Cabibbo angle anomalies: indication of new physics at TeV scale?

Abstract

Recent high-precision determinations of $V_{us}$ and $V_{ud}$ indicate towards anomalies in the first row of the CKM matrix. Namely, the determination of $V_{ud}$ from beta decays and of $V_{us}$ from kaon decays imply a violation of first row unitarity at about $3\sigma$ level. Moreover, there is tension between determinations of $V_{us}$ obtained from leptonic $K\mu 2$ and semileptonic $K\ell 3$ kaon decays. CKM unitarity anomaly can be explained if the Fermi constant $G_F$ is slightly smaller than the muon decay constant $G_\mu$, so that determinations of CKM elements should be rescaled. This situation can be the consequence of the presence of another muon decay channel in interference with the Standard Model one. Horizontal gauge symmetries between lepton families can explain the mass hierarchy between the generations and the relative gauge bosons induce an effective operator in interference with $W$-boson exchange in muon decay. Another explanation of the anomalies can be the mixing of SM quarks with vector-like quarks, with mass at the TeV scale, having large enough mixings with the lighter quarks. Mixing with vector-like doublets is the possible explanation to the discrepancy between determination from semileptonic kaon decays and leptonic decays. Although one extra multiplet cannot entirely explain all the discrepancies, a combination such as two species of isodoublet, or one isodoublet and up or/and down type isosinglet is a complete solution. These scenarios are testable with future experiments.