Electroweak corrections in the SMEFT: four-fermion operators at high energies

TL;DR

This paper develops and validates a high-energy Sudakov framework for electroweak corrections within the SMEFT, focusing on dimension-six four-fermion operators in tt̄ production at the LHC, tt̄ production at a muon collider, and Drell–Yan at the LHC. It demonstrates that EW corrections, captured via the Denner–Pozzorini Sudakov formalism extended to SMEFT, are process- and operator-dependent and can significantly alter both interference and squared SMEFT contributions, often in ways not reproducible by simple K-factors. The authors implement these corrections in MG5_aMC@NLO with a dedicated SMEFT UFO model, validate the approach against exact high-energy limits, and show that higher-order corrections can lift flat directions in the Wilson coefficient space as quantified by Fisher information. They find that EW corrections can provide genuinely new information about the SMEFT parameter space, particularly in Drell–Yan and high-energy tt̄ channels, and they release the tooling for public use to advance SMEFT precision phenomenology. Overall, the work highlights the necessity of including EW effects in SMEFT analyses for reliable interpretation of high-energy collider data and outlines a path toward automated, NLO EW SMEFT predictions.

Abstract

In the Standard Model (SM), electroweak (EW) corrections become significant at high energies, particularly at the tera-electronvolt scale and beyond, due to the presence of Sudakov logarithms. At these energy scales, the Standard Model Effective Field Theory (SMEFT) framework provides an enhanced sensitivity to potential new physics effects. This motivates the inclusion of EW corrections not only for SM predictions but also for analyses within SMEFT. In this work, we compute EW corrections in the high-energy limit for a selected set of dimension-six operators, specifically the class of four-fermion contact interactions, in key hard-scattering processes relevant to both current and future colliders: top-quark pair production at the Large Hadron Collider (LHC) and in a muon collider scenario, as well as the Drell-Yan process at the LHC. We first discuss the technical details and challenges associated with evaluating EW Sudakov logarithms in SMEFT, contrasting them with the SM case. We then present phenomenological results for the aforementioned processes, highlighting the non-trivial effects introduced by EW corrections arising from the insertion of dimension-six, four-fermion operators. Importantly, the resulting $K$-factors exhibit significant deviations from their SM counterparts, with dependencies not only on the process but also on the specific operators considered. Finally, we explore the potential to lift flat directions in the SMEFT parameter space by incorporating higher-order corrections, using Fisher information techniques.

Figures (18)

• Figure 1: Representative diagrams for one-loop EW corrections to $q \bar{q} \to t \bar{t}$ at ${\cal O}{(y_t^2)}$, with the insertion of $\mathcal{O}_{tG}$ denoted by the black blob. In Feynman gauge, similar diagrams involving the Goldstone bosons, $G^0$ and $G^\pm$, are also present.
• Figure 2: Illustration of the structure of ${\cal O}(\alpha_{ S})$ corrections in the SMEFT for an arbitrary $2 \to 2$ process with the inclusion of colour-octet four-fermion operators (black blob). Top row, from left to right: $\mathcal{M}_0^{\rm NP}$ at ${\cal O}(\alpha_{ S} / \Lambda^2)$ and $\mathcal{M}_0^{\rm SM}$ at ${\cal O}(\alpha_{ S})$. Bottom row, from left to right: one-loop perturbations to the corresponding amplitudes contributing to $\mathcal{M}_{1, {\rm QCD}}^{\rm NP}$.
• Figure 3: Illustration of the structure of ${\cal O}(\alpha)$ corrections in the SMEFT for an arbitrary $2 \to 2$ process with the inclusion of colour-octet (black blob) and colour-singlet (white blob) four-fermion operators. Top row, from left to right: $\mathcal{M}_0^{\rm NP}$ at ${\cal O}(\alpha_{ S} / \Lambda^2)$, $\mathcal{M}_{0'}^{\rm NP}$ at ${\cal O}(\alpha / \Lambda^2)$, $\mathcal{M}_0^{\rm SM}$ at ${\cal O}(\alpha_{ S})$, and $\mathcal{M}_{0'}^{\rm SM}$ at ${\cal O}(\alpha)$. Bottom row, from left to right: one-loop perturbations to the corresponding amplitudes contributing to $\mathcal{M}_{1, {\rm EW}}^{\rm NP}$.
• Figure 4: Tree-level diagrams contributing to $p \, p \to e^- \, e^+$ and $\mu^- \mu^+ \to t \, \bar{t}$, both in the SM and the SMEFT. The black blob represents the insertion of a dimension-six four-fermion operator.
• Figure 5: Left: Differential cross-section for top-quark pair production at the LHC, shown at QCD+EW$_{\text{SDK}}$ order as a function of the transverse momentum of the top quark, $p^{t}_{ T}$. The black line represents the SM, the red line indicates the linear term in $C_{Qd}^8$, and the blue line depicts the quadratic term. Insets illustrate the relative impact of the interference and quadratic terms compared to the SM at various perturbative orders. Right: Corresponding $K$-factors for $C_{Qd}^8$ at QCD order (dotted), EW$_{\text{SDK}}$ order (dashed), and the combined effect of the two (solid) at different orders in the EFT expansion.