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On the Δ t time scale in Bose-Einstein and Fermi-Dirac correlations

WPCF 2009. On the Δ t time scale in Bose-Einstein and Fermi-Dirac correlations. arXiv: 0910.0138 [hep-ph]. Gideon Alexander and Erez Reinherz-Aronis. Tel-Aviv University. OUTLINE. 1. A brief introduction. 4. Δ t as the particle emission time. 2. R 1D from Z 0 decays.

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On the Δ t time scale in Bose-Einstein and Fermi-Dirac correlations

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  1. WPCF 2009 On the Δt time scalein Bose-Einstein and Fermi-Dirac correlations arXiv: 0910.0138 [hep-ph] Gideon Alexander and Erez Reinherz-Aronis Tel-Aviv University OUTLINE 1. A brief introduction 4. Δt as the particle emission time 2. R1D from Z0decays 5. It’s consequence to heavy ions 6. Comments and remarks 3. A closer look at Δt

  2. Bose-Einstein Correlation (BEC)-Reminder 1-Dimension analysis of two identical bosons Correlation function: GGLP variable:

  3. π±π±BEC from heavy nuclei – dependence on A Taken from WA98 collaboration (2007) arXiv 0709.2477 R vs. the target A1/3 Note: only few BEC of K-pairs

  4. Aleph P.L. B475 (00) 395 ΛΛFDC Three reference samples No need for Coulomb correction ! 1. ΛΛ Spin-Spin correlation(Alexander & Lipkin P.L. B352 (1995) 162) The extension to Fermi-Dirac Correlation for di-fermions Does not need a reference sample nor Coulomb correction 2.The phase space density approach(Pauli Exclusion principle) Like in the BEC analysis one considers the density of the identical baryon pairs as Q  0

  5. R1D(m) fromBECandFDCanalysesof the Z0 hadronic decays at LEP

  6. R1D(m) fromBECandFDCanalysesof the Z0 hadronic decays at LEP

  7. R(m) derived from the Heisenberg uncertainty relations [G.Alexander, I.Cohen, E.Levin, Phys. Lett. B452 (99) 159, G.Alexander, Phys.Lett. B506 (2001) 45] The two bosons are near threshold in their CMS, i.e. non-relativistic Note: For m≠0 It was further assumed that: Represents the interaction strength i.e.~10-24 sec for S.I. Depends on the kinetic energy i.e. potential energy is small

  8. R1D(m) fromBECandFDCanalysesof the Z0 hadronic decays at LEP Uncertainty relations For S.I. QCD potential

  9. Bialas et al. P.R. D62 (00) 114007; Bialas et al. Acta Phys.Polon.B32 (01) 2901 mT [GeV] Application of the Bjorken-Gottfried relation to R(mT) There exists a linear relationqµ=λxµ between the 4-momentum and the time-space which implies λ=mT/τ where τ=(t2-z2)0.5 is the longitudinal proper time

  10. Question: Is this m dependence of R unique to the Z decays ? Δt=(1.28±0.04)x10-22 sec 1st time BEC of di-deuteron WA98 Collaboration (2007); arXiv:0709.2477 Central Pb +Pb collisions at 158 GeV/A

  11. Δt=10-12 sec Δt=10-19 sec Δt=10-24 sec Unfortunately so far no systematic BEC or FDC of WI particles have been measured ! π p,Λ K Q: IsΔta measure ofthe interaction strengthof the two identical outgoing particles? R1Das a function of m and Δt

  12. 100<KT <200 MeV 200<KT <300 MeV π [G. Alexander, P.L. B506 (2001) 45] γγ BEC in Pb + Pb at 158 GeV/A Aggarwal et al. (WA98) PRL 93 (04) 022301 Aggarwal et al. (WA98) arXiv:0709.2477 Δtlong=(1.61±0.05)x10-22 sec

  13. Z0 Hadronic decay Thus we assign Δt as a measure of the particle emission time

  14. a=0.91 fm As a next steplet us relate the R dependence on A with

  15. To get the particle emission time which depends on the surface area of the nucleus Question: Does it have an energy dependence? NA49 Collaboration, P.R. C77 (2008) 064908 found that

  16. Particle emission time Δt vs the Atomic number A From measured R calculate a=1.2 fm a=1 fm and insert a=0.8 fm [Data from: WA80, WA98, STAR Collaborations and from Chacon et. al,. (1991)] Δt(A=1)=Δt(proton)=2.4x10-24 sec for a=1 fm

  17. Comments and remarks 1) Δt is attributed to the particles’ emission time 2) One should have more BEC and FDC analyzes like that of WA98 3) In heavy ion collisions Heisenberg derived formulae are applied 4) A simple merge of the 1D Heisenberg derived formula with R vs A 5) Consistent with the data 6) The Δtdependence on A2/3  e.g. Fireball shell model ? 7) An extension of this work from 1D to 3D should be explored

  18. Comments and remarks (con’t) 7) BEC and/or FDC for WI particles are of interest to measure 8)FDC ofdirectly produced e±e±/µ±µ± are unlikely to be measured 9) An attractive possibility may be the BEC study of Z0Z0 pairs Because : a) It is a BEC of weak interacting particles (what is its Δt value?) b) R determination of a very high mass boson c) No Coulomb correction Experimental opportunity may be offered by the SLHC pp  Z0Z0+ X data

  19. Pythia MC study of ppZ0Z0 at 14 TeV Fraction of the ZZ->4ℓ (ℓ=e or μ) decay ~0.36% Fraction of Z->Jets Z->2ℓ (ℓ= e or μ) decay ~9.32%

  20. Pythia MC study of ppZ0Z0 at 14 TeV One parameter fit: R1D=0.019 ± 0.006 fm

  21. Last remark MANY THANKS FOR YOUR ATTENTION

  22. Backup slides

  23. Energy density of the hadron emitter [A simple minded approach , G. Alexander. RPP 66 (03) 481] Z0 hadrons [Dashed lines for

  24. See e.g., Delgado, Gustafson, Lönnblad,(LUND group) Eur. Phys. J.C. 52 (2007) 113 Baryon production in the Lund Model

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