Narrow Results

New developments in both the theories and experiments related to the extraction of the top-row Cabibbo–Kobayashi–Maskawa matrix elements $V_{ud}$ and $V_{us}$ led to a series of new anomalies, for instance, the apparent violation of the top-row unitarity relation. It is important to further reduce all the associated Standard Model theory uncertainties in order to better understand whether such observations point towards the possibility of physics beyond the Standard Model, or rather some unexpectedly large Standard Model effects. This requires improved studies of tree-level and higher-order Standard Model corrections that enter the beta decays of pions, neutron, nuclei and kaons. We will briefly review the recent progress along this direction and discuss possible improvements in the future.

We perform a bottom-up search for discrete non-Abelian symmetries capable of quantizing the Cabibbo angle that parameterizes CKM mixing. Given a particular Abelian symmetry structure in the up and down sectors, we construct representations of the associated residual generators which explicitly depend on the degrees of freedom present in our effective mixing matrix. We then discretize those degrees of freedom and utilize the Groups, Algorithms, Programming (GAP) package to close the associated finite groups. This short study is performed in the context of recent results indicating that, without resorting to special model-dependent corrections, no small-order finite group can simultaneously predict all four parameters of the three-generation CKM matrix and that only groups of ${𝒪}(10^2)$ can predict the analogous parameters of the leptonic PMNS matrix, regardless of whether neutrinos are Dirac or Majorana particles. Therefore, a natural model of flavour might instead incorporate small(er) finite groups whose predictions for fermionic mixing are corrected via other mechanisms.

It is shown that the following experimentally viable expressions for quark mixing angles ${\theta }_{12}$, ${\theta }_{23}$, ${\theta }_{13}$ and CP-violating phase $\delta$: $sin{\theta }_{12}=\sqrt{m_d/|m_s|}$, $sin{\theta }_{23}=2|m_s|/m_b$, $sin{\theta }_{13}\approx 2m_d/m_b$, $tan\delta =m_b^2{m}_c/6m_t{m}_s^2$ may be derived as stable points of certain fourth power in $V_{\mathrm{\text{CKM}}}$ flavor-invariant potentials built with traces of 3 $\times$ 3 quark up and down mass matrices and the Jarlskog invariant. There is no fine-tuning, potentials’ dimensionless constants are the integer numbers not above 10.

In this paper, we present the current situation of the determinations of the first-row CKM components and show the Cabibbo angle anomaly corresponding to a deficit in the first-row CKM unitarity condition at the $3\sigma$ level. In this contribution, we show two new physics interpretations: heavy vector-like quark models and a MeV scale sterile neutrino scenario. The super tau-charm facility will directly probe the other CKM unitarity conditions related to $V_{cd}$.

We review the renormalization group evolution of quark and lepton masses, mixing angles and phases both in the UED extension of the Standard Model (SM) and of the Minimal Supersymmetric Standard Model (MSSM). We consider two typical scenarios: all matter fields propagating in the bulk and matter fields constrained to the brane. The resulting renormalization group evolution equations in these scenarios are compared with the existing results in the literature, together with their implications.

The flavor mixing of the quarks is described by the CKM matrix, which is parametrized by three mixing angles and one phase parameter. We discuss a new texture for the two mass matrices of the six quarks. The three flavor mixing angles can be calculated — they are functions of the ratios of the quark masses. The third mixing angle is given by the CKM matrix element $\left|V_{cb}\right|$. We find: $\left|V_{cb}\right|\simeq 2(m_s/m_b)$. The calculated mixing angles agree with the mixing angles, measured in many experiments.

It is shown that in the scheme with a rotating fermion mass matrix (i.e. one with a scale-dependent orientation in generation space) suggested earlier for explaining fermion mixing and mass hierarchy, the theta angle term in the QCD action of topological origin can be eliminated by chiral transformations, while giving still nonzero masses to all quarks. Instead, the effects of such transformations get transmitted by the rotation to the CKM matrix as the KM phase giving, for θ of order unity, a Jarlskog invariant typically of order 10^-5, as experimentally observed. Strong and weak CP violations appear then as just two facets of the same phenomenon.

The CKM matrix describing quark mixing with three generations can be parametrized by three mixing angles and one CP-violating phase. In most of the parametrizations, the CP-violating phase chosen is not a directly measurable quantity and is parametrization dependent. In this work, we propose to use experimentally measurable CP-violating quantities, α, β or γ in the unitarity triangle as the phase in the CKM matrix, and construct explicit α, β and γ parametrizations. Approximate Wolfenstein-like expressions are also suggested. Since β is most accurately measured among these three phase angles, we consider β parametrization as the best one to use.

From the mass textures’ point of view, we present a comparative study of the $S_3$ flavor symmetry in the left–right symmetry model (LRSM) and the baryon minus lepton model (BLM) taking into account their predictions on the CKM mixing matrix. To do this, we recover the already studied quark mass matrix, that comes from some published papers, and under certain strong assumptions, one can show that there are predictive scenarios in the LRSM and BLM where the modified Fritzsch and nearest neighbor interaction (NNI) textures drive, respectively, the quark mixings. As the main result, the CKM mixing matrix is in good agreement with the last experimental data in the flavored BLM model.