Study of the multiparticle event structure with fractal dimension
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Study of the multiparticle event structure with fractal
dimensionOleg Rogachevsky
JINR
July 1st, 2011
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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
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STAR = 200 GeVO.R. Proceedings of ICHEP 2006
𝐹𝐷𝑖𝑛η𝑝𝑡−𝑠𝑝𝑎𝑐𝑒
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pT max
– momentum of a particle with the maximum momentum in the event
STAR = 200 & 62 GeV
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Disappearance of away side jet
Pedestal&flow subtracted
Phys. Rev. Lett. 91, 072304 (2003).
y < 0.7 4 < < 6 GeV/c,� 2 < < � � �
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Azimuthal anisotropy
sensitivity to the system geometry for production at all measured
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EmulsionA GeV/c
197Au + Em at 11.6 A GeV/c BNL AGS, Experiment E863
1165 minimum bias events
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Emulsion GeV/c
208Pb + Em at 158 A GeV/c CERN SPS, EMU12 Experiment
628 minimum bias events
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pC, dC, αC, CC @ 4.2A GeV/c
𝑑2𝑁2𝜋 𝑝𝑡𝑑𝑝𝑡 𝑑𝑦
=𝐵¿¿
Levy distribution
CC 4.2A GeV/c
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Events vs @ 4.2A GeV/c
Shifts with ABroadening with A
CC 4.2A GeV/c
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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