Test of the fourth quark generation from the Cabibbo–Kobayashi–Maskawa matrix

The structure of the mixing matrix in the electroweak quark sector with four generations of quarks is investigated. We conclude that the area of the unitarity quadrangle is not a good choice as a possible measure of the CP violation. In search of new physics, we analyze how the existence of the fourth quark family may influence on the values of the Cabibbo–Kobayashi–Maskawa matrix and we show that one can test for the existence of the fourth generation using the Jarlskog invariants of the known quarks only. The analysis based on the measured unitary triangle exhibits some tension with the assumption of three quark generations. The measurement of the unitarity triangle obtained from the scalar product of the second row/column of the CKM matrix by the complex conjugate of third row/column can provide information about the existence of the fourth generation of quarks.

Unitarity of neutrino mixing matrix

Neutrinos are neutral leptons and there exist three types of neutrinos (electron neutrinos νe, muon neutrinos νµ and tau neutrinos ντ). These classifications are referred to as neutrinos’s “flavors”. Oscillations between the different flavors are known as neutrino oscillations, which occurs when neutrinos have mass and non-zero mixing. Neutrino mixing is governed by the PMNS mixing matrix. The PMNS mixing matrix is constructed as the product of three independent rotations. With that, we can describe the numerical parameters of the matrix in a graphical form called the unitary triangle, giving rise to CP violation. We can calculate the four parameters of the mixing matrix to draw the unitary triangle. The area of the triangle is a measure of the amount of CP violation.

TREE FCNC AND NON-UNITARITY OF CKM MATRIX

We discuss possible signatures of the tree level FCNC, which results from the non-unitarity of CKM matrix. We first define the unitarity step-by-step, and possible test of the non-unitarity through the 4-value-KM parametrization. We, then, show how the phase angle of the unitary triangle would change in case of the vector-like down quark model. As another example of tree FCNC, we investigate the leptophobic Z′ model and its application to the recent Bs mixing measurements.

ANGULAR DISTRIBUTION ANALYSIS OF B → J/ψ K* AND RESOLVING DISCRETE AMBIGUITIES IN THE DETERMINATION OF ϕ1

We discuss the angular distribution analysis of B → J/ψ K* decays and a way to resolve discrete ambiguites in the determination of the unitary triangle ϕ1(=β). We study the status of factorization hypothesis in the color-suppressed B meson decays: B → J/ψ K(*) within the general factorization approach and QCD-factorization method.