The Matrix Element Method at next-to-leading order QCD using the example of single top-quark production at the LHC

TL;DR

This paper extends the Matrix Element Method to include next-to-leading order QCD corrections, improving the accuracy and reliability of parameter estimation in high energy physics analyses, demonstrated through top-quark mass determination at the LHC.

Contribution

It introduces the first formulation of the MEM at NLO accuracy, enabling more precise likelihood calculations and event generation for collider data analysis.

Findings

NLO corrections reduce bias in top-quark mass estimates.

The method allows for unweighted event generation at NLO accuracy.

Including NLO improves the reliability of theoretical uncertainty estimates.

Abstract

Analyses in high energy physics aim to put the Standard Model---the commonly accepted theory---to test. For convincing conclusions, analysis methods are needed which offer an unambiguous comparison between data and theory while allowing reliable estimates of uncertainties. The Matrix Element Method (MEM) is a Maximum Likelihood method which is especially tailored for signal searches and parameter estimation at colliders. The MEM has proven to be beneficial due to optimal use of the available information and a clean statistical interpretation of the results. But it has a big drawback: In its original formulation, the likelihood calculation is intrinsically limited to the leading perturbative order in the coupling. Higher-order corrections improve the accuracy of theoretical predictions and allow for unambiguous field-theoretical interpretation of the extracted information. In this work, the MEM incorporating corrections of next-to-leading order (NLO) in QCD by defining event weights suited for the likelihood calculation is presented for the first time. These weights also enable the generation of unweighted events following the cross section calculated at NLO accuracy. The method is demonstrated for top-quark events. The top-quark mass is determined with the MEM at NLO accuracy from the generated events. The extracted estimators are in agreement with the input values from the event generation. Repeating the mass determinations from the same events, without NLO corrections in the predictions, results in biased estimators. These shifts may not be accounted for by estimated theoretical uncertainties rendering the estimation of the theoretical uncertainties unreliable in the leading-order analysis. The results emphasise the importance of the inclusion of NLO corrections into the MEM.