Precision Measurement of the Mass of the $D^{*0}$ Meson and the Binding Energy of the $X(3872)$ Meson as a $D^0overline{D^{*0}}$ Molecule

A precision measurement of the mass difference between the $D^0$ and $D^{*0}$ mesons has been made using 316~pb$^{-1}$ of $e^{+}e^{-}$ annihilation data taken at $sqrt{s}=4170$~MeV using the CLEO-c detector. We obtain $Delta M equiv M(D^{*0})-M(D^0) =142.007pm0.015$(stat)~$pm$~0.014(syst)~MeV, as the average for the two decays, $D^0to K^-pi^+$ and $D^0to K^-pi^+pi^-pi^+$. The new measurement of $Delta M$ leads to $M(D^{*0})=2006.850pm0.049$~MeV, and the currently most precise measurement of the binding energy of the ``exotic meson X(3872) if interpreted as a $D^0D^{*0}$ hadronic molecule, $E_{b}(text{X}(3872))equiv M(D^0D^{*0})-M(text{X}(3872))=3pm192$ keV.