Number-ratio fluctuations in high-energy particle production

In this article we will discuss the previously proposed quantity ${\nu }_{\mathrm{dyn}}$ [C. Pruneau, S. Gavin, and S. Voloshin, Phys. Rev. C 66, 044904 (2002)], as a measure of the number-ratio fluctuations in high-energy particle production. We will show that ${\nu }_{\mathrm{dyn}}$ has pleasing mathematical properties making it ideal for the purpose. We will demonstrate its relation to two-particle correlations and how this measure can be generalized to higher-order correlations.

Figure 1

If two uncorrelated samples with different multiplicity distributions are mixed to define a sample, then ${\nu }_{\mathrm{dyn}}$ as a function of multiplicity will be nonzero only in the regions where the multiplicity overlaps.

Figure 2

A schematic drawing of three different possibilities of two-particle azimuthal correlations. In (a) the particle pairs are produced close in azimuth and a smaller azimuthal acceptance will essentially either keep both particles from a pair inside the acceptance or both particles will be lost. In (b) the particle pairs are produced back-to-back and a decrease of acceptance will essentially break all pairs. In (c) particles within a pair are uncorrelated in φ.

Figure 3

Simulation of the influence of particle misidentification. In (a) the effect on ${\nu }_{\mathrm{dyn}}$, when a certain percentage of the observed kaons are misidentified as pions, is studied. In (b) the effect on ${\nu }_{\mathrm{dyn}}$, when a certain percentage of the observed pions are misidentified as kaons, is studied. As can be seen in the plots, misidentified pions influence the ${\nu }_{\mathrm{dyn}}$ value much more than misidentified kaons.

Figure 4

Simulation of the influence of double-counting. In (a) the effect on ${\nu }_{\mathrm{dyn}}$, when a certain percentage of the observed kaons are double counted, is studied. In (b) the effect on ${\nu }_{\mathrm{dyn}}$, when a certain percentage of the observed pions are double counted, is studied. As can be seen in the plots, double-counted kaons influence the ${\nu }_{\mathrm{dyn}}$ value much more than double-counted pions.