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Two-Particle Correlations in High-Energy Collision : HBT Effect

Two-Particle Correlations in High-Energy Collision : HBT Effect. Jin- Hee Yoon Dept. of Physics, Inha University, Korea. HBT Effect. Interference : Young’s Double Slit Exp. Can measure the l of the light source. p 1. r 1. r 1 ‘. r 2. p 2. r 2 ‘. HBT Effect.

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Two-Particle Correlations in High-Energy Collision : HBT Effect

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  1. Two-Particle Correlations in High-Energy Collision : HBT Effect Jin-Hee Yoon Dept. of Physics, Inha University, Korea

  2. HBT Effect Interference : Young’s Double Slit Exp. Can measure the l of the lightsource.

  3. p1 r1 r1‘ r2 p2 r2‘ HBT Effect The photon measured by a detector has a correlation with the other photon measured at different space-time position! Hanbury-Brown and Twiss measured the size of star in 1956.

  4. p1 r1 r1‘ r2 p2 r2‘ HBT Effect Probability amplitude due to exchange symmetry

  5. p1 r1 r1‘ r2 p2 r2‘ HBT Effect Total Intensity

  6. HBT Effect Total Intensity Structure Function Correlation Function

  7. HBT Effect Goldhaber, Goldhaber, Lee and Pais measured space-time dimensions in pp annihilation using pions. [Phys.Rev.120, 300 (1960)]

  8. Beam direction Correlations in Phase-Space Space-time structure of QGP can be studied by HBT interferometry. Correlation function is typically parametrized as

  9. S(q) ~ exp(-q2R2/2) l 1/R Correlations in Phase-Space Meaning of the Gaussian Source S(r) ~ exp(-r2/2R2) C2 = 1+ lexp(-q2R2) • : Chaoticity • =1 for totally chaotic source • =0 for coherent source • R : Source Size

  10. What Information we get? • Only way to obtain the space-time structure • Source Sizes and shapes for • particle species : p, K, p .. • dynamic region of fireball • Source Evolution • emission duration : R0, Rout/Rside • lifetime : • Other Signal ?

  11. What Information we get? Source Sizes and shapes for particle species

  12. What Information we get? dynamic region of fireball from angular distribution

  13. What we expect from BEC radii ? What Information we get? • Source Evolution • emission duration : R0, Rout/Rside

  14. 200GeV - 130 GeV (fit to STAR 200GeV data only) Longitudinal radius: at 200GeV identical to 130 GeV What Information we get? Source Evolution - lifetime :

  15. Correlations in Phase-Space Hydrodynamic calculation predicts (D. H. Rischke and M. Gyulassy, Nucl. Phys. A608, 479 (1996); P. F. Kolb and U. Heinz, Quark Gluon Plasma 3, World Scientific, Singapore, 2004) But, experimental results are (STAR Collaboration, C. Adler et al., Phys. Rev. Lett. 87, 082301 (2001); PHENIX Collaboration, K. Adcox et al., Phys. Rev. Lett. 88, 192302 (2002); PHENIX Collaboration, A. Enokizono, Nucl. Phys. A715, 595 (2003)) HBT Puzzle

  16. Approaches • However, too messy systems and various effects considered (http://arxiv.org/abs/0907.1292) • Microscopic treatment of the final freeze-out • stage through hadronic rescattering • Fluctuation in the initial stage • Adjusting initial condition leading to stroger • longitudinal/trnasverse hydrodynamic acceleration • Including viscous effect/FSI • Non-Gaussian feature • …..

  17. OPACITY and REFRACTIVITY Correlations in Phase-Space RHIC Experimental Data(Au+Au@200 GeV) showsDense Medium Purpose : Quantum mechanical treatment of Opacity & Refractive effects which reproduces

  18. Correlations in Phase-Space Theoretically, the observables are expressed by Subscript 0 means no final state interaction (FSI).

  19. : full scattering outgoing wave function Final State Interaction FSI replaces Includes two 4-dimensional integration

  20. Wigner Emission Function Using the hydrodynamic source parameterization (B. Tomasik and U. W. Heinz, Eur. Phys. J. C4, 327 (1998); U. A. Wiedermann and U. W. Heinz, Phys. Rep. 319, 145 (1999)) With boost-invariant longitudinal dynamics

  21. Wigner Emission Function : cylindrically symmetric source density : transverse flow rapidity Since KL=0 for midrapidity data Parameters : RWS , aWS , t0 , Dt , Dh , mp , hf , T

  22. Full Scattering Wavefunction Assumption : Matter is cylindrically symmetric with a long axis in a central collision region Reduced 2-dimensional Klein-Gordon Eq.

  23. Optical Potential At p=0, no opacity :real Parameters : w0 , w2 Full Scattering Wavefunction Using partial wave expansion, we can solve K-G Eq. exactly.

  24. Full Scattering Wavefunction In Impulse Approximation, central optical potential f : complex forward scattering amplitude r0 : central density For low energy p-p interaction Using Significant opacity

  25. Correlation Function Now our Emission Function is with Large Source Approximation : b’~1/T~1 fm << RWS

  26. Correlation Function Correlation Function

  27. Here, Are Modified Bessel function . Correlation Function Correlation Function

  28. HBT Radii HBT Radii Then our transverse radii can be calculated by with

  29. T(MeV) hf RWS(fm) aWS(fm) Dt(fm/c) w0(fm-2) w2 t0(fm/c) Dh mp(MeV) Fitting Parameters Fitting Parameters c2 /N ~ 7.8

  30. Temperature T (173 MeV) ~ Tc (160 MeV) hf=1.31 maximum flow velocity ~ 0.85c Source Size RWS (11.7 fm) ~ RAu (7.3 fm)+4.4 fm Expansion time t0 (8.2 fm/c) average expansion velocity ~ 0.5c Emission duration Dt(2.9 fm/c) << t0(8.2 fm/c) Longitudinal length Dh(1.06) system’s axial length ~ 2t0Dh(17.5 fm) : large enough for long cilyndrical symmetry Fitting Parameters Check

  31. full calculation no potential no flow Boltzmann for BE thermal distribution no refraction

  32. full calculation no potential no flow Boltzmann for BE thermal distribution no refraction

  33. Thank you.

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