Global Electroweak Fit and Vector-Like Leptons in Light of the Cabibbo Angle Anomaly

TL;DR

This paper investigates the Cabibbo Angle Anomaly and explores how vector-like leptons can modify W couplings to explain the anomaly, performing a comprehensive global fit that shows certain VLL combinations significantly improve agreement with experimental data.

Contribution

It provides the first detailed global fit of gauge-invariant dimension-6 operators involving vector-like leptons to address the Cabibbo Angle Anomaly, considering all possible representations.

Findings

Single VLL representations do not significantly improve the fit.

Multiple VLL representations can explain the anomaly and improve the electroweak fit.

Best fit with multiple VLLs is more than 4 sigma preferred over the SM.

Abstract

The "Cabibbo Angle Anomaly" (CAA) originates from the disagreement between the CKM elements $V_{ud}$ and $V_{us}$ extracted from superallowed beta and kaon decays, respectively, once compared via CKM unitarity. It points towards new physics with a significance of up to $4\,\sigma$, depending on the theoretical input used, and can be explained through modified $W$ couplings to leptons. In this context, vector-like leptons (VLLs) are prime candidates for a corresponding UV completion since they can affect $W\ell\nu$ couplings at tree-level, such that this modification can have the dominant phenomenological impact. In order to consistently asses the agreement with the data, a global fit is necessary which we perform for gauge-invariant dimension-6 operators and all patterns obtained for the six possible representations (under the SM gauge group) of VLLs. We find that even in the lepton flavour universal case, including the measurements of the CKM elements $V_{us}$ and $V_{ud}$ into the electroweak fit has a relevant impact, shifting the best fit point significantly. Concerning the VLLs we discuss the bounds from charged lepton flavour violating processes and observe that a single representation cannot describe experimental data significantly better than the SM hypothesis. However, allowing for several representations of VLLs at the same time, we find that the simple scenario in which $N$ couples to electrons via the Higgs and $\Sigma_1$ couples to muons not only explains the CAA but also improves the rest of the electroweak fit in such a way that its best fit point is preferred by more than $4\,\sigma$ with respect to the SM.