Inclusive Semielectronic Decays of the $D_s^+$ Meson

We present an analysis of the semielectronic decays of the $\Ds$ meson. We analyze data collected by the BESIII experiment from $e^+e^-$ collisions provided by the BEPCII collider with center-of-mass energies between $4.18\text{ GeV}$ and $4.23\text{ GeV}$. We employ a double-tag technique with the $D_s^-\to K^-K^+\pi^-$ tag mode, which yields $ 262660. \pm 1137$ signal $D_s^+$ for analysis. The inclusive electronic momentum spectrum in the lab frame is recovered with the use of matrix unfolding procedures for electrons with measured momentum greater than $200 \text{ MeV}/c$. By extrapolating the measured spectrum below $200 \text{ MeV}/c$, we determine the inclusive semielectronic branching fraction to be $\semilepBF=\left(6.34\pm0.13\pm 0.10\right)\%$. We determine the branching fraction of unobserved exclusive $\Ds$ semielectronic modes to be $\left(0.05\pm 0.24\right)\%$ and the ratio of $\Ds$ and $D^0$ semielectronic widths to be $\frac{\Gamma(D_{s}^{+}\rightarrow Xe^+\nu_e)}{\Gamma(D^0\rightarrow Xe^+\nu_e)}=0.793\pm 0.026$ by employing other known results. An input/output check with a Monte Carlo sample five times larger than data is also presented as a demonstration of the validity of our analysis method. Our results are consistent with and more precise than the previous measurement by the CLEO-$c$ collaboration, $\semilepBF=\left(6.52\pm0.39\pm 0.15\right)\%$.