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We report the results of the first search for Standard Model and baryon-number-violating two-body decays of the neutral B mesons to ^0 and ^ (*) 0c using 711~ fb^{-1} of data collected at the (4S) resonance with the Belle detector at the KEKB asymmetric-energy e^+ e^- collider. We observe no evidence of signal from any such decays and set 95\% confidence-level upper limits on the products of B⁰ and B⁰ branching fractions for these two-body decays with B (₂^0 ^+ ^-) in the range between 9. 5~ 10^-8 and 31. 2~ 10^-8.
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