Study of the multiparticle event structure with fractal

dimensionOleg Rogachevsky

JINR

July 1st, 2011

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, …

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Some effects in high energy AuAu collisions

Pedestal&flow subtracted

Phys. Rev. Lett. 91, 072304 (2003).

ν2𝑣𝑠𝑝𝑡Disappearance of away side jet

and more others ...

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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

A fractal is a shape made of parts

similar to the whole in some way

E.Feder

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)/1(log)(loglim

0 rrND

r

Koch’s arc

...261.13log4log

3log4loglim'

n

n

n

arcsKochD

r - scaleN(r) - number of elements in fractal at given scale

Fractal dimension

The fractal dimension of sets observed in the dynamics can be used as

quantitative measure of the chaoticity

STAR = 200 GeVO.R. Proceedings of ICHEP 2006

𝐹𝐷𝑖𝑛η𝑝𝑡−𝑠𝑝𝑎𝑐𝑒

pT max

– momentum of a particle with the maximum momentum in the event

STAR = 200 & 62 GeV

Disappearance of away side jet

Pedestal&flow subtracted

Phys. Rev. Lett. 91, 072304 (2003).

y < 0.7 4 < < 6 GeV/c,� 2 < < � � �

Azimuthal anisotropy

sensitivity to the system geometry for production at all measured

EmulsionA GeV/c

197Au + Em at 11.6 A GeV/c BNL AGS, Experiment E863

1165 minimum bias events

Emulsion GeV/c

208Pb + Em at 158 A GeV/c CERN SPS, EMU12 Experiment

628 minimum bias events

pC, dC, αC, CC @ 4.2A GeV/c

𝑑2𝑁2𝜋 𝑝𝑡𝑑𝑝𝑡 𝑑𝑦

=𝐵¿¿

Levy distribution

CC 4.2A GeV/c

Events vs @ 4.2A GeV/c

Shifts with ABroadening with A

CC 4.2A GeV/c

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

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Thanks for attention&

To organizers for invitation

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Pythia