The role of non-universal $Z$ couplings in explaining the $V_{us}$ anomaly

TL;DR

This paper explores how non-universal Z boson couplings could resolve the V_{us} anomaly, suggesting new gauge-invariant operators and minimal vector-like lepton models that impact electroweak precision tests and Higgs decays.

Contribution

It introduces gauge-invariant dimension-6 operators affecting Z and W couplings, providing a model-independent framework to address the V_{us} anomaly and analyzing minimal vector-like lepton extensions.

Findings

Non-universal Z couplings can alleviate the V_{us} tension.

Additional gauge-invariant Z couplings are favored by current data.

Effects on h → ττ decay are minimal in minimal VLL models.

Abstract

The tension among measurements of $V_{us}$ from different channels, the so-called Cabibbo Angle Anomaly, can be interpreted as a signal of lepton flavor universality (LFU) violation in the $W$ boson couplings. We investigate this issue in the framework of effective field theory, keeping the gauge structure of the Standard Model (SM) unchanged. We introduce gauge-invariant dimension-6 effective operators that couple the Higgs doublet to leptons, thereby giving non-universal tree-level contributions to the couplings of electroweak gauge bosons. Due to the $SU(2)_L$ gauge symmetry, a tension arises between the $V_{us}$ measurements that are affected by new $W$ couplings, and the electroweak precision measurements, which are also affected by the new $Z$ couplings. We show that this tension can be alleviated by allowing additional sources of gauge-invariant couplings of $Z$ boson to left- or right-handed leptons, and find the optimal regions indicated by the current data in the Wilson-coefficient space. We illustrate our model-independent results with the examples of minimal extensions of the SM involving the vector-like lepton (VLL) models. We point out that dimension-6 operators coupling the Higgs doublet to leptons can affect the rate of $h \to \tau \tau$ decay significantly in general, however this effect is restricted to less than a per cent level for the minimal VLL models.