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Using $230\times 10^6$ $B\bar{B}$ events recorded with the {BABAR} detector at
the $e^+e^-$ storage rings {PEP-II}, we reconstruct approximately 4100
$B^0\rightarrow J/\psi K^+\pi^-$ and 9930 $B^+\rightarrow J/\psi K^+$ decays
with $J/\psi\rightarrow\mu^+\mu^-$ and $e^+e^-$. From the measured $B$-momentum
distributions in the $e^+e^-$ rest frame, we determine the mass difference
$m(B^0)-m(B^+)=(+0.33\pm 0.05\pm 0.03)\,\mathrm{MeV}\!/c^2$.
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