Two-body $D_s^{+}$ decays to $\eta {\pi }^{+}$, ${\eta }^{\prime }{\pi }^{+}$, $\eta {\rho }^{+}$, ${\eta }^{\prime }{\rho }^{+}$, and $\phi {\rho }^{+}$

We have made measurements of several $D_s$ branching ratios, relative to the $\phi {\pi }^{+}$ mode. We have observed two previously unseen two-body hadronic decays of the $D_s^{}{}_{}{}^{+}$, namely $\eta {\rho }^{+}$ and ${\eta }^{\prime }{\rho }^{+}$, and measured relative branching ratios of 2.86±$0.38_{}^{+0.36\mathrm{}}{}_{-0.38\mathrm{}}{}^{}$ and 3.44±$0.62_{}^{+0.44\mathrm{}}{}_{-0.46\mathrm{}}{}^{}$, respectively. We have determined the relative branching ratio for the decay into $\phi {\rho }^{+}$ to be 1.86±$0.26_{}^{+0.29\mathrm{}}{}_{-0.40\mathrm{}}{}^{}$. In addition, we have measured relative branching ratios for the $\eta {\pi }^{+}$ and ${\eta }^{\prime }{\pi }^{+}$ states, for which there had previously been conflicting measurements; our results are 0.54±0.09±0.06 and 1.20±0.15±0.11, respectively. Combining these new measurements with previous results and using (3.7±1.2)% for the value of $\mathcal{B}(D_s\to \phi {\pi }^{+})$, we can account for ≅(79±26)% of all $D_s^{}{}_{}{}^{+}$ decays. In addition we have also measured relative branching ratios or set upper limits on $D^{+}$ decays to all of the above-mentioned final states.