Measurement of the decays $D^0\to {\pi }^{-}{\pi }^{+}$ and $D^0\to K^{-}{K}^{+}$

Using data from Fermilab photoproduction experiment E691, we measure the ratio of branching fractions between the Cabibbo-suppressed modes $\frac{B(D^0\to K^{-}{K}^{+})}{B(D^0\to {\pi }^{-}{\pi }^{+})}$ to be 1.95±0.34±0.22. We also report branching fractions for the modes $D^0\to K^{-}{K}^{+}$ and $D^0\to {\pi }^{-}{\pi }^{+}$ relative to the Cabibbo-allowed decay $D^0\to K^{-}{\pi }^{+}$. Furthermore, we place an upper limit of 0.45 at the 90% C.L. on the $\mathrm{CP}$-violating asymmetry in $D^0\to K^{-}{K}^{+}$ vs ${\overline{D}}^0\to K^{-}{K}^{+}$ decays.