Physics:Bunching parameter
Bunching parameter [1] [2][3] is a parameter used to calculate a degree of deviation of a counting distribution from a Poisson distribution. 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:
- [math]\displaystyle{ \eta_q = \frac{q}{q-1}\frac{P_q P_{q-2}} {P_{q-1}^2}, }[/math]
where [math]\displaystyle{ P_n }[/math] is probability of observing [math]\displaystyle{ n }[/math] objects inside of some phase space regions. The bunching parameters measure deviations of the multiplicity distribution [math]\displaystyle{ P_n }[/math] from a Poisson distribution, since for this distribution
- [math]\displaystyle{ \eta_q=1 }[/math].
Uncorrelated particle production leads to the Poisson statistics, thus deviations of the bunching parameters from the Poisson values mean correlations between particles and dynamical fluctuations.
Bunching parameters are discussed in the context of quantum optics measurements in [4]. Relations between bunching parameters and other correlation properties of hadronic systems are given in [5] Bunching parameters in high-energy physics were studied by several international collaborations at the CERN laboratory (see, for example, [6]) and in hadron-hadron collisions [7]. Computation aspects of bunching parameters are discussed in [8].
Normalised factorial moments have also similar properties. They are defined as
- [math]\displaystyle{ F_q =\langle n \rangle^{-q} \sum^{\infty}_{n=q} \frac{n!}{(n-q)!} P_n. }[/math]
References
- ↑ Chekanov, S.V.; Kuvshinov, V.I. (1994). "Bunching Parameter and Intermittency in High-Energy Collisions". Acta Physica Polonica B 25: 1189–1197. Bibcode: 1996hep.ph....5379C. http://th-www.if.uj.edu.pl/acta/vol25/pdf/v25p1189.pdf.
- ↑ Chekanov, S.V.; Kittel, W.; Kuvshinov, V.I. (1996). "Multifractal Multiplicity Distribution in Bunching-Parameter Analysis". Journal of Physics G 22 (5): 601–610. doi:10.1088/0954-3899/22/5/007. Bibcode: 1996JPhG...22..601C.
- ↑ Chekanov, S.V.; Kuvshinov, V.I.; Kuvshinov, V. I. (1997). "Generalized Bunching Parameters and Multiplicity Fluctuations in Restricted Phase-Space Bins". Zeitschrift für Physik C 74 (3): 517–529. doi:10.1007/s002880050414.
- ↑ S. Ya. Kilin, Quantum Optics: Fields and Their Detection (Malvern Physics Series), 1995, ISBN-13: 978-0750302326 ISBN-10: 0750302321
- ↑ W. Kittel, E. A. De Wolf, Soft Multihadron Dynamics, Book. World Scientific, 2005 - Science - 652 pages, ISBN9812562958
- ↑ L3 Collaboration, Local multiplicity fluctuations in hadronic Z decay, Phys. Lett. B 429 (1998) 375-386 [1]
- ↑ Ding-Wei Huang, Bunching parameters and multiplicity fluctuations in hadron-hadron collisions, Acta Physica Polonica. Series B; ISSN 0587-4254; Worldcat; v. 28(5); p. 1207-1215
- ↑ Numeric Computation and Statistical Data Analysis on the Java Platform (Book). S.V.Chekanov, Springer, (2016) ISBN 978-3-319-28531-3, 700 pages, [2]
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