Partially Conserved Axial-Vector Current, Charge Commutators, Off-Mass-Shell Correction, and the Broken SU(3) Symmetry
We point out that the extension of the PCAC (partially conserved axial-vector current) relation ∂μAμπ=Cπφπ to ∂μAμK=CKφK and the use of charge commutators typified by AK=[VK,Aπ] are useful in the study of broken SU(3) symmetry. The use of the ∂μAμK=CKφK condition usually confronts us with a considerable off-mass-shell extrapolation mK-->0. However, by using the above charge commutators and the approximation we propose, the off-mass-shell extrapolation mK-->0 may be replaced by a more comfortable one, mπ-->0, effectively to first order in the symmetry-breaking interaction. This approach is applied to the study of the SU(3) symmetry breaking. Encouraging results have been obtained in the case of V-->P+P (i.e., K*-->K+π and ρ-->π+π) decays and in the direct determination of the f-f' mixing angle from their decay widths. We also make some estimate of the off-shell extrapolation mK-->0 compared with the case mπ-->0. Another useful application of the above charge commutators is for the weak leptonic decays. We can derive a set of sum rules for the axial-vector coupling constants of the leptonic decays of hyperons which seem to give new insight into the Cabibbo theory of leptonic interactions.