1. Study of the multiparticle event structure with fractal dimension Oleg Rogachevsky JINR July 1st, 2011

2. Self-similarity & scaling in nuclear collisions Recently, a large variety of experimental results indicated that multiparticle production in high energy collisions possesses a self-similarity property when the resolution in phase space is increased. In analogy with the well known phenomena in geometrical and statistical systems exhibiting self-similarity, it was suggested that the ideas and methods of deterministic chaos in nonlinear physics can be used to analyze the data of multiplicity production at high energy collisions. Intermittency, Z – scaling, Π-scaling, …

3. Some effects in high energy AuAu collisions 3 Pedestal&flow subtracted Phys. Rev. Lett. 91, 072304 (2003). Disappearance of away side jet and more others...

4. Collections of small entities (particles or whatever) behave haphazardly, even though physical laws govern the particles individually Deterministic chaos  chaos results from deterministic process 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” Deterministic chaos 4 A fractal is a shape made of parts similar to the whole in some way E.Feder

5. Koch’s arc r - scale N(r) - number of elements in fractal at given scale Fractal dimension 5 The fractal dimension of sets observed in the dynamics can be used as quantitative measure of the chaoticity

6. O.R. Proceedings of ICHEP 2006

7. p T max – momentum of a particle with the maximum momentum in the event

8. Disappearance of away side jet Pedestal&flow subtracted Phys. Rev. Lett. 91, 072304 (2003).

9. Azimuthal anisotropy

10. 197 Au + Em at 11.6 A GeV/c BNL AGS, Experiment E863 1165 minimum bias events

11. 208 Pb + Em at 158 A GeV/c CERN SPS, EMU12 Experiment 628 minimum bias events

12. pC, dC, αC, CC @ 4.2A GeV/c Levy distribution CC 4.2A GeV/c

13. Shifts with A Broadening with A CC 4.2A GeV/c

14. Summary  Fractal dimension is sensitive to the global event structure  Fractal dimension analysis is useful to understand features in events  More specific methods which could be implemented to small number of the particles are needed

15. 15 Thanks for attention & To organizers for invitation

16. Pythia 16