Intermittency (particle physics)

Intermittency in particle physics ^[1] is the intermittent pattern of fluctuations in high energy which can be observed by calculating the scaled factorial moments. The term is analogies to Intermittency, which is a manifestation of scale invariance and randomness in physical systems.

Multiplicity distributions and correlations between final-state particles are an important testing ground for perturbative QCD and for phenomenological models describing the hadronic final state ^[2] Short-range correlations in particle multiplicities for a given observable [math]\displaystyle{ \Omega }[/math] can studied in terms of the normalized factorial moments:

$$ F_q(\Delta\Omega)=\langle n(n-1)\ldots (n-q+1)\rangle / \langle n \rangle^q, \qquad q=2,3 .. $$

where [math]\displaystyle{ n }[/math] is the number of particles inside a phase-space region of size [math]\displaystyle{ \Delta \Omega }[/math] and angled brackets [math]\displaystyle{ \langle \ldots\rangle }[/math] denote the average over all events. The factorial moments, along with cumulants ^[3] and bunching parameters ^{[4] [5]} are convenient tools to characterize the multiplicity distributions when [math]\displaystyle{ \Delta\Omega }[/math] becomes small. For uncorrelated particle production within [math]\displaystyle{ \Delta\Omega }[/math], Poisson statistics holds and [math]\displaystyle{ F_q=1 }[/math] for all [math]\displaystyle{ q }[/math]. Correlations between particles lead to broadening of the multiplicity distribution or dynamical fluctuations. In this case the factorial moments increase with decreasing [math]\displaystyle{ \Delta \Omega }[/math]. If this rise follows a power law, this effect is frequently called intermittency.

The intermittency in this case means that the normalized factorial moments, normalized commulants or bunching parameters exhibit the power law behavior vs. the resolution  :

$$ F_q(\Delta\Omega) \simeq (1/\Delta\Omega)^f_{q} $$

where the strength of intermittency is characterized by the intermittency exponents [math]\displaystyle{ f_q }[/math], which are directly related to the anomalous fractal dimensions [math]\displaystyle{ d_q }[/math]

$$ d_q = f_q / (q-1) $$

The theoretical understanding of intermittency in high energy experiments is missing as yet because we are unable to relate this phenomenon to the fundamental properties of the theory of strong interactions. However this because can be reproduced by various self-similar random cascading models and Monte Carlo simulations of particle collisions that include short-range correlations in the parton cascade, fragmentation and Bose-Einstein correlations between final-state particles.

References

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