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Fireball Granularity Can We Measure It?

Fireball Granularity Can We Measure It?. Vojtech Petracek Kiev 2007. Outline. Motivation Fireball instability and granularity Event-by-event fluctuation in particle density in 1D and 2D Multi-resolution analysis of particle density fluctuations Droplet generator Event selection

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Fireball Granularity Can We Measure It?

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  1. Fireball GranularityCan We Measure It? Vojtech Petracek Kiev 2007

  2. Outline • Motivation • Fireball instability and granularity • Event-by-event fluctuation in particle density in 1D and 2D • Multi-resolution analysis of particle density fluctuations • Droplet generator • Event selection • Strategy of domain analysis • Effective source size for events with granular source • Another application - jet detection • Summary & outlook

  3. Motivation => ?

  4. Can we detect the critical point? B. Tomasik • Onset of spinodal instability for larger  ? • Source structure in crossover region (bags) ?

  5. Fireball instability • Fast cooling can bring the system to the unstable configuration • Fireball decomposes as it reaches the spinodal point • Cooling must be fast bubble nucleation rate < expansion rate V B. Tomasik

  6. Granular fireball • Fireball can decompose to spherical droplets • Or to objects with more complicated shapes with larger surface/volume ratio • Or nothing like that happens • Can we distinguish between these options?

  7. Event-by-event fluctuations (1D) • Rapidity spectra averaged over many events are smooth • Rapidity spectra in each event will look differently if the granular source is present • 1D approach is possible (Tomasik et. al.), but more information can be obtained in 2D analysis

  8. Multi-resolution analysis (MRA) • MRA method uses 2D Cauchy-Lorentz function • We can observe -particledensitydistribution with different resolution • We can characterize fluctuation between different resolutions

  9. Example - MRA in 1D This method can isolate large scale structures which would be otherwise hidden in noise If we define a set of resolutions, it is possible to reconstruct from L and F functions recursively the original density distribution like in wavelet transform Compared to the discrete wavelet transformation method this approach doesn’t have problem with domain splitting

  10. Mother & Father functions L1 L2 F12 • Mother functions L smooth the high freq. noise • Father functions F determine the fluctuation between the two resolution scales • Original domain is optimally reproduced when its characteristic scale coincide with resolution

  11. Event-by-event fluctuation domain detection • Events with isotropic particle distribution are used for the detection threshold calibration • Threshold is set to 2, so that ~5% of random signal is above it • Events containing non-statistical local fluctuations in particle density will have the fraction of signal above the threshold significantly higher

  12. Droplet generator by Boris Tomasik • MC generator of (momenta and positions of) particles • some particles are emitted from droplets (clusters) • droplets are generated from a blast-wave source(tunable parameters) • droplets decay exponentially in time (tunable time, T) • tunable size of droplets: Gamma-distributed or fixed • no overlap of droplets • also directly emitted particles (tunable amount) • chemical composition: equilibrium with tunable params. • rapidity distribution: uniform or Gaussian • possible OSCAR output

  13. Generator setup - ALICE T = 175 MeV b = 0 s = 0 Droplet size 100fm3 fixed Variable fraction of particles from droplets y  <-2,2>

  14. Event-by-event spectra Granular source ~ 120 droplets No droplets Event-by-event spectra are barely significantly different

  15. Individual droplet MF 2D analysis Characteristic droplet dimensions ~ 0.5y x Pi/4 For small number of droplets (<20) is possible direct droplet counting For larger numbers droplets merge

  16. Individual droplet FF 2D analysis When the direct droplet counting is possible, the best estimate is the # of maxima in FF over certain threshold

  17. Whole event MF Detection of domains of non-statistical density fluctuation at different resolution scales

  18. Whole event MF Detection of domains of non-statistical density fluctuation at different resolution scales

  19. Event selection • Distribution of fraction of the area covered by detected domain • Red : 100% particles from droplets • Green : 0% particles from droplets • Scale 1

  20. Event selection • Distribution of fraction of the area covered by detected domain • Red : 100% particles from droplets • Green : 0% particles from droplets • Scale 2

  21. Event selection • Distribution of fraction of the area covered by detected domain • Red : 100% particles from droplets • Green : 0% particles from droplets • Scale 3 Sensitivity for cases when >20% of particles is produced from droplets

  22. Strategy of domain analysis • Compare P in domain to surrounding => identify jet • Check the charge symmetry. Asymmetry => DCC • Density fluctuation due to the droplet • Try HBT for event (or even for particles in domain) to estimate the source size

  23. Effective source size • HBT event-by-event should be possible in ALICE • For selected events we should see effective source size smaller then for the generic case • What will be the effect of droplet/bag shape on HBT result ??

  24. Jet reconstruction Example of jet reconstruction using the described MRA method Jet containing 30 particles in 0.1y x 0.3rad Background 6500 particles Pt weighting – very useful

  25. Summary & outlook • Area of the , plane covered by domains with non-statistically high particle density fluctuation is a robust measure which can be used for detection of events with granular source responsible at least for 20% of particle production (for 100 fm3 droplets) • For small number of droplets the direct droplet counting is possible • Events with granular source can be analyzed using the correlation techniques to estimate the mean droplet size • Effect of droplet shape should be investigated • Minimum droplet size generating non-statistical density fluctuation will be estimated

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