Matrix element method at NLO: A fine proof of concept in POWHEG

Abstract

The matrix element method (MEM) provides a fully probabilistic approach to confront experimental events with theory, retaining all correlations in the scattering matrix element. While leading-order MEM is widely used and automated, extending it to next-to-leading order (NLO) in QCD is challenging due to infrared divergences, negative weights, extra final-state partons, and multi-dimensional phase-space integration. We demonstrate that the POWHEG method offers a practical path to MEM at NLO accuracy. By projecting real-emission events onto Born kinematics via the mappings inherited from the $\tilde{B}(\Phi )$ function, our method consistently includes the hardest QCD radiation while preserving the NLO-accurate normalization. As a proof of concept, we apply the method to fully leptonic $W^{+}{W}^{-}$ production in the Standard Model effective field theory (SMEFT), considering a CP-even dimension-six triple-gauge-boson operator. At the parton level, the resulting NLO MEM exploits spin and polarization correlations in the final-state lepton kinematics, yielding enhanced discrimination between the SM and BSM hypotheses compared with conventional cut-and-count observables. Our results demonstrate the feasibility of incorporating NLO QCD corrections into the MEM and establish a framework for future applications to a broad range of collider processes.

arXiv comment45 pages, 15 figures, 3 tables; v2: extended and improved version of the manuscript as accepted for publication in JHEP