Measurement of theD→ππ branching fractions

Using data from CLEO II at the Cornell Electron Storage Ring we provide a new measurement of the branching fraction for ${\mathit{D}}^0$→${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$, and we present the first measurements of ${\mathit{D}}^0$→${\mathrm{\pi }}^0$ ${\mathrm{\pi }}^0$ and of ${\mathit{D}}^{+}$→${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^0$, which is due to an isospin changing ΔI=3/2 transition. From these data we extract the ratio of isospin amplitudes ‖${\mathit{A}}_2$/${\mathit{A}}_0$‖, and the cosine of the relative phase δ=${\mathrm{\delta }}_2$-${\mathrm{\delta }}_0$ between these amplitudes, for D→ππ decays. Unlike the situation in kaon decay where ${\mathit{A}}_2$ is strongly suppressed, we find ‖${\mathit{A}}_2$/${\mathit{A}}_0$‖=0.72±0.13±0.11 and cosδ=0.14±0.13±0.09.