Branching fractions for D⁰ → K⁺K^- and D⁰ → π⁺π^-, and a search for CP violation in D⁰ decays

Using the large hadroproduced charm sample collected in experiment E791 at Fermilab, we have measured ratios of branching fractions for the two-body singly-Cabibbo-suppressed charged decays of the D⁰: Γ(D⁰ → K⁺K^-)/Γ(D⁰ → K^-π⁺) = 0.109 ± 0.003 ± 0.003, Γ(D⁰ → π⁺π^-)/Γ(D⁰ → K^-π⁺) = 0.040 ± 0.002 ± 0.003, and Γ(D⁰ → K⁺K^-)/Γ(D⁰ → π⁺π^-) = 2.75 ± 0.15 ± 0.16. We have looked for differences in the decay rates of D⁰ and D̄⁰ to the CP eigenstates K⁺K^- and π⁺π^-, and have measured the CP asymmetry parameters A_CP(K⁺K^-) = -0.010 ± 0.049 ± 0.012 and A_CP(π⁺π^-) = -0.049 ± 0.078 ± 0.030, both consistent with zero.