Semileptonic decays of charmed mesons produced in electron-positron annihilation

In this paper we study a few models for the inclusive semileptonic decays as well as a few exclusive decays of the charmed meson $D\left(1865\right)\mathrm{}$, recently discovered at SPEAR. We calculate the electron distributions for the sequence $e^{+}+e^{-}\to {\overline{D}}^{*}+D\to \overline{D}+\pi +D$ followed by $D\to e+\nu +\cdots$, at the center-of-mass energy 4.1 GeV. The results are compared with the recent findings of a DESY experiment carried out at center-of-mass energies between 4.0 and 4.2 GeV by Braunschweig et al. We conclude that $D\to e+\nu +K^{*}$ is most likely the dominant semileptonic decay mode of the $D$ meson. Furthermore, the decay structure for $D\to e+\nu +K^{*}$ favors a phenomenological ($V+A$)($V-A$) form, as is dictated by an underlying charm scheme. This may be viewed as an indirect, and another partial confirmation of the weak-interaction scheme of charm. We also present results for dilepton production, for the afore-mentioned sequence of production and decay. The lepton distributions for the sequence of $e^{+}+e^{-}\to D^{+}+D^{-}$ followed by $D\to e+\nu +K^{*}$ (or $K$), at the center-of-mass energy 3.9 GeV, is also calculated.