Even-wave harmonic-oscillator theory of baryonic states. III. Decay analysis of baryon resonances

A new classification of 70 states, i.e., ($l,u$) for $L^P=1^{-}$ and ($l,m,u$) for $L^P=2^{+}$, as well as a relativistic formulation of orbital matrix elements for their decays, derived in two earlier papers (I and II of the series), are employed in this paper to make an extensive analysis of various pseudoscalar decay modes in the language of "direct" versus "recoil" quark couplings. A 56-70 betet mixing angle ($cot\theta =-\sqrt{2}$), which was needed in II to produce several important low-energy fits, is also found to play a crucial role in the present analysis which makes a priori quantum assignments for the various states on the basis of their mass positions. By making one exception to the rule of SU(6) unsplit states in this theory, i.e., an upward mass shift of $l\left(8_q\right)$ states so as to overlap with their $u$ counterparts, it is not only possible to understand the earlier successes of this model on the anomaly implicit in $p\gamma$ and $n\gamma$ photoproduction of $D_{15}$ but also to account for a few other similar anomalies [especially the $\mathrm{NK}$ versus $\Sigma \pi$ modes of $D_{05}\mathrm{}\left(1830\right)\mathrm{}$], none of which are amenable to the usual harmonic-oscillator-type description without elaborate mixing assumptions. On the other hand, most other $u$-type states which cause the bulk of the proliferation of the low-lying states in this theory -do not pose a serious problem of immediate detection in view of their generally low partial widths compared to their $l$-type counterparts.