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In view of the projected high number of produced $B$ mesons in Belle II experiment ($\sim 10^{10}$ per year), in addition to the presently ongoing LHC-b, we calculate the rate of decay for the rare decays of $B$ mesons via a sterile on-shell neutrino $N$, which subsequently may decay leptonically or semileptonically within the detector: $B \to (D^{(*)}) \ell_1^{\pm} N$, then $N \to \ell_1^{\pm} \ell_2^{\mp} \nu$ or $N \to \ell^{\pm} \pi^\mp$.
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