One-loop electroweak Sudakov logarithms: a revisitation and automation

TL;DR

This paper revisits and automates the calculation of one-loop electroweak Sudakov logarithms, improving accuracy and extending applicability to NLO corrections with QCD, using the MadGraph5_aMC@NLO framework for high-energy processes.

Contribution

It introduces an automated algorithm for electroweak Sudakov logarithms, including angular dependence, imaginary terms, and QCD corrections, enhancing precision in high-energy collider calculations.

Findings

The algorithm accurately reproduces NLO EW corrections in various processes.

Inclusion of angular-dependent logarithms improves approximation accuracy.

The new approach for removing the QED component can outperform traditional methods.

Abstract

In this work we revisit the algorithm of Denner and Pozzorini for the calculation of one-loop electroweak Sudakov logarithms and we automate it in the MadGraph5_aMC@NLO framework. We adapt the formulas for modern calculations, keeping light-quarks and photons strictly massless and dealing with infrared divergences via dimensional regularisation. We improve the approximation by taking into account additional logarithms that are angular dependent. We prove that an imaginary term has been previously omitted and we show that it cannot be in general neglected for $2\rightarrow n$ processes with $n> 2$. We extend the algorithm to NLO EW corrections to squared matrix-elements that involve also QCD corrections on top of subleading LO terms. Furthermore, we discuss the usage of this algorithm for approximating physical observables and cross sections. We propose a new approach in which the QED component is consistently removed and we show how it can be superior to the commonly used approaches. The relevance of all the novelties introduced in this work is corroborated by numerical results obtained for several processes in a completely automated way. We thoroughly compare exact NLO EW corrections and their Sudakov approximations both at the amplitude level and for physical observables in high-energy hadronic collisions.