Time evolution of particle production in e+e- annihilation from Bose-Einstein Correlations

1. Tamás Novák Károly Róbert College 27-11-2008 Time evolution of particle production in e+e- annihilation from Bose-Einstein Correlations

2. Tamás Novák Questions and answers What is the aim of this work? To reconstract the pion emission function. It says where and when and how many pions are produced. (See later)‏ What is the emission function? Using the Bose-Einstein Correlations. (See now)‏ How to reach it?

3. Bose-Einstein Correlations • This topic is almost 50 years old in high energy physics (Intensity Interferometry)‏ • In multiple particle production BECs were discovered accidentally as a byproduct of an unsuccessfull attempt to find the ρ meson. • GGLP effect Tamás Novák

4. Bose-Einstein Correlation • Analogous effect had been discovered earlier (HBT effect)‏ Determination of the angular radii of stars Determination of the size of the source ˜ Tamás Novák

5. Bose-Einstein Correlation In theory: Tamás Novák

6. Examples The correlation function will be investigated as a function of Q, the invariant four-momentum difference. (See later)‏ Source function Correlation function Gaussian Coherence parameter Edgeworth expansion Symmetric Lévy stable Tamás Novák

7. Tamás Novák Bose-Einstein Correlation In experience: Two particle number density (Data)‏ Two particle density without BEC (Reference sample)‏

8. Tamás Novák Puzzles in the late 80’s First, the measured correlation functions are consistent with the invariant Q dependence. (the statistics were not large enough)‏ Second, the correlation function is more peaked than a Gaussian. There was no theoretical model which predicted a mere Q dependence.

9. Tamás Novák Large Electron Positron (LEP) collider

10. Tamás Novák The L3 detector

11. Tamás Novák Data Sample • Hadronic Z decays using L3 detector • ‘Standard’ event and track selection ≈ 1 million events • Concentrate on 2-jet events using Durham algorithm ≈ 0,5 million events • Correct distribution bin-by-bin by MC

12. Tamás Novák Beyond the Gaussian ĸ=0,71 ± ± α=1,34 0,04 0,06 Far from Gaussian Poor CLs. Edgeworth and Lévy better than Gaussian. Problem is the dip in the region 0,6 <Q< 1,5 GeV.

13. Tamás Novák The τ-model It is assumed that the average production point of particles and the four momentum are strongly correlated. Thiscorrelation is much narrower than the proper-time distribution. In the plane-wave approxiamtion, using the Yano-Koonin formula, one gets for two-jet events:

14. Tamás Novák Further assumptions where τ0is the proper time of the onset of particle production Δτis a measureof the width of the dist. Assume a Lévy distribution for H(τ). Since no particle production before the interaction,H(τ)is one-sided. Then α is the index of stability

15. Before fitting in two dimensions , assume an ‘average’ dependence by introducing effective radius Also assumed τ0= 0.Then Tamás Novák

16. Before fitting in two dimensions , assume an ‘average’ dependence by introducing effective radius Also assumed τ0= 0.Then For three-jet event Tamás Novák

17. Tamás Novák τ0=0,0 Δτ=1,8 ± ± α=0,43 ± 0,01 fm 0,4 fm 0,01 Results CLs are good. Parameters are approx. independent of mt.

18. Δτ≈ 1,8fm Emission function of 2-jet events In the τ-model, the emission function is: For simplicity, assume where So using experimental distributions and , H(τ) from BEC, we can reconstruct the emission function. Tamás Novák

19. Tamás Novák The emission function Integrating over r ‘Boomerang shape’; Particle production close to the light cone

20. Tamás Novák The shortest movie of nature

21. Summary Thank you for your attention! Tamás Novák