Production and Decay of the $\phi \mathrm{}\left(1680\right)\mathrm{}$ in ${\pi }^{+}d\to \mathrm{pp}{\pi }^{+}{\pi }^{-}{\pi }^0$ at 6.95 $\frac{\mathrm{GeV}}{c}$

An analysis of the 1.68-GeV mass region of the $m\left({\pi }^{+}{\pi }^{-}{\pi }^0\right)$ spectrum in our ${\pi }^{+}d\to {\pi }^{+}{\pi }^{-}{\pi }^0$ data confirms the existence of an $I^G=0^{-}$ enhancement at this mass, the $\phi \mathrm{}\left(1680\right)\mathrm{}$, which is distinct from the $I=1\mathrm{}{A}_3$ meson. This resonance was found to decay preferentially into $\rho \pi$ with a $\frac{3\pi }{(3\mathrm{}\pi +\rho \pi )}$ branching ratio of <30%. A spin-parity analysis of the $\phi \mathrm{}\left(1680\right)\mathrm{}$ favors $J^P=1^{-},2^{+},3^{-}$ for spins ≤3, although $J^P=1^{+},2^{-}$ cannot be rigorously excluded. The mass and favored natural spin-parity of the $\phi \mathrm{}\left(1680\right)\mathrm{}$ suggest that it may be the Regge recurrence of the ${\omega }^0$ meson. Assuming a natural-spin-parity assignment, the decay angular distributions of the $\phi \mathrm{}\left(1680\right)\mathrm{}$ suggest that there exists a contribution from unnatural-parity exchange in the production mechanism. The $t$ dependence of the differential cross section and the energy dependence of the total cross section for ${\pi }^{+}n\to \phi \mathrm{}\left(1680\right)p$ were found to be similar to those of ${\pi }^{+}n\to ({\omega }^0,A_2^0)p$ also seen in the data. As with these latter processes, the energy dependence of the cross section for ${\pi }^{+}n\to \phi \mathrm{}\left(1680\right)p$ cannot be explained by simple $\rho$ Regge exchange. The $I=1\mathrm{}$ $f^0{\pi }^0$ cross section in the $A_3^0$ mass region was found to be small, and suggests that the production cross section of the $A^3$ meson by charge exchange is significantly less than that observed in non-charge-exchange reactions such as ${\pi }^{-}p\to A_3^{-}p$.