantum statistics (QS). p 1. BE enhancement. x 1. x 2. p 2. - Gamov factor. point-like source only.

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Coulomb final state interactions and modelling B-E correlations

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  1. Coulomb final state interactions and modelling B-E correlations O.Utyuzh The Andrzej Sołtan Institute for Nuclear Studies (SINS), Warsaw, Poland

  2. Correlations: quantum statistics (QS) p1 BE enhancement x1 x2 p2 O.Utyuzh/SINS

  3. - Gamov factor point-like source only Correlations: QS+Coulomb FSI p1 BE+FSIenhancement BE enhancement x1 x2 p2 O.Utyuzh/SINS

  4. NA49 Collab., Eur. Phys. J. C2(1998) 661 *G. Baym and P. Braun-Munzinger, Nucl. Phys.A610 (1996) 286c. O.Utyuzh/SINS

  5. - determined from a fit of the - Gamov factor NA49 Collab., nucl-ex/9808006, presented at CRIS’98 O.Utyuzh/SINS

  6. halo core momentum resolution Core-Halo model* direct direct short-lived sources short-lived sources long-lived sources long-lived sources *S.Nickerson, T.Csörgő and D.Kiang, Phys.Rev. C57 (1998) 3251 O.Utyuzh/SINS

  7. Core-Halo model (Coulomb FSI)* proposed byYu.M. Sinyukov et al., Phys. Lett.B432 (1998) 248 adopted byCERES Collab., Nucl. Phys.A714 (2003) 124 HALO CORE Integration over Gaussian source of 5 fm size* *G. Baym and P. Braun-Munzinger, Nucl. Phys.A610 (1996) 286c. O.Utyuzh/SINS

  8. Bertsch-Pratt HBT radius parameters CERES Collab., Nucl. Phys.A714 (2003) 124 no Coulomb repulsion full Coulomb strength partial Coulomb repulsion with The inclusion of (kT) into the Coulomb termK’ accounts for the apparent depletion of λ due to the finite momentumresolution and assures the appropriate scaling of the Coulomb correction. partial Coulomb repulsion with kT dependent reduction of λdue to finite momentumresolution Rout and correspondingly Rout/Rside are very sensitive tothe procedureemployed O.Utyuzh/SINS

  9. STAR Collab.,Phys. Rev.C71 (2004) 044906 standard dilution Under assumption f=λ(λ is the fraction of primary pions): ROincreasesby 10-15% λdecreases by 10-15% Bowler-Sinyukov similar to the values for dilution procedure Rout and correspondingly Rout/Rside are very sensitive tothe procedureemployed O.Utyuzh/SINS

  10. Many of relatively long-lived particles (e.g.), which have a Bose-Einstein interference too narrow to be resolved by experiment, also have a Coulomb interaction. introduce a new parameter,, todecouple the Coulomb and Bose-Einstein fractions. PHENIX Collab., Phys. Rev. Lett.93 (2004) 152302 HALO CORE HALO CORE Coulomb only O.Utyuzh/SINS

  11. PHENIX Collab.,Phys. Rev. Lett. 93 (2004) 152302 Full Coulomb correction by S. Pratt, Phys. Rev.D33 (1986) 72 full corrected uncorrected (1) (2) O.Utyuzh/SINS

  12. PHENIX Collab.,Phys. Rev. Lett.93 (2004) 052302 O.Utyuzh/SINS

  13. PHOBOS Collab., nucl-ex/0409001 HALO CORE O.Utyuzh/SINS

  14. PHOBOS Collab.,nucl-ex/0409001 STAR PHOBOS PHENIX results showed no significant change using either correction method. If λ=1, all methods are equivalent O.Utyuzh/SINS

  15. Gideon Alexander,Rep.Prog.Phys.66(2003), 481 The Coulomb correction to the BEC correlation function (a) for two identical charged-pion systems as a function of Q2 and (b) for the three charged pion systems as a function of Q3. n – particle Coulomb O.Utyuzh/SINS

  16. OPAL Collab.,Eur.Phys.J.C5(1998) 239 w/o Coulomb w/ Coulomb O.Utyuzh/SINS

  17. * E.O.Alt, T.Csörgő, B.Lörstad and J.Schmidt-Sørensen,Phys.Lett.B458 (1999) 407 E.O.Alt, T.Csörgő, B.Lörstad and J.Schmidt-Sørensen, Eur. Phys. J.C13 (2000) 663 O.Utyuzh/SINS

  18. STAR Collab.,Phys. Rev.C71 (2004) 044906 The “central” Coulomb potential p1 p`1 - x1 The Coulomb interaction between the outgoing charged pions and the residual positive charge in the source is negligible D. Hardtke and T. J. Humanic, Phys. Rev.C57 (1998) 3314 x2 - p`2 p2 *G. Baym and P. Braun-Munzinger, Nucl. Phys.A610 (1996) 286c. O.Utyuzh/SINS

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

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

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

  22. 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

  23. non-identicalVSidenticalBoltzmannVSBose-Einstein Quantum statistics GEOMETRICAL symmetrization* BOSE-EINSTEIN * - 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

  24. Boltzmann particles production Numerical modeling of BEC EXAMPLE O.Utyuzh/SINS

  25. add particles to cells until firstfailure Numerical modeling of BEC elementary emitting cells (EEC) O.Utyuzh/SINS

  26. smearing particleenergy inthecells Numerical modeling of BEC O.Utyuzh/SINS

  27. Coulomb Final State Interaction (FSI) Correlate x·p according to instead of under condition model (3D) p-Space x-Space symetrization x·p-correlations 3D-model 1D-model O.Utyuzh/SINS

  28. W - dependence O.Utyuzh/SINS

  29. T - dependence O.Utyuzh/SINS

  30. P0 - dependence O.Utyuzh/SINS

  31.  - dependence O.Utyuzh/SINS

  32. O.Utyuzh/SINS

  33. Coulomb Final State Interaction (FSI) Correlate x·p according to instead of O.Utyuzh/SINS

  34. Back-up Slides O.Utyuzh/SINS

  35. H. Heiselberg,Phys.Lett.B379(1996) 27 Resonance contributions to the correlation function as function of Qout Curves include successively direct pions, ρ, Δ, K∗, Σ∗, ω and η+ η′ + K0S + Σ + ... from RQMD O.Utyuzh/SINS

  36. D.H.Boal, C.Gelbke and B.K.Jennings Rev. Mod.Phys.62 (1990) 553 Charged-particle multiplicity (Nch) dependence of the correlation function for reaction ppbar→2π+X at sqrts=630 GeV. O.Utyuzh/SINS

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

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

  39. 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

  40. 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

  41. 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

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