Stable Bose-Einstein correlations

TL;DR

This paper derives the shape of Bose-Einstein correlation functions for particles emitted from a stable source, revealing a stretched exponential form characterized by Lévy stability parameters, with implications for understanding particle emission processes.

Contribution

It introduces a theoretical framework linking stable source distributions to the shape of Bose-Einstein correlations, including the role of Lévy stability and asymmetry parameters.

Findings

Correlation functions follow a stretched exponential form with Lévy index $eta$.

Gaussian shape is a special case with $eta=2$.

Asymmetry parameter $eta$ relates to three-particle cumulant correlations.

Abstract

The shape of Bose-Einstein (or HBT) correlation functions is determined for the case when particles are emitted from a stable source, obtained after convolutions of large number of elementary random processes. The two-particle correlation function is shown to have a {\it stretched exponential} shape, characterized by the L\'evy index of stability $ 0 < \alpha \le 2$ and the scale parameter $R$. The normal, Gaussian shape corresponds to a particular case, when $\alpha = 2$ is selected. The asymmetry parameter of the stable source, $\beta$ is shown to be proportional to the angle, measured by the normalized three-particle cumulant correlations.