Partially Conserved AxialVector Current, Charge Commutators, OffMassShell Correction, and the Broken SU(3) Symmetry
Abstract
We point out that the extension of the PCAC (partially conserved axialvector current) relation ∂_{μ}A_{μ}^{π}=C_{π}φ^{π} to ∂_{μ}A_{μ}^{K}=C_{K}φ^{K} and the use of charge commutators typified by A_{K}=[V_{K},A_{π}] are useful in the study of broken SU(3) symmetry. The use of the ∂_{μ}A_{μ}^{K}=C_{K}φ^{K} condition usually confronts us with a considerable offmassshell extrapolation m_{K}>0. However, by using the above charge commutators and the approximation we propose, the offmassshell extrapolation m_{K}>0 may be replaced by a more comfortable one, m_{π}>0, effectively to first order in the symmetrybreaking 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 ff' mixing angle from their decay widths. We also make some estimate of the offshell extrapolation m_{K}>0 compared with the case m_{π}>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 axialvector coupling constants of the leptonic decays of hyperons which seem to give new insight into the Cabibbo theory of leptonic interactions.
 Publication:

Physical Review
 Pub Date:
 June 1967
 DOI:
 10.1103/PhysRev.158.1594
 Bibcode:
 1967PhRv..158.1594M