Direct measurements of the cross sections for e+e−→hadrons|non-DD¯ in the range from 3.65 to 3.87 GeV and the branching fraction for ψ(3770)→non-DD¯

By tagging the largest energy of the assumed kaon in the final states of e+e−→hadrons, we measured the cross sections for e+e−→hadrons|non-DD¯ in the range from 3.65 to 3.87 GeV. Analyzing these cross sections yields the branching fraction for the decay ψ(3770)→non-DD¯ to be BF[ψ(3770)→non-DD¯]=(15.1±5.6±1.8)%, and the observed non-DD¯ and DD¯ cross sections to be σhad-non-DD¯obs=(1.08±0.40±0.15) nb and σDD¯obs=(6.07±0.40±0.35) nb, respectively, at the center-of-mass energy Ecm=3.7724 GeV.