Systematic Interpretability and the Likelihood for Boosted Top Quark Identification

Identification of boosted, hadronically-decaying top quarks is a problem of central importance for physics goals of the Large Hadron Collider. We present a theoretical analysis of top quark tagging, establishing zeroth-order, minimal assumptions that should be satisfied by any purported top-tagged jet, like existence of three hard subjets, a bottom-tagged subjet, total mass consistent with the top quark, and a pairwise subjet mass consistent with the W boson. From these minimal assumptions, we construct the optimal discrimination observable, the likelihood ratio, for the binary discrimination problem of top quark-initiated versus bottom quark-initiated jets through next-to-leading order in the strong coupling. We compare and compute corresponding signal and background efficiencies both analytically and from simulated data, validating an understanding of the relevant physics identified and exploited by the likelihood. In the process, we construct a method for systematic interpretability of the likelihood ratio for this problem, and explicitly establish a hard floor on possible discrimination power. These results can correspondingly be applied to understanding and interpreting machine learning studies of this problem.