Bunching parameter

In statistics as applied in particular in particle physics, when fluctuations of some observables are measured,it is convenient to transform the multiplicity distribution to the bunching parameters::$eta\_q\; =frac\{q\}\{q-1\}frac\{P\_q\; P\_\{q-2\{P\_\{q-1\}^2\},$where $P\_n$ is probability of observing$n$ objects inside of some phase space regions.The bunching parameters measure deviations ofthe multiplicity distribution $P\_n$from a Poisson distribution, sincefor this distribution

:$eta\_q=1$.

Uncorrelated particle production leadsto the Poisson statistics, thusdeviations of the bunching parameters from the Poisson valuesmean correlations between particles and dynamical fluctuations.

Normalised factorial momentshave also similar properties.They are defined as

:$F\_q\; =langle\; n\; angle^\{-q\}sum^\{infty\}\_\{n=q\}\; frac\{n!\}\{(n-q)!\}\; P\_n.$

ee also

References

* [http://arxiv.org/abs/hep-ph/9605379] Bunching Parameter and Intermittency in High-Energy Collisions;Authors: S.V.Chekanov and V.I.Kuvshinov;Ref: Acta Phys. Pol. B25 (1994) p.1189-1197
* [http://arxiv.org/abs/hep-ph/9606202] Multifractal Multiplicity Distribution in Bunching-Parameter Analysis; Authors: S.V.Chekanov and V.I.Kuvshinov;Ref: J. Phys G22 (1996), p.601-610
* [http://arxiv.org/abs/hep-ph/9606335] Generalized Bunching Parameters and Multiplicity Fluctuations in Restricted Phase-Space Bins;Authors: S.V.Chekanov, W.Kittel and V.I.Kuvshinov; Ref: Z. Phys. C74 (1997) p.517-529

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