Study of $\psi(3770) \to non-D\bar{D}$ at BESIII

We describe a measurement of the branching ratio for $\psi(3770)\to non-D\bar{D}$ final states using 2.92~fb$^{-1}$ of $e^+e^-$ annihilation data collected with the BESIII detector at the BEPCII collider at $E_{CM}=3.773$~GeV. The naive expectation is that $\psi(3770)$ decays are dominated by $D\bar{D}$ final states. Published data paint an inconsistent picture, however, with reported non-$D\bar{D}$ rates ranging from consistent with zero to $\sim15\%$. We determine the yield for $\psi(3770) \to non-D\bar{D}$ in our sample by measuring the total number of hadronic events and subtracting the contributions from all expected processes. The $D\bar{D}$ component is directly measured in data with a double-$D$-tag counting technique. Continuum $q\bar{q}$ and most QED are determined with data collected at five energy points below $D\bar{D}$ threshold. Other processes, including initial-state radiation to $J/\psi$ and $\psi(3686)$, $\tau^+\tau^-$ and two-photon production, are estimated by Monte Carlo. Preliminary results for event yields and cross sections will be presented and interpreted.