Multifractal multiplicity distribution in bunching parameter analysis

Abstract

A new multiplicity distribution with multifractal properties which can be used in high-energy physics and quantum optics is proposed. It may be considered as a generalization of the negative-binomial distribution. We find the structure of the generating function for such distribution and discuss its properties.

Intriguing feature of multiplicity distributions

“…(d) Coefficients C j emerging from the CMS data used in panel (a) compared with the NB and 2-NBD fits shown there and with the C j obtained from the MNB with modifications proposed in [9] and shown in panel (c). by some other forms of P(N) [1,[5][6][7][8]. However, as seen in Fig.…”

Intriguing properties of multiplicity distributions

“…Usually the first choice of P (N ) in fitting data is a single NBD [6]. However, with growing energy and number of produced secondaries the NBD increasingly deviates from data for large N (see [4]) and is replaced either by combinations of two [7,8], three [9], or multi-component NBDs [10], or by some other form of P (N ) [1,6,[11][12][13]. However, such a procedure only improves the agreement at large N , whereas the ratio R = data/f it deviates dramatically from unity at small N for all fits [4,5].…”

Generalized bunching parameters and multiplicity fluctuations in restricted phase-space bins

“…where f "1 according to (6) and (8). Therefore, O ( ) calculated from experiment gives information on the fluctuations described by the theoretical probability density w( ), since Poissonian contributions cancel at small .…”

“…In order to reveal intermittent structure of multiparticle production, it is, in fact, sufficient to study the behavior of the probability distribution near multiplicity n"q!1 by means of the so-called bunching parameters (BPs) [7,8] O ( )" q q!1…”