Invariant properties of weak interactions and the Cabibbo angle in chiral dynamics

A. A. Khelashvili


Abstract: It is shown that if the Cabibbo angle is introduced by an axial (and not vector) rotation about the seventh axis in $SU_3$-space, and it is assumed that the pion is massless before the rotation, the well-known contradiction between the allowed regions of values of the parameters of the broken $SU_3\otimes SU_3$ chiral symmetry can be eliminated. Different models are discussed and an investigation made of the Hamiltonian of the $SU_3\otimes SU_3$ chiral symmetry breaking before the Cabibbo rotation. The results are generalized to $SU_4\otimes SU_4$. The invariance properties of the weak interactions under permutation of the quark isodoublets in the Glashow–Iliopoulos–Maiani model are used. Corresponding unitary transformations are constructed and a theorem proved about the structure of the Hamiltonian of the $SU_4\otimes SU_4$ chiral symmetry breaking.

Received: 29.09.1977

 English version: Theoretical and Mathematical Physics, 1978, 36:3, 765–772

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