SU(3) trace identities and the calculation of effective couplings in a baryon-loop model of weak radiative kaon decays

A simple algorithm for the recursive reduction of the trace of a product of any number of the f and d matrices of SU (3) is given. SU (3) trace identities (through fourth order) are used to construct effective interaction Lagrangians in the baryon-loop model for PVV, PVγ, and weak (strangeness-changing) PVγ couplings. At the same time it is shown that the effects of baryon-mass breaking on the PVV coupling are negligible in the loop model. The usefulness of this formal compaction is further illustrated in the calculation of the contributions of all vector-meson poles to K₂⁰→π⁺π^-γ decay. It is found that the previous neglect of the contribution of K* poles in this case is justified.