Testing Theories in Particle Physics Using Maximum Likelihood and Adaptive Bin Allocation

摘要

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 Teva-tron 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).