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

Abstract

A precision measurement of the mass difference between the $D^0$ and $D^{\ast 0}$ 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 $\hat{I}”M\equiv M(D^{\ast 0})-M(D^0)=142.007\pm 0.015$(stat)~$\pm$~0.014(syst)~MeV, as the average for the two decays, $D^0\to K^{-}\ddot{I}{€}^{+}$ and $D^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}$. The new measurement of $\hat{I}”M$ leads to $M(D^{\ast 0})=2006.850\pm 0.049$~MeV, and the currently most precise measurement of the binding energy of the ``exotic'' meson X(3872) if interpreted as a $D^0{D}^{\ast 0}$ hadronic molecule, $E_b(\text{X}(3872))\equiv M(D^0{D}^{\ast 0})-M(\text{X}(3872))=3\pm 192$ keV.

5 pages, 3 figures, published in PRD(RC)