Parameter Inference from Event Ensembles and the Top-Quark Mass

TL;DR

This paper compares different methodologies for measuring the top-quark mass using ensemble data, finding that linear regression methods trained on sorted event ensembles outperform traditional and machine learning approaches, potentially reducing uncertainties significantly.

Contribution

It introduces and evaluates linear regression techniques trained on sorted event ensembles for top-quark mass measurement, demonstrating their effectiveness over traditional and other machine learning methods.

Findings

Linear regression on sorted ensembles outperforms individual event training.

Training on sorted ensembles reduces Monte-Carlo uncertainty by about a factor of 2.

Machine learning methods show broad potential for collider physics measurements.

Abstract

One of the key tasks of any particle collider is measurement. In practice, this is often done by fitting data to a simulation, which depends on many parameters. Sometimes, when the effects of varying different parameters are highly correlated, a large ensemble of data may be needed to resolve parameter-space degeneracies. An important example is measuring the top-quark mass, where other physical and unphysical parameters in the simulation must be marginalized over when fitting the top-quark mass parameter. We compare three different methodologies for top-quark mass measurement: a classical histogram fitting procedure, similar to one commonly used in experiment optionally augmented with soft-drop jet grooming; a machine-learning method called DCTR; and a linear regression approach, either using a least-squares fit or with a dense linearly-activated neural network. Despite the fact that individual events are totally uncorrelated, we find that the linear regression methods work most effectively when we input an ensemble of events sorted by mass, rather than training them on individual events. Although all methods provide robust extraction of the top-quark mass parameter, the linear network does marginally best and is remarkably simple. For the top study, we conclude that the Monte-Carlo-based uncertainty on current extractions of the top-quark mass from LHC data can be reduced significantly (by perhaps a factor of 2) using networks trained on sorted event ensembles. More generally, machine learning from ensembles for parameter estimation has broad potential for collider physics measurements.