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We report a search for B -> J/psi D decays, based on a sample of 124
10^6 BBbar events collected with the BABAR detector at the PEP-II
storage ring of the Stanford Linear Accelerator Center. No
significant signal is found. We obtain upper limits on the branching
fractions of 1.3 10^{-5} for B0 -> J/psi D0bar and 1.2 10^{-4} for B+ ->
J/psi D+ at 90% confidence level.
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