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We review the recent experimental and theoretical progress in the determination of |V_{ud}| and |V_{us}|, and the status of the most stringent test of CKM unitarity. Future prospects on |V_{cd}| and |V_{cs}| are also briefly discussed.
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Maximally extending the Higgs sector of the Glashow-Salam-Weinberg model by including all scalar and pseudoscalar J=0 states expected for 2 generations of quarks, I demonstrate that the Cabibbo angle is given by tan^2(theta_c) = (1/m_K^2-1/m_D^2)/(1/m_pi^2-1/m_{D_s}^2) approx (m_pi^2 /m_K^2)(1-m_K^2/m_D^2 + m_pi^2/m_{D_s}^2).
We identify a single six-dimensional effective operator $O_{ellell}$ that can account for the Cabibbo angle anomaly naturally, without any tension with the electroweak precision observables. The renormalization group running of $O_{ell ell}$ yields the required new couplings of $W$ and $Z$ bosons in exactly the right proportion. When generated as a result of a $Z$ model, the non-universal leptonic coupling needed for this operator can also contribute to the lepton flavor universality violating $R_{K^{(*)}}$ anomaly, generating the preferred relation $C_9=-C_{10}$ between the Wilson coefficients. We find the region in parameter space of $Z$ mass and couplings that offer a simultaneous solution to both these anomalies, and argue that $O_{ell ell}$ is a unique single operator that can offer such a resolution. Our arguments may also be extended to multi-operator scenarios like $U_1$ vector leptoquark, which is known to address multiple anomalies that violate the lepton flavor universality.
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 $Well u$ 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.
We present a flavor model of quarks and leptons with the non-Abelian discrete symmetry $S_4$ in the framework of the SU(5) SUSY GUT. Three generations of $bar 5$-plets in SU(5) are assigned to ${bf 3}$ of $S_4$ while the first and second generations of 10-plets in SU(5) are assigned to ${bf 2}$ of $S_4$, and the third generation of 10-plet is assigned to ${bf 1}$ of $S_4$. Right-handed neutrinos are also assigned to ${bf 2}$ for the first and second generations and ${bf 1}$ for the third generation. We predict the Cabibbo angle as well as the tri-bimaximal mixing of neutrino flavors. We also predict the non-vanishing $U_{e3}$ of the neutrino flavor mixing due to higher dimensional mass operators. Our predicted CKM mixing angles and the CP violation are consistent with experimental values. We also study SUSY breaking terms in the slepton sector. Our model leads to smaller values of flavor changing neutral currents than the present experimental bounds.
Significant deviations from the Standard Model are observed in semileptonic charged and neutral-current B-decays, the muon magnetic moment, and the extraction of the Cabibbo angle. We propose that these deviations point towards a coherent pattern of New Physics effects induced by two scalar mediators, a leptoquark $S_1$ and a charged singlet $phi^+$. While $S_1$ can provide solutions to charged-current $B$-decays and the muon magnetic moment, and $phi^+$ can accommodate the Cabibbo-angle anomaly independently, their one-loop level synergy can also address neutral-current $B$-decays. This framework provides the most minimal explanation to the above-mentioned anomalies, while being consistent with all other phenomenological constraints.
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