Study of the decay ${\mathit{D}}^{+}$→K${\mathrm{¯}}^{0\mathrm{¯}}$${\mathit{e}}^{+}$${\nu }_{\mathit{e}}$

We have studied the exclusive semileptonic decay mode ${\mathit{D}}^{+}$→K${\mathrm{¯}}^0$ ${\mathit{e}}^{+}$ ${\nu }_{\mathit{e}}$ in the Fermilab photoproduction experiment E691. We find the ratio of B(${\mathit{D}}^{+}$→K${\mathrm{¯}}^0$ ${\mathit{e}}^{+}$ ${\nu }_{\mathit{e}}$)/B(${\mathit{D}}^{+}$→${\mathit{K}}^{\mathrm{-}}$ ${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{+}$) to be 0.66±0.09±0.14, corresponding to a ${\mathit{D}}^{+}$→K${\mathrm{¯}}^0$ ${\mathit{e}}^{+}$ ${\nu }_{\mathit{e}}$ branching ratio of 6.1±0.9±1.6)%. Combining this result with our measurement of the ${\mathit{D}}^{+}$ lifetime, we find Γ(${\mathit{D}}^{+}$→K${\mathrm{¯}}^0$ ${\mathit{e}}^{+}$ ${\nu }_{\mathit{e}}$)=(5.6±0.8±1.5)×${10}^{10}$ ${\mathrm{s}}^{\mathrm{-}1}$. We also find, using E691 averages, the ratio of decay rates Γ(D→${\mathit{K}}^{\mathrm{*}}$eν)/Γ(D→Keν) to be 0.55±0.14.