Use of cumulants to quantify uncertainties in the HBT measurements of the homogeneity regions

Abstract

Let us denote by p(x|K) the space density of the points where identical particles of some kind, e.g. π + mesons, with momentum K are produced. When using the HBT method to determine p(x|K) one encounters ambiguities. We show that these ambiguities do not affect the even cumulants of the distribution p(x|K). In particular, the HBT radii of the homogeneity regions, which are given by the second order cumulants, and the distribution of distances between the pairs of production points for particles with momentum K can be reliably measured. The odd cumulants are ambiguous. They are, however, correlated. In particular, when the average position x (K) is known as a function of K there is no further ambiguity.

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