BrokenU(3)Symmetry and Semileptonic Weak Interactions

A phenomenological field-theoretic model of $U\left(3\right)\mathrm{}$-symmetry breakdown is proposed. It allows a unified treatment of both mass renormalization and field renormalization of the phenomenological fields associated with particles. Specifically, we have calculated the renormalization effects on the semileptonic weak coupling constants. Based on our model, it is shown that the empirically observed damping factor for $\left|\Delta Y\right|=1\mathrm{}$ transitions cannot be explained by symmetry-breaking effects and therefore the Cabibbo angle is intrinsic to weak-interaction theory. From our calculation, we expect a 20% renormalization effect on all $\left|\Delta Y\right|=1\mathrm{}$ axial-vector coupling constants for baryon leptonic decays. This renormalization effect is supported by the present experimental information about the $\frac{G_A}{G_V}$ ratio of lambda beta decay. To make a sharp test of our model, more accurate experimental data concerning the $\frac{G_A}{G_V}$ ratios of the baryon leptonic decays are required. Our model also reproduces the Ademollo-Gatto theorem on the nonrenormalization of the $\left|\Delta Y\right|=1\mathrm{}$ vector transitions and Okubo's speculated mass formulas for vector mesons.