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The first observation of the decay of a meson to a purely baryonic final state, , is reported. The proton-proton collision data sample used was collected with the LHCb experiment at center-of-mass energies of 7 and 8 TeV and corresponds to an integrated luminosity of 3.0 fb. The branching fraction is determined to be where the first uncertainty is statistical and the second systematic. The decay mode is the rarest decay of the meson observed to date. The decay $B_s^0 \to p \bar{p}{\cal B}(B_s^0 \to p \bar{p}) < 1.5 \times 10^{-8}$ at 90% confidence level is set on the branching fraction.

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