1. The Pion Emission Function in Z-Decay from Bose-Einstein Correlations
Tamás Novák
(L3 Collaboration)
Radboud University Nijmegen, The Netherlands
Károly Róbert College, Hungary
11-Sept-2008

2. Questions and answers What is the aim of this work?
To reconstract the pion emission function.
What is the emission function?
It says where and when and how many pions are produced. (See later)
How to reach it?
Using the Bose-Einstein Correlations. (See now)
29 December, 2018
Tamás Novák

3. Bose-Einstein Correlation
In theory:
29 December, 2018
Tamás Novák

4. Examples Intercept parameter Source function Correlation function
The correlation function will be investigated as a function of Q, the invariant four-momentum difference. (See later)
Source function
Correlation function
Gaussian
Intercept parameter
Edgeworth expansion
Symmetric Lévy stable
29 December, 2018
Tamás Novák

5. Bose-Einstein Correlation
In experience:
Two particle number density
(Data)
Two particle density without BEC
(Reference sample)
29 December, 2018
Tamás Novák

6. There was no theoretical model which predicted a mere Q dependence.
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.
29 December, 2018
Tamás Novák

7. Large Electron Positron (LEP) collider
29 December, 2018
Tamás Novák

8. The L3 detector
29 December, 2018
Tamás Novák

9. 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
29 December, 2018
Tamás Novák

10. Beyond the Gaussian ĸ =0,71 ± α=1,34 ±
0,06
α=1,34
0,04
Far from Gaussian
Poor CLs. Edgeworth and Lévy better than Gaussian.
Problem is the dip in the region 0,6 < Q < 1,5 GeV.
29 December, 2018
Tamás Novák

11. The τ-model
It is assumed that the average production point of particles and the four momentum are strongly correlated.
This correlation is much narrower than the proper-time distribution.
In the plane-wave approxiamtion, using the Yano-Koonin formula, one gets for two-jet events:
29 December, 2018
Tamás Novák

12. Further assumptions α is the index of stability
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
where
τ0 is the proper time of the onset of particle production
Δτ is a measure of the width of the dist.
29 December, 2018
Tamás Novák

13. Before fitting in two dimensions , assume an ‘average’
dependence by introducing effective radius
Also assumed τ0 = 0. Then
29 December, 2018
Tamás Novák

14. Before fitting in two dimensions , assume an ‘average’
dependence by introducing effective radius
Also assumed τ0 = 0. Then
For three-jet event
29 December, 2018
Tamás Novák

15. Results
CLs are good. Parameters are approx. independent of mt.
τ0=0,0
0,01 fm
α=0,43
0,01
Δτ=1,8
0,4 fm
29 December, 2018
Tamás Novák

16. Emission function of 2-jet events
In the τ-model, the emission function is:
For simplicity, assume
Δτ ≈ 1,8fm
where
So using experimental distributions and , H(τ) from BEC, we can reconstruct the emission function.
29 December, 2018
Tamás Novák

17. ‘Boomerang shape’; Particle production close to the light cone
The emission function
Integrating over r
‘Boomerang shape’; Particle production close to the light cone
29 December, 2018
Tamás Novák

18. The shortest movie of nature
29 December, 2018
Tamás Novák

19. Summary
Thank you for your attention!
29 December, 2018
Tamás Novák