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\mathrm{.}Weobtain$$\mathcal{B}$(D^0 \to X e^+ \nu_e) = (6.46 \pm 0.09 \pm 0.11)$$$\mathcal{B}$(D^+ \to X e^+ \nu_e) = (16.13 \pm 0.10 \pm 0.29)$$$\mathcal{B}$(D^+_s \to X e^+ \nu_e) = (6.52 \pm 0.39 \pm 0.15)$%, 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 $\Gamma (D^+ \to X e^+ \nu_e) / \Gamma (D^0 \to X e^+ \nu_e) = 0.985 \pm 0.015 \pm 0.024$and$\Gamma (D^+_s \to X e^+ \nu_e) / \Gamma (D^0 \to X e^+ \nu_e) = 0.828 \pm 0.051 \pm 0.025$. 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.