Statistical moments in superposition models and strongly intensive measures

First, we present a concise glossary of formulas for composition of standard, cumulant, factorial, and factorial cumulant moments in superposition (compound) models, where final particles are created via independent emission from a collection of sources. Explicit mathematical formulas for the composed moments are given to all orders. We discuss the composition laws for various types of moments via the generating-function methods and list the formulas for the unfolding of the unwanted fluctuations. Second, the technique is applied to the difference of the scaled multiplicities of two particle types. This allows for a systematic derivation and a simple algebraic interpretation of the so-called strongly intensive fluctuation measures. With the help of the formalism we obtain several new strongly intensive measures involving higher-rank moments. The reviewed as well as the new results may be useful in investigations of mechanisms of particle production and event-by-event fluctuations in high-energy nuclear and hadronic collisions, and in particular in the search for signatures of the QCD phase transition at a finite baryon density.

Figure 1

Summary of the transformations between various kinds of moments. $B$ denotes the transformation with partial Bell polynomials [as in Eqs. (5) and (12)], and $S$ denotes the transformation with the Stirling numbers [as in Eq. (11)].

Figure 2

Graphical interpretation of the composition formulas for the moments in the superposition model. The dark blobs connected with shaded regions correspond to the sources, and the empty squares to the produced particles. A particle is linked with the source which produced it. Ovals encircling particles indicate the connected correlations. See text for more details.