Global fit of modified quark couplings to EW gauge bosons and vector-like quarks in light of the Cabibbo angle anomaly

Abstract

There are two tensions related to the Cabibbo angle of the CKM matrix. First, the determinations of V$_{us}$ from K$_{μ2}$, K$_{ℓ3}$, and τ decays disagree at the 3σ level. Second, using the average of these results in combination with β decays (including super-allowed β decays and neutron decay), a deficit in first-row CKM unitarity with a significance of again about 3σ is found. These discrepancies, known as the Cabibbo Angle anomaly, can in principle be solved by modifications of W boson couplings to quarks. However, due to SU(2)$_{L}$ invariance, Z couplings to quarks are also modified and flavour changing neutral currents can occur. In order to consistently assess the agreement of a new physics hypothesis with data, we perform a combined analysis for all dimension-six Standard Model Effective Field Theory operators that generate modified W couplings to first and second generation quarks. We then study models with vector-like quarks, which are prime candidates for a corresponding UV completion as they can affect W -quark couplings at tree level, and we perform a global fit including flavour observables (in particular loop effects in ∆F = 2 processes). We find that the best fit can be obtained for the SU(2)$_{L}$ doublet vector-like quark Q as it can generate right-handed W-u-d and W-u-s couplings as preferred by data.