Study of the multiparticle
event structure with fractal
dimension
Oleg 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, …
Some effects in high energy AuAu collisions
Disappearance of away side jet
ν2 𝑣𝑠 𝑝𝑡
Pedestal&flow
subtracted
Phys. Rev. Lett. 91, 072304 (2003).
and more others ...
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Deterministic chaos
Collections of small entities (particles or whatever) behave haphazardly, even though
physical laws govern the particles individually
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”
A fractal is a shape made of parts
similar to the whole in some way
E.Feder
Deterministic chaos  chaos
results from deterministic process
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Fractal dimension
Koch’s arc
The fractal dimension of sets observed
in the dynamics can be used as
quantitative measure of the chaoticity
D  lim
r 0
log N (r )
log (1 / r )
r - scale
N(r) - number of elements in fractal at given scale
D
Koch ' s arc
log 4 n log 4
 lim

 1.261...
n
log 3
n   log 3
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STAR √𝑠𝑁𝑁 = 200 GeV
O.R.
Proceedings of ICHEP 2006
𝐹𝐷 𝑖𝑛 η𝑝𝑡 − 𝑠𝑝𝑎𝑐𝑒
STAR √𝑠𝑁𝑁 = 200 & 62 GeV
pT max – momentum of a particle with the
maximum momentum in the event
Disappearance of away side jet
Phys. Rev. Lett. 91, 072304 (2003).
Pedestal&flow subtracted
y < 0.7
𝑡𝑟𝑖𝑔
4 < †𝑝𝑡
< 6 GeV/c,
𝑡𝑟𝑖𝑔
2 < †𝑝𝑡𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 < †𝑝𝑡 †
Azimuthal anisotropy
sensitivity to the system geometry for production at all measured 𝑝𝑡
Emulsion
197Au
197
𝐴𝑢 @ 11.6A GeV/c
+ Em at 11.6 A GeV/c
BNL AGS, Experiment E863
1165 minimum bias events
Emulsion
208Pb
208
𝑃𝑏 @ 158𝐴 GeV/c
+ Em at 158 A GeV/c
CERN SPS, EMU12 Experiment
628 minimum bias events
pC, dC, αC, CC @ 4.2A GeV/c
CC 4.2A GeV/c
Levy distribution
𝑑2𝑁
𝐵
=
2𝜋𝑝𝑡 𝑑𝑝𝑡 𝑑𝑦 (1 + (𝑚𝑡 − 𝑚0 )/𝑛𝑇)𝑛
Events vs
𝑚𝑎𝑥
𝑝𝑡
@ 4.2A GeV/c
CC 4.2A GeV/c
Shifts with A
Broadening with A
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
Thanks for attention
&
To organizers
for invitation
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Pythia
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