Geometry and Information in Precision Collider Physics

Abstract

The next era of collider physics will be limited less by what we can measure than by what we can reliably predict. The cascades of QCD radiation that fill every collision are typically simulated at the lowest orders in perturbation theory, with correspondingly large uncertainties. Hadronization is modeled rather than derived from first principles. The effective field theories meant to capture new physics in a model-independent way carry far more operators than experiments can confidently constrain. I will describe recent progress on each of these and argue that two tools do much of the work: information theory and geometry. Information theory, with the machine learning built on it, teaches our simulations state of the art theory with honest uncertainties, selects the measurements that matter, and pushes hadronization from model to theory. Geometry, in the field space of effective theories, resums infinite families of operators into finite physical quantities, and information theory ranks the few that experiment could ever resolve. Together they define a path towards reliably extracting all available physics information from the wealth of data at the LHC and future colliders.