Quantitative Characterisation of Correlation Function Shapes With a Multivariate Edgeworth Expansion

Second-order HBT correlation functions can be expanded in terms of correlated gaussian ellipsoids and their derivatives. The resulting multidimensional Edgeworth expansion in terms of cumulants and hermite tensors contains 15 fourth-order and 28 sixth-order cumulants which act as shape parameters. Off-diagonal terms dominate both the character and magnitude of shape changes. We show how cumulants can be measured directly and so the procedure has no need for fitting.