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

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Presentation transcript:

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

WPCF'2005 KromerizO.Utyuzh/SINS2 Correlations: quantum statistics (QS) x1x1 x2x2 p1p1 p2p2 BE enhancement

WPCF'2005 KromerizO.Utyuzh/SINS3 Correlations: QS+Coulomb FSI x1x1 x2x2 p1p1 p2p2 BE enhancement BE+FSI enhancement - Gamov factor point-like source only

WPCF'2005 KromerizO.Utyuzh/SINS4 NA49 Collab. NA49 Collab., Eur. Phys. J. C2 (1998) 661 * G. Baym and P. Braun-Munzinger, Nucl. Phys. A610 (1996) 286c.

WPCF'2005 KromerizO.Utyuzh/SINS5 - Gamov factor - determined from a fit of the NA49 Collab. NA49 Collab., nucl-ex/ , presented at CRIS’98

WPCF'2005 KromerizO.Utyuzh/SINS6 short-lived sources long-lived sources direct halo core short-lived sources Core-Halo model * * S.Nickerson, T.Csörgő and D.Kiang, Phys. Rev. C57 (1998) 3251 long-lived sources momentum resolution

WPCF'2005 KromerizO.Utyuzh/SINS7 CERES Collab. Nucl. Phys. A714 (2003) 124 adopted by CERES Collab., Nucl. Phys. A714 (2003) 124 Integration over Gaussian source of 5 fm size * * G. Baym and P. Braun-Munzinger, Nucl. Phys. A610 (1996) 286c. Core-Halo model (Coulomb FSI) * proposed by Yu.M. Sinyukov et al., Phys. Lett. B432 (1998) 248 HALOCORE

WPCF'2005 KromerizO.Utyuzh/SINS8 The inclusion of  (k T ) into the Coulomb term K ’ accounts for the apparent depletion of λ due to the finite momentum resolution and assures the appropriate scaling of the Coulomb correction. k T dependent reduction of λ due to finite momentum resolution full Coulomb strength partial Coulomb repulsion with no Coulomb repulsion partial Coulomb repulsion with Bertsch-Pratt HBT radius parameters CERES Collab. Nucl. Phys. A714 (2003) 124 CERES Collab., Nucl. Phys. A714 (2003) 124 R out and correspondingly R out /R side are very sensitive to the procedure employed R out and correspondingly R out /R side are very sensitive to the procedure employed

WPCF'2005 KromerizO.Utyuzh/SINS9 standard dilution Bowler-Sinyukov STAR Collab. STAR Collab., Phys. Rev. C71 (2004) Under assumption f=λ (λ is the fraction of primary pions): R O increases by 10-15% λ decreases by 10-15% Under assumption f=λ (λ is the fraction of primary pions): R O increases by 10-15% λ decreases by 10-15% similar to the values for dilution procedure R out and correspondingly R out /R side are very sensitive to the procedure employed R out and correspondingly R out /R side are very sensitive to the procedure employed

WPCF'2005 KromerizO.Utyuzh/SINS10 PHENIX Collab. PHENIX Collab., Phys. Rev. Lett. 93 (2004) introduce a new parameter,, to decouple the Coulomb and Bose-Einstein fractions. HALOCORECoulombonly HALOCORE 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.

WPCF'2005 KromerizO.Utyuzh/SINS11 PHENIX Collab. PHENIX Collab., Phys. Rev. Lett. 93 (2004) full correcteduncorrected Full Coulomb correction by S. Pratt, Phys. Rev. D33 (1986) 72 (1) (2)

WPCF'2005 KromerizO.Utyuzh/SINS12 PHENIX Collab. PHENIX Collab., Phys. Rev. Lett. 93 (2004)

WPCF'2005 KromerizO.Utyuzh/SINS13 PHOBOS Collab.nucl-ex/ PHOBOS Collab., nucl-ex/ HALOCORE

WPCF'2005 KromerizO.Utyuzh/SINS14 STARPHOBOSPHENIX PHOBOS Collab. PHOBOS Collab., nucl-ex/ results showed no significant change using either correction method. results showed no significant change using either correction method. If λ=1, all methods are equivalent

WPCF'2005 KromerizO.Utyuzh/SINS15 The Coulomb correction to the BEC correlation function (a) for two identical charged-pion systems as a function of Q 2 and (b) for the three charged pion systems as a function of Q 3. Gideon Alexander, Rep.Prog.Phys. 66 (2003), 481 n – particle Coulomb

WPCF'2005 KromerizO.Utyuzh/SINS16 w/o Coulombw/ Coulomb OPAL Collab. OPAL Collab., Eur.Phys.J. C5 (1998) 239

WPCF'2005 KromerizO.Utyuzh/SINS17 * 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

WPCF'2005 KromerizO.Utyuzh/SINS18 x1x1 x2x2 p1p1 p2p2 p`1p`1 p`2p`2  - -  - - The “central” Coulomb potential * G. Baym and P. Braun-Munzinger, Nucl. Phys. A610 (1996) 286c. V s (MeV) R s (fm) R o (fm) R l (fm) λ ± ± ± ± (  -  - ) 5.53 ± ± ± ± (  +  + ) 5.33 ± ± ± ±0.02 D. Hardtke and T. J. Humanic, Phys. Rev. C57 (1998) 3314 STAR Collab. STAR Collab., Phys. Rev. C71 (2004) The Coulomb interaction between the outgoing charged pions and the residual positive charge in the source is negligible

WPCF'2005 KromerizO.Utyuzh/SINS19 Monte-Carlo event generators (MC) change MC output to simulate proper behaviour

WPCF'2005 KromerizO.Utyuzh/SINS20 Numerical modeling of BEC * L.Lönblad, T.Sjöstrand, Eur.Phys.J. C2 (1998) 165 Momenta shifting * (a) Momenta shifting *

WPCF'2005 KromerizO.Utyuzh/SINS21 * L.Lönblad, T.Sjöstrand, Eur.Phys.J. C2 (1998) 165 Momenta shifting * (a) Momenta shifting * Numerical modeling of BEC

WPCF'2005 KromerizO.Utyuzh/SINS22 Numerical modeling of BEC * K.Fiałkowski,R.Wit,J.Wosiek, Phys.Rev. D57 (1998) 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

WPCF'2005 KromerizO.Utyuzh/SINS23 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 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 BOSE-EINSTEIN

WPCF'2005 KromerizO.Utyuzh/SINS24 Numerical modeling of BEC Boltzmann particles production EXAMPLE

WPCF'2005 KromerizO.Utyuzh/SINS25 Numerical modeling of BEC add particles to cells until first failure elementary emitting cells (EEC)

WPCF'2005 KromerizO.Utyuzh/SINS26 Numerical modeling of BEC smearing particle energy in the cells

WPCF'2005 KromerizO.Utyuzh/SINS27 model (3D) p-Spacex-Space  x·  p-correlations symetrization 1D-model 3D-model under condition Coulomb Final State Interaction (FSI) Correlate  x·  p according to instead of

WPCF'2005 KromerizO.Utyuzh/SINS28 WT  T P0P / / / / / /3.29 W - dependence

WPCF'2005 KromerizO.Utyuzh/SINS29 T  T P0P / / / / / /2.42 T - dependence

WPCF'2005 KromerizO.Utyuzh/SINS30 T  T P0P / / / / / /2.26 P 0 - dependence

WPCF'2005 KromerizO.Utyuzh/SINS31  - dependence T  T P0P / / / / / /2.29

WPCF'2005 KromerizO.Utyuzh/SINS32 WT  T P0P0 1/ / / / /2.39

WPCF'2005 KromerizO.Utyuzh/SINS33 Coulomb Final State Interaction (FSI) Correlate  x·  p according to instead of

WPCF'2005 KromerizO.Utyuzh/SINS34 Back-up Slides

WPCF'2005 KromerizO.Utyuzh/SINS35 Resonance contributions to the correlation function as function of Q out Curves include successively direct pions, ρ, Δ, K ∗, Σ ∗, ω and η + η′ + K 0 S + Σ +... from RQMD H. Heiselberg, Phys.Lett. B379 (1996) 27

WPCF'2005 KromerizO.Utyuzh/SINS36 Charged-particle multiplicity (N ch ) dependence of the correlation function for reaction ppbar→2π+X at sqrts=630 GeV. D.H.Boal, C.Gelbke and B.K.Jennings Rev. Mod.Phys. 62 (1990) 553

WPCF'2005 KromerizO.Utyuzh/SINS37 cell formation until first failure smearing particle energy in the cells MC particles production example model (momenta correlations) phase space (1D)

WPCF'2005 KromerizO.Utyuzh/SINS38 model (1D) phase space (1D) inputinput output

WPCF'2005 KromerizO.Utyuzh/SINS39 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

WPCF'2005 KromerizO.Utyuzh/SINS40 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

WPCF'2005 KromerizO.Utyuzh/SINS41 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)