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Fireball Instability and Granularity Study for Event-by-Event Fluctuations in Particle Density

This outline provides insights into fireball instability and granularity, focusing on event-by-event fluctuations in particle density in both 1D and 2D. It includes a discussion on multi-resolution analysis, a droplet generator, event selection, and the strategy for domain analysis. The effective source size for events with granular sources and the application of jet detection are also covered. This study aims to detect the critical point and distinguish between different decompositions of fireballs to understand their structures better.

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Fireball Instability and Granularity Study for Event-by-Event Fluctuations in Particle Density

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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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