Stable Bose-Einstein correlations

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 stretched exponential shape, characterized by the Lévy index of stability 0 < α ≤ 2 and the scale parameter R. The normal, Gaussian shape corresponds to a particular case, when α = 2 is selected. The asymmetry parameter of the stable source, β is shown to be proportional to the angle, measured by the normalized three-particle cumulant correlations. In high energy nuclear and particle physics, the space-time structure of particle emitting sources is often investigated with the help of the two-particle Bose-Einstein correlation functions. In heavy ion physics, these correlations are frequently called as HBT correlations to honor the astronomers R. Hanbury Brown and R.Q. Twiss, who invented a similar method [1] in radio astronomy to measure the angular diameter of main sequence stars. The two-particle correlation function C2(k1,k2) is defined as C2(k1,k2) = N2(k1,k2) N1(k1)N1(k2) (1) where ki is the momentum of particle i = 1, 2, and N1(k1) is the single particle invariant momentum distribution (IMD), while N2(k1,k2) is the two-particle invariant momentum distribution. In this manuscript we highlight some of the results of ref. [2], where we have investigated in great detail the Bose-Einstein or HBT correlation functions under the following three experimental conditions: i) The correlation function tends to a constant for large values of the relative momentum q = k1 − k2. ii) Near |q| = 0, the correlation function deviates from its asymptotic, large |q| value in a certain domain of its argument.