Decays of $B^0$ and $B_{s}^0$ mesons to the charmless baryonic final states $p \overline{p} h^+ h^{\prime}$, where $h$ and $h^\prime$ each denote a kaon or a pion, are searched for using the LHCb detector. The analysis is based on a sample of protonproton collision data collected at centerofmass energies of $7$ and $8 $TeV, corresponding to an integrated luminosity of $3 $fb$^{1}$. Fourbody charmless baryonic $B_{s}^0$ decays are observed for the first time. The decays $B^0_{s}\to p \overline{p} K^+ K^$, $B^0_{s}\to p \overline{p} K^\pm \pi^\mp$, $B^0\to p \overline{p} K^\pm \pi^\mp$ and $B^0\to p \overline{p} \pi^+\pi^$ are observed with a significance greater than $5$ standard deviations; evidence at $4.1$ standard deviations is found for the $B^0\to p \overline{p} K^+ K^$ decay and an upper limit is set on the branching fraction for $B^0_{s}\to p \overline{p} \pi^+ \pi^$. Branching fractions in the kinematic region $m(p \overline{p})<2850 $MeV$/c^2$ are measured relative to the $B^0 \to J/\psi (\to p \overline{p}) K^*(892)^0$ channel.
Invariant mass distributions for $ B ^0_{{\scriptscriptstyle (} s {\scriptscriptstyle )}} $ candidates in the (top left) $ p \overline p K K $, (top right) $ p \overline p K \pi $, (bottom left) $ p \overline p \pi \pi $ final state and (bottom right) invariant mass distribution of $ B ^0 \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^*(892)^0$ in the $ p \overline p K \pi $ final state. The results of the fits are shown with blue solid lines. In the first three figures signals for $ B ^0 $ and $ B ^0_ s $ decays are shown, respectively, with green dotted and red dotdashed lines, combinatorial backgrounds are shown with black dashed lines and crossfeed backgrounds are shown with violet dotdashed lines. In the bottom right figure the normalization signal is shown with a green dotted line, the $ K \pi $ Swave component is displayed with a red dotdashed line and the combinatorial background with a black dashed line. 
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Efficiencycorrected and backgroundsubtracted (left) $m( h h^{\prime} )$ and (right) $m( p \overline p )$ distributions from (top) $ B ^0 \rightarrow p \overline p K \pi $, (middle) $ B ^0_ s \rightarrow p \overline p K K $, and (bottom) $ B ^0 \rightarrow p \overline p \pi \pi $ candidates. Events with entries in the charmonium or $D^0$ mass regions have been removed from the samples. All distributions are normalized to unity. 
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Animated gif made out of all figures. 
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Fitted yields, signal yield significances and branching fractions computed using Eq. (1). The uncertainties on the yields are statistical only. The first uncertainty on each branching fraction is statistical, the second systematic, the third comes from the uncertainty on the branching fraction of the normalization mode and the fourth, where present, is due to the uncertainty on $f_d/f_s$. 
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Ratios of branching fractions among different $ B ^0_{{\scriptscriptstyle (} s {\scriptscriptstyle )}} \rightarrow p \overline p h h^{\prime} $ modes. The first uncertainty is statistical, the second systematic and the third, where present, comes from the uncertainty on $f_d/f_s$. 
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Supplementary material full pdf 
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This ZIP file contains supplemetary material for the publication LHCbPAPER2017005. The files are: Supplementary.pdf : An overview of the extra figures and tables Sup*.pdf, Sup*.png, Sup*.eps, Sup*.C : The figures in various formats TabSup*.pdf, TabSup*.tex : The tables in various formats 
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Created on 21 October 2019.