Measurements of the cross sections for $e^+e^- \to {\rm hadrons}$ at 3.650, 3.6648, 3.773 GeV and the branching fraction for $\psi(3770)\to {\rm non-}D\bar D$

Using the BES-II detector at the BEPC Collider, we measured the lowest order cross sections and the $R$ values ($R=\sigma^0_{e^+e^- \to {\rm hadrons}}/\sigma^0_{e^+e^- \to \mu^+\mu^-}$) for inclusive hadronic event production at the center-of-mass energies of 3.650 GeV, 3.6648 GeV and 3.773 GeV. The results lead to $\bar R_{uds}=2.224\pm 0.019\pm 0.089$ which is the average of these measured at 3.650 GeV and 3.6648 GeV, and $R=3.793\pm 0.037 \pm 0.190$ at $\sqrt{s}=3.773$ GeV. We determined the lowest order cross section for $\psi(3770)$ production to be $\sigma^{\rm B}_{\psi(3770)} = (9.575\pm 0.256 \pm 0.813)~{\rm nb}$ at 3.773 GeV, the branching fractions for $\psi(3770)$ decays to be $BF(\psi(3770) \to D^0\bar D^0)=(48.9 \pm 1.2 \pm 3.8)%$, $BF(\psi(3770) \to D^+ D^-)=(35.0 \pm 1.1 \pm 3.3)%$ and $BF(\psi(3770) \to D\bar{D})=(83.9 \pm 1.6 \pm 5.7)%$, which result in the total non-$D\bar D$ branching fraction of $\psi(3770)$ decay to be $BF(\psi(3770) \to {\rm non}-D\bar D)=(16.1 \pm 1.6 \pm 5.7)%$.