Geodesic
Invariant properties of weak interactions and the Cabibbo angle in chiral dynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 3, pp. 324-334 
A. A. Khelashvili. Invariant properties of weak interactions and the Cabibbo angle in chiral dynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 3, pp. 324-334. http://geodesic.mathdoc.fr/item/TMF_1978_36_3_a3/
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     author = {A. A. Khelashvili},
     title = {Invariant properties of weak interactions and the {Cabibbo} angle in chiral dynamics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {324--334},
     year = {1978},
     volume = {36},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_36_3_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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