Unbinned inclusive cross-section measurements with machine-learned systematic uncertainties

TL;DR

This paper presents a new machine learning-based method for more accurate unbinned cross-section measurements in collider physics, improving over traditional binned approaches by capturing full parameter dependence.

Contribution

It introduces a neural network approach to model systematic uncertainties and likelihood ratios, enabling near-optimal unbinned inference in collider experiments.

Findings

Significant improvements over traditional binned methods demonstrated.

Method successfully applied to Higgs to tau tau cross-section measurement.

Code GOLLUM made publicly available for broader use.

Abstract

We introduce a novel methodology for addressing systematic uncertainties in unbinned inclusive cross-section measurements and related collider-based inference problems. Our approach incorporates known analytic dependencies on parameters of interest, including signal strengths and nuisance parameters. When these dependencies are unknown, as is frequently the case for systematic uncertainties, dedicated neural network parametrizations provide an approximation that is trained on simulated data. The resulting machine-learned surrogate captures the complete parameter dependence of the likelihood ratio, providing a near-optimal test statistic. As a case study, we perform a first-principles inclusive cross-section measurement of $\textrm{H}\rightarrow\tau\tau$ in the single-lepton channel, utilizing simulated data from the FAIR Universe Higgs Uncertainty Challenge. Results in Asimov data, from large-scale toy studies, and using the Fisher information demonstrate significant improvements over traditional binned methods. Our computer code ``Guaranteed Optimal Log-Likelihood-based Unbinned Method'' (GOLLUM) for machine-learning and inference is publicly available.