Duality and theπ−ηDegeneracy

In the context of duality and the absence of exotic resonances, we discuss the question of the $\pi -\eta$ degeneracy. This is crucial for an understanding of the internal symmetry incorporated in the meson spectrum. We examine the situation where the $\pi$ is exchange degenerate with $A_1$ and not $B$, which is in accord with experiment. The $\eta$ should not then be degenerate with the $\pi$. Nevertheless, an inconsistency is demonstrable when factorization constraints are applied to the leading trajectory couplings in $\mathrm{PV}\to \mathrm{PV}$ meson reactions. This follows from an assumption of $\mathrm{SU}\left(2\right)\mathrm{}$ only, not $\mathrm{SU}\left(3\right)\mathrm{}$. The inconsistency is removed by assuming degenerate doubling of the particles on the $A_1$ and $D$ trajectories.