Group theoretical structure of the charmed weak current and the chiralSU 4×SU 4 symmetry breaking Hamiltonian

Quarks Mixing in Chiral Symmetries

“…Its value, calculated by Oakes, does not contradict the experimental data. Before the charmed particles were discovered Glashow, Iliopoulos and Maiani [11] have suggested the generalization of a strong interaction symmetry to SU 4 [6]. The charged weak current is then given as follows…”

“…The hierarchy of chiral symmetry breaking [1][2][3] has been investigated since seventies of the previous century [4][5][6][7][8]. The symmetry breaking and mixing of quarks are connected with the rotation of quark currents and Hamiltonian densities.…”

“…The problem of determining the Cabibbo angle in SU 4 * SU 4 symmetry has arisen. It is considered in [5][6] and the method of calculating the Cabibbo angle in SU 4 * SU 4 symmetry is described in [7]. It is known that the formula describing the rotation angle is not changed if the symmetry is extended.…”

“…The problem of chiral SU 4 * SU 4 symmetry breaking in the limit of exact SU 2 * SU 2 symmetry is considered in [6]. Symmetry breaking is connected with the transformation of rotation around the tenth axis in SU 4 space.…”

“…All the cases of symmetry breaking considered in [4][5][6][7][8] can be described by formula (24). Let us give simple examples: a) for k = 2, n = 3 a is the original Cabibbo angle Θ associated with rotation around the seventh axis in SU 3 subspace [4][5][6][7].…”