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

TL;DR

This paper demonstrates that even cumulants, including HBT radii, can be reliably measured in HBT analyses, while odd cumulants are ambiguous but correlated, especially when the average position is known.

Contribution

The study shows that even cumulants are unaffected by ambiguities in HBT measurements, providing reliable information on homogeneity regions.

Findings

Even cumulants are unaffected by measurement ambiguities.

HBT radii can be reliably measured.

Odd cumulants are ambiguous but correlated.

Abstract

Let us denote p(x|K) the space density of the points where identical particles of some kind, e.g. pi+ 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. The are, however, correlated. In particular, when the average position <x>(K) is known as a function of K there is no further ambiguity.