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Dependence of the event fractal dimensions on the colliding nuclei masses

Dependence of the event fractal dimensions on the colliding nuclei masses. Oleg Rogachevsky VHMP 2007 Dubna. What is a fractal ?. A fractal is a shape made of parts similar to the whole in some way E.Feder. Koch’s arc.

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Dependence of the event fractal dimensions on the colliding nuclei masses

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  1. Dependence of the event fractal dimensions on the colliding nuclei masses Oleg Rogachevsky VHMP 2007 Dubna

  2. What is a fractal ? A fractal is a shape made of parts similar to the whole in some way E.Feder Koch’s arc The fractal dimension of sets observed in the dynamics can be used as quantitative measure of the chaoticity • r - scale • N(r) number of elements in fractal at given scale VHMP-2007

  3. Fractals deal with geometric patterns (represented chaos) and quantitative way of characterizing these patterns. Chaos, in contrast, deals with time evolution and its underlying or distinguishing characteristics Garnett P. Williams “Chaos Theory Tamed” Fractals in Heavy Ion Collisions Collections of small entities (particles or whatever) behave haphazardly, even though physical laws govern the particles individually Deterministic chaos  chaos results from deterministic process VHMP-2007

  4. -1 < x < 1, 0 < y < 2 Dcorr Npoints 2 dimension random distribution VHMP-2007

  5. Au+Au s = 200 GeV  multiplicity dependence minbias VHMP-2007

  6. Fractal dimensions in  and ptspaces Au+Au s = 200 GeV VHMP-2007

  7. Fractal dimensions in pTspace Au+Au s = 200 GeV VHMP-2007

  8. STAR Au+Au s = 200 & 62 GeV Fractal dimensions in ptspace (pt > .15 GeV/c) entropy events jet events pT max– maximum transverse momentum among the particles in the event VHMP-2007

  9. STAR Au+Au s = 200 GeV Ptmax of events (pt > .15 GeV/c) VHMP-2007

  10. STAR Au+Au s = 200 GeV Nucl. Phys. A 757 (2005) 102 VHMP-2007

  11. STAR Au+Au s = 200 GeV Binary-scaled yield ratio RCP (pT ) for central (0-5%) relative to peripheral(40-60%, 60-80%) collisions for charged hadrons from 200 GeV Au+Au collisions Nucl. Phys. A 757 (2005) 102 Entropy events make main yield in pT spectra from 2.5 to 4 GeV/c but the bump above 2.5 GeV/c in entropy events decreases with growth of centrality VHMP-2007

  12. HIJING Cu+Cu s = 62&200 GeV VHMP-2007

  13. HIJING Au+Au s = 62&200 GeV VHMP-2007

  14. HIJING Au+Au s = 62&200 GeV VHMP-2007

  15. HIJING Au+Au s = 62&200 GeV VHMP-2007

  16. HIJING Au+Au s = 62&200 GeV VHMP-2007

  17. HIJING d+Au s = 62&200 GeV VHMP-2007

  18. HIJING s = 200 GeV SiSi&InIn VHMP-2007

  19. Summary • Fractal dimension analysis are feasible to study event features in the heavy ion collisions • Different dynamics of the particle interactions reveals throw changes of the event fractal dimensions • Changes of fractal dimension caused by jet quenching become more evident with increasing collision energy and masses of colliding nuclei • Fractal dimension analysis can be applied to study event structure at LHC, CBM and NICA. VHMP-2007

  20. STAR Au+Au s = 200 & 62 GeV VHMP-2007

  21. Factorial moments (A. Bialas et al.) Fractal moments (R. Hwa) Scaled correlation analysis (T. Trainor) Wavelet decomposition analysis Renyi entropy analysis (I. Dremin) Scale dependent analysis The scale dependent analysis is a space-scale decomposition where the space corresponds to any physical variable and the scale is the space size VHMP-2007

  22. STAR Au+Au s = 200 & 62 GeV Fractal dimensions in ptspace (pt > .15 GeV/c) entropy events jet events The yield of entropy events increases with growth of multiplicity and collisions energy VHMP-2007

  23. STAR events analysis • Au+Au s = 200 GeV • STAR ~ 2 000 Kevents • HIJING ~ 73 Kevents • Au+Au s = 62 GeV • STAR ~ 1100 K events • HIJING ~ 21 K events events: particles: all charged particles with: < 1. Azimuthal angle 2 pT > 0.15 GeV/c Nhits > 25 Nhits / N poss.hits > .52 VHMP-2007

  24. Fractal dimensions in  and pt spaces Au+Au s = 62 GeV VHMP-2007

  25. Fractal dimensions in pT space Au+Au s = 62 GeV VHMP-2007

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