Towards consistent Electroweak Precision Data constraints in the SMEFT

TL;DR

The paper tackles how neglected higher-dimension SMEFT effects influence EWPD fits by deriving 2→2 fermion scattering to $\mathcal{O}(\bar{v}_T^2/\Lambda^2)$ on/off the $Z$ pole and highlighting corrections from $\psi^4$ operators and dimension-8 terms. It develops a consistent framework for EWPD predictions by redefining input parameters and vector-boson couplings within the SMEFT, and demonstrates that near- and off-pole observables acquire nontrivial SMEFT corrections that can relax previously tight bounds on dimension-6 operators. A minimal EWPD fit illustrates the theoretical uncertainties and prior dependencies that arise, underscoring the need to include SMEFT theoretical errors in global analyses. The authors advocate RG-running of the EWPD constraint χ^2 to a common scale before performing a global fit, enabling more reliable connections to LHC measurements and a coherent picture of SMEFT constraints across energy scales.

Abstract

We discuss the impact of many previously neglected effects of higher dimensional operators when fitting to Electroweak Precision data (EWPD) in the Standard Model Effective Field Theory (SMEFT). We calculate the general case of $2 \rightarrow 2$ fermion scattering in the SMEFT to order $\mathcal{O}(\bar{v}_T^2/Λ^2)$ valid on and off the $Z$ pole, in the massless fermion limit. We demonstrate that previously neglected corrections scale as $Γ_Z M_Z/\bar{v}_T^2$ in the partial widths extracted from measured cross sections at LEPI, compared to the leading effect of dimension six operators in anomalous $Z$ couplings. Further, constraints on leading effects of anomalous $Z$ couplings are also modified by neglected perturbative corrections and dimension eight operators. We perform a minimal EWPD fit to illustrate the size of the error these corrections induce, when bounding leading effects. These considerations relax bounds compared to a naive leading order analysis, and show that constraints that rise above the percent level are subject to substantial theoretical uncertanties. We also argue that renormalization group running global constraints expressed through $χ^2$ functions to a common scale, and then minimizing and performing a global fit of all data allows more consistent constraints to be obtained in the SMEFT.

Figures (2)

• Figure 1: Diagrams contributing to near $Z$ pole $2 \rightarrow 2$ scattering in the SMEFT. The black box indicates the insertion of $\mathcal{L}^{(6)}$.
• Figure 2: Mixing of a $\psi^4$ operator into an effective $Z$ coupling to fermions.