HBT shape analysis with q -cumulants

Abstract

Taking up and extending earlier suggestions, we show how two-and three-dimensional shapes of secondorder HBT correlations can be described in a multivariate Edgeworth expansion around Gaussian ellipsoids, with expansion coefficients, identified as the cumulants of pair momentum difference q, acting as shape parameters. Off-diagonal terms dominate both the character and magnitude of shapes. Cumulants can be measured directly and so the shape analysis has no need for fitting.

Determining Source Cumulants in Femtoscopy With Gram–charlier and Edgeworth Series

“…Application to experimental data will require generalisation to three dimensions using the existing 3D machinery of Refs [15,18]. Furthermore, sampling fluctuations of experimental cumulants will have to be taken into account.…”

“…In Fig. 1, we show respectively the percentage deviation of GGC expansions (17) and (18), truncated at mth order, from the exact answers (22) 4 Edgeworth series…”

“…with γ 4 ≡ γ (q) 4 (1). The algebraic simplicity of the above compared to the equivalent GGC relations (17)- (18) and the GEW relation (28) is due to the fact that SNIG kurtoses obey…”

Efficient experimental designs for isotropic generalized diffusion tensor MRI (IGDTI)

“…Moving forward, it is convenient to adopt the so-called "occupation number" notation (24) [3] where m nx ny nz ¼ n! nx !ny !nz!…”

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