Towards consistent Electroweak Precision Data constraints in the SMEFT

TL;DR

This paper investigates the effects of higher-dimensional operators in SMEFT on electroweak precision data analysis, revealing that neglecting these effects can lead to underestimated uncertainties and proposing a more consistent global fitting approach.

Contribution

It introduces a comprehensive calculation of fermion scattering in SMEFT, including previously neglected corrections, and advocates for a renormalization group based global fit methodology.

Findings

Neglected corrections significantly affect Z width measurements.

Constraints on anomalous Z couplings are more uncertain than previously thought.

A global fit approach improves the consistency of SMEFT constraints.

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 $\mathcal{O}(\bar{v}_T^2/\Lambda^2)$ valid on and off the $Z$ pole, in the massless fermion limit. We demonstrate that previously neglected corrections scale as $\Gamma_Z M_Z/\bar{v}_T^2$ 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 $\chi^2$ 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.