  A search for the rare hadronic decay $B_s^0\to p \bar{p}$ is performed using
proton-proton collision data recorded by the LHCb experiment at a
center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6
fb$^{-1}$. No evidence of the decay is found and an upper limit on its
branching fraction is set at ${\cal B}(B_s^0\to p \bar{p}) < 4.4~(5.1) \times
10^{-9}$ at 90% (95%) confidence level; this is currently the world's best
upper limit. The decay mode $B^0\to p \bar{p}$ is measured with very large
significance, confirming the first observation by the LHCb experiment in 2017.
The branching fraction is determined to be ${\cal B}(B^0\to p \bar{p}) = \rm
(1.27 \pm 0.15 \pm 0.05 \pm 0.04) \times 10^{-8}$, where the first uncertainty
is statistical, the second is systematic and the third is due to the external
branching fraction of the normalization channel $B^0\to K^+\pi^-$. The
combination of the two LHCb measurements of the $B^0\to p \bar{p}$ branching
fraction yields ${\cal B}(B^0\to p \bar{p}) = \rm (1.27 \pm 0.13 \pm 0.05 \pm
0.03) \times 10^{-8}$.
