Measurement of the $B^0$ and $B^{+}$ meson masses from $B^0\to {\psi }^{{(}^{\prime })}{\mathrm{K}}_S^0$ and $B^{+}\to {\psi }^{{(}^{\prime })}{\mathrm{K}}^{+}$ decays

Using a sample of $9.6\times {10}^{6}B\overline{B}$ meson pairs collected with the CLEO detector, we have fully reconstructed 135 $B^0\to {\psi }^{{(}^{\prime })}{K}_S^0$ and 526 $B^{+}\to {\psi }^{{(}^{\prime })}{K}^{+}$ candidates with very low background. We fitted the ${\psi }^{{(}^{\prime })}K$ invariant mass distributions of these $B$ meson candidates and measured the masses of the neutral and charged $B$ mesons to be ${M(B}^0)=5279.1\mathrm{}\pm 0.7[\mathrm{stat}]\pm 0.3[\mathrm{}\mathrm{syst}]\mathrm{MeV}{/c}^2$ and ${M(B}^{+})=5279.1\mathrm{}\pm 0.4[\mathrm{stat}]\pm 0.4[\mathrm{}\mathrm{syst}]\mathrm{MeV}{/c}^2.$ The precision is a significant improvement over previous measurements.