| Abstract |
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We report on a search for the flavor-changing neutral current
decays $D^0\to e^+e^-$ and $D^0\to\mu^+\mu^-$,
and the lepton-flavor violating
decay $D^0\to e^\pm\mu^\mp$. The measurement is based on
$122\,\mbox{fb}^{-1}$ of data collected by the BaBar detector
at the PEP-II asymmetric $e^+e^-$ collider. No evidence is
found for any of the decays. The upper limits on the branching
fractions, at the 90\,\% confidence level, are
$1.2\times 10^{-6}$ for
$D^0\to e^+e^-$, $1.3\times 10^{-6}$ for $D^0\to\mu^+\mu^-$,
and $8.1\times 10^{-7}$ for $D^0\to e^\pm\mu^\mp$.
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