Precision measurement of $D$ meson mass differences

Using three- and four-body decays of $D$ mesons produced in semileptonic $b$-hadron decays, precision measurements of $D$ meson mass differences are made together with a measurement of the $D^{0}$ mass. The measurements are based on a dataset corresponding to an integrated luminosity of 1.0 fb$^{-1}$ collected in $pp$ collisions at 7~TeV. Using the decay $D^0 \rightarrow K^{+} K^{-} K^{-} \pi^{+}$, the $D^0$ mass is measured to be \begin{alignat*}{3} M(D^0) \phantom{ghd} &=&~1864.75 \pm 0.15 \,({\rm stat}) \pm 0.11 \,({\rm syst}) \, \textrm{MeV}/c^2. \end{alignat*} The mass differences \begin{alignat*}{3} M(D^{+}) - M(D^{0}) &=& 4.76 \pm 0.12 \,({\rm stat}) \pm 0.07 \,({\rm syst}) \, \textrm{MeV}/c^2, \\ M(D^{+}_s) - M(D^{+}) &=& \phantom{00}98.68 \pm 0.03 \,({\rm stat}) \pm 0.04 \,({\rm syst}) \, \textrm{MeV}/c^2 \end{alignat*} are measured using the $D^0 \rightarrow K^{+} K^{-} \pi^{+} \pi^{-}$ and $D^{+}_{(s)} \rightarrow K^{+}K^{-} \pi^{+}$ modes.