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Measurement of absolute branching fractions of inclusive semileptonic decays of charm and charmed-strange mesons

We have measured the inclusive semileptonic branching fractions of $D^0$, $D^+$, and $D^+_s$ mesons. For these measurements, we have used the full CLEO-c open-charm data samples, 818 pb$^{-1}$ at $E_\text{CM} = 3.774$ GeV, giving $D^0 \bar{D}^0$ and $D^+ D^-$ events, and 602 pb$^{-1}$ at $E_\text{CM} = 4.170$ GeV, giving $D^{\ast \pm}_s D^\mp_s$ events. We obtain $\mathcal{B}(D^0 \to X e^+ ν_e) = (6.46 \pm 0.09 \pm 0.11)$%, $\mathcal{B}(D^+ \to X e^+ ν_e) = (16.13 \pm 0.10 \pm 0.29)$%, and $\mathcal{B}(D^+_s \to X e^+ ν_e) = (6.52 \pm 0.39 \pm 0.15)$%, where the first uncertainties are statistical and the second are systematic. From these and lifetimes obtained elsewhere, we obtain the ratios of semileptonic decay widths $Γ(D^+ \to X e^+ ν_e) / Γ(D^0 \to X e^+ ν_e) = 0.985 \pm 0.015 \pm 0.024$ and $Γ(D^+_s \to X e^+ ν_e) / Γ(D^0 \to X e^+ ν_e) = 0.828 \pm 0.051 \pm 0.025$. The ratio of $D^+$ and $D^0$ is consistent with the isospin symmetry prediction of unity, and the ratio of $D^+_s$ and $D^0$ differs from unity, as expected.