Testing theories in particle physics using maximum likelihood and adaptive bin allocation

Abstract

We describe a methodology to assist scientists in quantifying the degree of evidence in favor of a new proposed theory compared to a standard baseline theory. The figure of merit is the log-likelihood ratio of the data given each theory. The novelty of the proposed mechanism lies in the likelihood estimations; the central idea is to adaptively allocate histogram bins that emphasize regions in the variable space where there is a clear difference in the predictions made by the two theories. We describe a software system that computes this figure of merit in the context of particle physics, and describe two examples conducted at the Tevatron Ring at the Fermi National Accelerator Laboratory. Results show how two proposed theories compare to the Standard Model and how the likelihood ratio varies as a function of a physical parameter (e.g., by varying the particle mass). © Springer-Verlag Berlin Heidelberg 2005.