This is an extension of the study in an earlier paper on meson-decuplet scattering to two sets of coupled reactions: (1) $P{B}_{10}\to P{B}_{10}$, $P{B}_{10}\to P{B}_8$, $P{B}_8\to P{B}_8$ and (2) $\mathrm{PV}\to \mathrm{PV}$, $\mathrm{PV}\to \mathrm{PP}$, $\mathrm{PP}\to \mathrm{PP}$. $P$ and $V$ refer to the pseudoscalar-meson octet and vector-meson nonet, respectively, while $B_8$ and $B_{10}$ correspond to the octet of $J^P={\frac{1}{2}}^{+}$ baryons and decuplet $J^P={\frac{3}{2}}^{+}$ baryons, respectively. Some consequences of local duality are examined and compared with experiment in limited energy regions for the above reactions. The assumption that the imaginary parts of the direct-channel helicity amplitudes vanish in the forward (backward) scattering if the crossed $t$ channel ($u$ channel) is exotic leads to systems of equations relating resonance contributions in the direct channel. The solutions predict certain patterns of particles degenerate in mass but with different $\mathrm{SU}$ (3), spin, and parity assignments. In particular, the inclusion of spin considerations yields the result that the particles on leading trajectories must be accompanied by daughters with prescribed ratios of coupling constants between the parent and daughter states. We discuss the link between our results and those which follow from a complementary description in terms of Regge residues.

Close

PrevNext

View figure in article