Automation of electroweak corrections for LHC processes

TL;DR

This work addresses the growing importance of next-to-leading order electroweak corrections for LHC processes and the need for automated, process-independent computation. It presents a practical framework that leverages GoSam for virtual one-loop amplitudes and MadDipole for infrared subtraction, including detailed treatment of regularization-scheme (CDR vs. DRED) and EW renormalization. The authors illustrate the approach with a full EW NLO calculation of pp → W+2 jets, examining virtual and real contributions, pole cancellations, and the impact on differential distributions, which show sizable effects in high-energy regions while total cross sections remain modest. The study underscores the critical role of automation in enabling precise SM predictions and reliable interpretations of high-energy collider data, guiding future developments toward broader EW NLO automation and photon-induced processes.

Abstract

For the Run 2 of the LHC next-to-leading order electroweak corrections will play an important role. Even though they are typically moderate at the level of total cross sections they can lead to substantial deviations in the shapes of distributions. In particular for new physics searches but also for a precise determination of Standard Model observables their inclusion in the theoretical predictions is mandatory for a reliable estimation of the Standard Model contribution. In this article we review the status and recent developments in electroweak calculations and their automation for LHC processes. We discuss general issues and properties of NLO electroweak corrections and present some examples, including the full calculation of the NLO corrections to the production of a W boson in association with two jets computed using GoSaM interfaced to MadDipole.

Figures (8)

• Figure 1: One loop electroweak corrections to $V \to f \bar{f}'$. The diagram on the left gives rise to the $\mathcal{V}_a$ contributions, while the $\mathcal{V}_b$ terms come from the diagram on the right.
• Figure 2: LO and virtual NLO electroweak diagrams for the process $u \bar{u} \to c \bar{c}$.
• Figure 3: Example diagrams for a QCD Born (left diagram) and an electroweak Born (right diagram). At leading order only the left diagrams are taken into account.
• Figure 4: Schematical representation of the two different kinds of insertion operators, representing QED singularities (l.h.s.) and QCD singularities (r.h.s.). This also illustrates the two different types of real emission contributions.
• Figure 5: Different virtual contributions. In the upper row the left plot denotes the interference between a QCD tree-level diagram with an electroweak one-loop diagram, the right plot displays the interference between an electroweak tree-level diagram and a QCD one-loop diagram. As the two pieces contribute at the same order both have to be taken into account. The lower row shows an example diagram for each of the two types of one-loop amplitudes.