Coulomb final state interactions and modelling BE correlations

Coulomb final state interactions and modelling B-E correlations O. Utyuzh The Andrzej Sołtan Institute for Nuclear Studies (SINS), Warsaw, Poland WPCF'2005 Kromeriz O. Utyuzh/SINS

Correlations: quantum statistics (QS) p 1 BE enhancement x 1 x 2 p 2 WPCF'2005 Kromeriz O. Utyuzh/SINS 2

Correlations: QS+Coulomb FSI p 1 BE+FSI enhancement BE enhancement x 1 x 2 p 2 - Gamov factor WPCF'2005 Kromeriz O. Utyuzh/SINS point-like source only 3

NA 49 Collab. , Collab. Eur. Phys. J. C 2 (1998) 661 *G. Baym and P. Braun-Munzinger, Nucl. Phys. A 610 (1996) 286 c. WPCF'2005 Kromeriz O. Utyuzh/SINS 4

NA 49 Collab. , Collab. nucl-ex/9808006, presented at CRIS’ 98 - Gamov factor - determined from a fit of the WPCF'2005 Kromeriz O. Utyuzh/SINS 5

Core-Halo model* direct halo short-lived sources long-lived sources core momentum resolution *S. Nickerson, T. Csörgő and D. Kiang, Phys. Rev. C 57 (1998) 3251 WPCF'2005 Kromeriz O. Utyuzh/SINS 6

Core-Halo model (Coulomb FSI)* proposed by Yu. M. Sinyukov et al. , Phys. Lett. B 432 (1998) 248 adopted by CERES Collab. , Collab. Nucl. Phys. A 714 (2003) 124 HALO CORE Integration over Gaussian source of 5 fm size* *G. Baym and P. Braun-Munzinger, Nucl. Phys. A 610 (1996) 286 c. WPCF'2005 Kromeriz O. Utyuzh/SINS 7

k. T dependent reduction Bertsch-Pratt HBT radius parameters of λ due to finite CERES Collabmomentum. , Nucl. Phys. A 714 (2003) 124 resolution Rout and correspondingly Rout/Rside are very sensitive to the procedure employed full Coulombof strength partial Coulomb The inclusion (k. T) into the Coulomb term K’ repulsion accountswith for the apparent no Coulomb repulsion partial Coulomb repulsion depletion of λ due to the finite momentum resolution andwith assures the appropriate scaling of the Coulomb correction. WPCF'2005 Kromeriz O. Utyuzh/SINS 8

STAR Collab. , Collab. Phys. Rev. C 71 (2004) 044906 standard dilution Under assumption f=λ (λ is the fraction of primary pions): RO increases by 10 -15% λ decreases by 10 -15% Bowler-Sinyukov similar to the values for dilution procedure Rout and correspondingly Rout/Rside are very sensitive to the procedure employed WPCF'2005 Kromeriz O. Utyuzh/SINS 9

PHENIX Collab. , Collab. Phys. Rev. Lett. 93 (2004) 152302 HALO CORE 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. HALO introduce a new parameter, fractions. WPCF'2005 Kromeriz CORE Coulomb only , to decouple the Coulomb and Bose-Einstein O. Utyuzh/SINS 10

Collab. , 93 Rev. (2004) 152302 Collab. Phys. Full. PHENIX Coulomb correction by S. Rev. Pratt, Lett. Phys. D 33 (1986) 72 (1) (2) full corrected WPCF'2005 Kromeriz uncorrected O. Utyuzh/SINS 11

PHENIX Collab. , Collab. Phys. Rev. Lett. 93 (2004) 052302 WPCF'2005 Kromeriz O. Utyuzh/SINS 12

PHOBOS Collab. , Collab. nucl-ex/0409001 HALO WPCF'2005 Kromeriz O. Utyuzh/SINS CORE 13

results showed no. significant change PHOBOS Collab , nucl-ex/0409001 using either correction method. If λ=1, all methods are equivalent STAR WPCF'2005 Kromeriz PHOBOS O. Utyuzh/SINS PHENIX 14

n – particle Coulomb 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 Q 2 and (b) for the three charged pion systems as a function of Q 3. WPCF'2005 Kromeriz O. Utyuzh/SINS 15

OPAL Collab. , Eur. Phys. J. C 5 (1998) 239 w/o Coulomb WPCF'2005 Kromeriz w/ Coulomb O. Utyuzh/SINS 16

* E. O. Alt, T. Csörgő, B. Lörstad and J. Schmidt-Sørensen, Phys. Lett. B 458 (1999) 407 E. O. Alt, T. Csörgő, B. Lörstad and J. Schmidt-Sørensen, Eur. Phys. J. C 13 (2000) 663 WPCF'2005 Kromeriz O. Utyuzh/SINS 17

The “central” Coulomb potential STAR Collab. , Collab. Phys. Rev. C 71 (2004) 044906 p 1 p`1 - x 1 The Coulomb interaction between the charged residual D. Hardtke and T. outgoing J. Humanic, Phys. pions Rev. and C 57 the (1998) 3314 positive charge in the source is negligible x 2 Vs (Me. V) 0. 0 -5. 0 ( - - ) 5. 0 ( + +) *G. Rs (fm) - Ro (fm) Rl (fm) λ 5. 55 ± 0. 12 6. 37 ± 0. 26 8. 13 ± 0. 63 ± 0. 03 p` 2 5. 53 ± 0. 09 6. 17 ± 0. 06 6. 73 ± 0. 13 0. 54 ± 0. 01 p 2 5. 33 ± 0. 10 6. 14 ± 0. 16 7. 38 ± 0. 22 0. 62 ± 0. 02 Baym and P. Braun-Munzinger, Nucl. Phys. A 610 (1996) 286 c. WPCF'2005 Kromeriz O. Utyuzh/SINS 18

Monte-Carlo event generators (MC) change MC output to simulate proper WPCF'2005 Kromeriz O. Utyuzh/SINS behaviour 19

Numerical modeling of BEC (a) Momenta shifting* * L. Lönblad, T. Sjöstrand, Eur. Phys. J. C 2 (1998) 165 WPCF'2005 Kromeriz O. Utyuzh/SINS 20

Numerical modeling of BEC (a) Momenta shifting* * L. Lönblad, T. Sjöstrand, Eur. Phys. J. C 2 (1998) 165 WPCF'2005 Kromeriz O. Utyuzh/SINS 21

Numerical modeling of BEC (b) weighting of events* j i for each Ei event one should take events recounting Ej events * K. Fiałkowski, R. Wit, J. Wosiek, Phys. Rev. D 57 (1998) 0940013 WPCF'2005 Kromeriz O. Utyuzh/SINS 22

non-identical VS identical Boltzmann VS Bose-Einstein Quantum statistics GEOMETRICAL symmetrization* BOSE-EINSTEIN * - E. M. Purcell, Nature 174 (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 WPCF'2005 Kromeriz O. Utyuzh/SINS 23

Numerical modeling of BEC EXAMPLE Boltzmann particles production WPCF'2005 Kromeriz O. Utyuzh/SINS 24

Numerical modeling of BEC elementary emitting cells (EEC) add particles to cells until first failure WPCF'2005 Kromeriz O. Utyuzh/SINS 25

Numerical modeling of BEC smearing particle energy in the cells WPCF'2005 Kromeriz O. Utyuzh/SINS 26

model (3 D) Coulomb Final State Interaction (FSI) p-Space x-Space Correlate x· p according to instead of symetrization x· p-correlations 1 D-model 3 D-model under condition WPCF'2005 Kromeriz O. Utyuzh/SINS 27

W - dependence T W T 45. 6 3. 5 0. 3 1. 05 0. 7 10. 83 4. 292 1. 54/1. 02 3. 23/1. 61 91. 2 3. 5 0. 3 1. 05 0. 7 20. 88 6. 370 1. 55/1. 05 6. 31/2. 39 182. 4 3. 5 0. 3 1. 05 0. 7 WPCF'2005 Kromeriz P 0 <nch> 41. 97 <nch 2> <npart> <ncell> 8. 985 1. 57/1. 08 12. 60/3. 29 O. Utyuzh/SINS 28

T - dependence T T P 0 <nch> <nch 2> <npart> <ncell> 0. 3 0. 93 0. 7 23. 34 6. 696 1. 56/1. 04 7. 12/2. 50 3. 5 0. 3 1. 05 0. 7 20. 88 6. 370 1. 55/1. 05 6. 31/2. 39 3. 9 0. 3 0. 7 18. 86 6. 075 1. 57/1. 07 5. 72/2. 42 3. 1 1. 17 WPCF'2005 Kromeriz O. Utyuzh/SINS 29

P 0 - dependence T T P 0 <nch> <nch 2> 3. 5 0. 3 1. 05 0. 6 19. 91 5. 714 1. 41/0. 70 6. 74/2. 46 3. 5 0. 3 1. 05 0. 7 20. 88 6. 370 1. 55/1. 05 6. 31/2. 39 3. 5 0. 3 1. 05 0. 8 22. 15 7. 301 1. 79/1. 55 5. 89/2. 26 WPCF'2005 Kromeriz O. Utyuzh/SINS <npart> <ncell> 30

- dependence T T P 0 <nch> <nch 2> <npart> <ncell> 3. 5 0. 1 0. 35 0. 7 21. 84 6. 927 1. 57/1. 07 6. 62/2. 44 3. 5 0. 3 1. 05 0. 7 20. 88 6. 370 1. 55/1. 05 6. 31/2. 39 3. 5 0. 7 19. 65 5. 816 1. 56/1. 04 5. 99/2. 29 1. 75 WPCF'2005 Kromeriz O. Utyuzh/SINS 31

W T T P 0 <nch> <nch 2>1/2 91. 2 3. 5 0. 0 0. 7 22. 03 7. 081 1. 57/1. 07 6. 69/2. 46 91. 2 3. 5 0. 3 1. 05 0. 7 20. 88 6. 370 1. 55/1. 05 6. 31/2. 39 WPCF'2005 Kromeriz O. Utyuzh/SINS <npart> <ncell> 32

Coulomb Final State Interaction (FSI) Correlate x· p according to WPCF'2005 Kromeriz instead of O. Utyuzh/SINS 33

Back-up Slides WPCF'2005 Kromeriz O. Utyuzh/SINS 34

H. Heiselberg, Phys. Lett. B 379 (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′ + K 0 S + Σ +. . . from RQMD WPCF'2005 Kromeriz O. Utyuzh/SINS 35

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 Ge. V. WPCF'2005 Kromeriz O. Utyuzh/SINS 36

model (momenta correlations) MC particles production example phase space (1 D) cell formation until first failure phase space (1 D) smearing particle energy in the cells phase space (1 D) WPCF'2005 Kromeriz O. Utyuzh/SINS 37

model (1 D) output input phase space (1 D) WPCF'2005 Kromeriz O. Utyuzh/SINS 38

correlated Clan 1 Clan 3 correlated Clan 2 correlated Hadronic Source Independent production Clan model* * L. Van Hove and A. Giovannini, XVII Int. Symp. On Mult. Dyn. , ed. by M. Markitan (World Scientific, Singapore 1987), p. 561 WPCF'2005 Kromeriz O. Utyuzh/SINS 39

correlated Clan 1 Clan 3 correlated Clan 2 correlated Hadronic Source Independent production Clan model* * L. Van Hove and A. Giovannini, XVII Int. Symp. On Mult. Dyn. , ed. by M. Markitan (World Scientific, Singapore 1987), p. 561 WPCF'2005 Kromeriz O. Utyuzh/SINS 40

Clan model … (MD) v Quantum statistics* Negative Binominal ( NB ) multiplicity distribution v Pólya-Aeppli ( PA ) multiplicity distribution * J. Finkelstein, Phys. Rev. D 37 (1988) 2446 and Ding-wei Huang, Phys. Rev. D 58 (1998) 017501 WPCF'2005 Kromeriz O. Utyuzh/SINS 41