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A Short introduction to HBT Qinghui Zhang

A Short introduction to HBT Qinghui Zhang. Heavy Ion Collisions requires understanding particle distributions in coordinate and momentum space. GGLP Goldhaber, Goldhaber, Lee and Pais (1960) First application of “intensity interferometry” in particle physics HBT

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A Short introduction to HBT Qinghui Zhang

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  1. A Short introduction to HBTQinghui Zhang Q. H. Zhang

  2. Heavy Ion Collisions requires understanding particle distributions in coordinate and momentum space Q. H. Zhang

  3. GGLP • Goldhaber, Goldhaber, Lee and Pais (1960) • First application of “intensity interferometry” in particle physics • HBT • Hanbury-Brown and Twiss (1950’s) • Revolutionary development of intensity interferometry in astronomy • B-E • Bose-Einstein (1920’s) • Role of Bose statistics in fluctuations Q. H. Zhang

  4.    Q. H. Zhang

  5. Neglects • Momentum dependence of source • Quantum mechanics up to x and y • Final State Interactions after x and y C2(q) contains shape information Q. H. Zhang

  6. That is, squared Fourier Transforms measure (only) relative separations of source coordinates • Very different sources r(x)can give very similar distributions in relative separation Sphere vs hemisphere qOUT R  Q. H. Zhang

  7. That is, q0 is not an independent quantity in the F.T.(e.g., note that ) • Fourier Transform has support in only half of the q0-q plane • Fourier Transform provides one time and three space extensions of source • BUT: Q. H. Zhang

  8. So Fourier transform (+ two-particle kinematics) already provides conclusion: • Additional dynamic effects (expansion, thermal source, …) will also lead to systematic dependence of extracted “radii” on VPAIR (or mT or kT or …) Q. H. Zhang

  9. There are other decompositions... Q. H. Zhang

  10. Choose frame so that • x = “Out” (that is, parallel to VPAIR) • y = “Side” • z = “Long”: y x z • Simplest possible (yet still very useful) case: Q. H. Zhang

  11. Most experiments with charged tracking and particle identification have HBT results: • BNL AGS: E859, E866 E877 E895 • CERN SPS: NA44 NA49 WA98 • RHIC PHENIX STAR Q. H. Zhang

  12. The Great Puzzle: • Why so little variation with ECM ? • Why are lifetimes (t) ~ 0 ?? ( especiallyat RHIC ) Q. H. Zhang

  13. systematic errors in experimental data is required: • Definition of C2 • Coulomb corrections • Role of l, dependence of R on same • Contributions from resonances (especially when comparing between different experiments) • A better understanding of theoretical assumptions and uncertainties is required: • Resonance contributions • Lorentz effects • Modeling of expansion, velocity profiles Q. H. Zhang

  14. Our favorite (charged) bosons never have pure plane-wave states • Even our ideal-case Fourier transform becomes a “Coulomb transform” • This particular case is easy to treat analytically via “Gamow” or “Coulomb” corrections: Q. H. Zhang

  15. RTSide(--) > RTOut(--) • RTSide(++) < RTOut(++) Some indication from both AGS and SPS that RSide(--) > RSide(++) • E877 (AGS): RSide(--) ~ (1.5 +/- 0.4)*RSide(++) • NA44 (SPS): • Note external Coulomb • Systematic in RSIDE • Cancels in ROUT Q. H. Zhang

  16. versus observed value of 1.1-1.5 • This is parameterized away viaC2(q) = 1+ l | r(q)|2, l ~0.1-0.5 • “Understood” via assumed resonance contributions: Q. H. Zhang

  17. 2(1-fCORE )fCORE fCORE fCORE (1-fCORE )(1-fCORE ) Momentum resolution  • How do resonances affect l ? • By creating a “halo” around the source “core”: • Some culprits: • r  pp (G = 150 MeV  S ~ 1.3 fm ) • K* Kp (G = 50 MeV  S ~ 4 fm ) • w  ppp (G = 8.4 MeV  S ~ 20 fm ) • h,  hpp (G = 0.2 MeV  S ~ 200 fm ) • (and many more…) • Effect: C2 develops structure near q=0 to describe the various sources: Q. H. Zhang

  18. Use ~this in cascade codes • Using Wigner function: • See for example: Chao, Gao and Zhang Phys. Rev. C 49,3224 (1994) Q. H. Zhang

  19. Expect C2 to depend on q and K B.R. Schlei and N. Xu: Q. H. Zhang

  20. RQMD vs. Data for HBT Final state phase space points xi are weighted by 1 + cos[(pa-pb)(xa-xb)] Q. H. Zhang

  21. with Final state phase space points xi are weighted by 1 + cos[(pa-pb)(xa-xb)] • This approach is • Plausible • WRONG • Advantage: • Uses precisely what codes produce • Disadvantage • Can lead to non-physical oscillations in C2 • First noted empirically by Weiner et al and • Later matin et al. • Theoretical analysis by Q.H. Zhang et al. • Phys. Lett. B 407, 33 (1997) • Quantitatively, is it significant for heavy ion collisions? • Answer 1: No (Empirical) • Answer 2: Not yet? (see next slide) Q. H. Zhang

  22. S=0 K x S=0.33 S=0.9 • Study these effects with a source that explicitly parameterizes x-p correlations: Examples for R=5fm, P=200 MeV/c Q. H. Zhang

  23. x = • This can be done analytically with parameterization on previous slide: Q. Can one remove these pathologies from ~classical predictions? A. Yes (Q.H. Zhang et al.): • Smear the phase space points (x,p) with minimum uncertainty wave-packets:with s ~ 1 fm • Pictorially: Q. H. Zhang

  24. What are the Lorentz properties of C2(q)? • How to write our favorite practice Gaussian in an explicitly Lorentz invariant way? • Answered in F.B. Yano and S.E. Koonin, Phys. Lett. B78, 556 (1978). Q. H. Zhang

  25. p1 VPAIR uS Beamaxis p2 • Apply this to ~1-d motion in “Out” direction: • Can Lorentz effects “distort” information? • Apply Yano-Koonin-Podgoretzsky result to another toy model: • Nota Bene: This last case allows ROUT<RSIDEeven for t ~RSIDE Q. H. Zhang

  26. The chief lesson from last 10-15 years of (theoretical) HBT work: • The “radii” are a (potentially) complicated mixture of • Space-time distribution • Spatial flow gradients • Temperature gradients • More correct terminology:“radii”  “lengths of homogeneity” • In the presence of source dynamics, “radii” depend on mean pair(energy, momentum, transverse mass,…) Q. H. Zhang

  27. But : ROUT/RSIDE trend completely eliminates one “hydro” calculation Soff, Bass, Dumitru, Phys. Rev. Lett. 86, 3981 (2001) Q. H. Zhang

  28. RHIC SPS AGS • Plotted versus KT, there is an amazing consistency between data from AGS, SPS, and RHIC, spanning a factor of 100 in CM energy(!): Q. H. Zhang

  29. There is now an extensive experimental and theoretical literature built on 20+ years of “HBT” studies • We’re now ready to start doing things right: • Experimentally • Measure resonance contributions • Measure like and unlike particle effects • Understand systematic errors • Theoretically • Cascade codes for RHIC • Right parametrization • Coulomb systematics Q. H. Zhang

  30. Multipion correlations Each events has large number of pions, therefore, multi-pion correlation will affect Two-pion interferometry (1): If the pion correlation formula is right? (2): If it is not right, which kind of formula should we use! Q. H. Zhang

  31. Seems right! • Zhang, Phys. Rev. C58, 22 (1998) • Proved that for a class model, the present pion correlation function formula is right. However generally, the formula is not right! Zhang, Phys. Rev. C59,1646 (1999). Q. H. Zhang

  32. The formula is : C(p1,p2)= A(p1,p2)[1+R(p1,p2)] A(p1,p2) is a function of p1,p2. R(p1,p2) can be written as the same as above. Q. H. Zhang

  33. Three-pions correlations Q. H. Zhang

  34. Q. H. Zhang

  35. Q. H. Zhang

  36. Q. H. Zhang

  37. Q. H. Zhang

  38. Q. H. Zhang

  39. Some of slides taken from W. A. Zajc, R. Wilson. Thank you! Q. H. Zhang

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