Gaussian and non-Gaussian-based Gram-Charlier and Edgeworth expansions for correlations of identical particles in HBT interferometry
Date
2009-03
Authors
De Kock, Michiel Burger
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
Abstract
Hanbury Brown-Twiss interferometry is a correlation technique by which the size and shape
of the emission function of identical particles created during collisions of high-energy leptons,
hadrons or nuclei can be determined. Accurate experimental datasets of three-dimensional
correlation functions in momentum space now exist; these are sometimes almost Gaussian
in form, but may also show strong deviations from Gaussian shapes. We investigate the
suitability of expressing these correlation functions in terms of statistical quantities beyond
the normal Gaussian description. Beyond means and the covariance matrix, higher-order
moments and cumulants describe the form and di erence between the measured correlation
function and a Gaussian distribution. The corresponding series expansion is the Gram-
Charlier series and in particular the Gram-Charlier Type A expansion found in the literature,
which is based on a Gaussian reference distribution. We investigate both the Gram-Charlier
Type A series as well as generalised forms based on non-Gaussian reference distributions,
as well as the related Edgeworth expansion. For testing purposes, experimental data is
initially represented by a suite of one-dimensional analytic non-Gaussian distributions. We
conclude that the accuracy of these expansions can be improved dramatically through a
better choice of reference distribution, suggested by the sign and size of the kurtosis of
the experimental distribution. We further extend our investigation to simulated samples
of such test distributions and simplify the theoretical expressions for unbiased estimators
(k-statistics) for the case of symmetric distributions.
Description
Thesis (MSc (Physics))--University of Stellenbosch, 2009.
Keywords
Intensity interferometry, Multiparticle correlations, Dissertations -- Physics, Theses -- Physics