$D^0-D^0$ mass difference from a dispersion relation

We study the standard model prediction for the mass difference between the two neutral D meson mass eigenstates, $\Delta m.\mathrm{}$ We derive a dispersion relation based on heavy quark effective theory that relates $\Delta m$ to an integral of the width difference of heavy mesons, $\Delta \Gamma ,$ over varying values of the heavy meson mass. Modeling the $m_D$ dependence of certain D decay partial widths, we investigate the effects of SU(3) breaking from phase space on the mass difference. We find that $\Delta m$ may be comparable in magnitude to $\Delta \Gamma$ in the standard model.