Binary Discrimination Through Next-to-Leading Order

Binary discrimination between well-defined signal and background datasets is a problem of fundamental importance in particle physics. With detailed event simulation and the advent of extensive deep learning tools, identification of the likelihood ratio has typically been reserved as a computational problem. However, this approach can obscure overtraining or excessive sensitivity to tuned features of the simulation that may not be well-defined theoretically. Here, we present the first analysis of binary discrimination for signal and background distributions for which their likelihood ratio is infrared and collinear safe, and can therefore be calculated order-by-order in perturbation theory. We present explicit, general formulas for receiver operator characteristic curves and the area under it through next-to-leading order. As a demonstration of this formalism, we apply it to discrimination of highly-boosted Higgs decays from gluon splitting to bottom quarks. Effects at next-to-leading order are first sensitive to the flow of color in the jet and significantly modify discrimination performance at leading-order. In the limit of infinite boost, these events can be perfectly discriminated because only the gluon will radiate at finite angles from the bottom quarks, and we find that large effects persist at energies accessible at the Large Hadron Collider. Next-to-leading order is therefore required to qualitatively understand results using machine-learning methods.