The results of a search for the rare twobody charmless baryonic decays $B^0 \to p \bar{p}$ and $B_s^0 \to p \bar{p}$ are reported. The analysis uses a data sample, corresponding to an integrated luminosity of 0.9 fb$^{1}$, of $pp$ collision data collected by the LHCb experiment at a centreofmass energy of 7 TeV. An excess of $B^0 \to p \bar{p}$ candidates with respect to background expectations is seen with a statistical significance of 3.3 standard deviations. This is the first evidence for a twobody charmless baryonic $B^0$ decay. No significant $B_s^0 \to p \bar{p}$ signal is observed, leading to an improvement of three orders of magnitude over previous bounds. If the excess events are interpreted as signal, the 68.3 confidence level intervals on the branching fractions are {eqnarray} \cal{B}(B^0 \to p \bar{p}) & = & (1.47 ^{+0.62}_{0.51} ^{+0.35}_{0.14}) \times 10^{8} , *{0.3cm} \cal{B}(B_s^0 \to p \bar{p}) & = & (2.84 ^{+2.03}_{1.68} ^{+0.85}_{0.18}) \times 10^{8} , {eqnarray} where the first uncertainty is statistical and the second is systematic.
Invariant mass distribution of $ K ^+ \pi ^ $ candidates after full selection. The fit result (blue, solid) is superposed together with each fit model component as described in the legend. The normalised fit residual distribution is shown at the bottom. 
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Invariant mass distribution of $ p \overline p $ candidates after full selection. The fit result (blue, solid) is superposed with each fit model component: the $ B ^0 \rightarrow p \overline p $ signal (red, dashed), the $ B ^0_ s \rightarrow p \overline p $ signal (grey, dotted) and the combinatorial background (green, dotdashed). 
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Negative logarithm of the profile likelihoods as a function of (left) the $ B ^0 \rightarrow p \overline p $ signal yield and (right) the $ B ^0_ s \rightarrow p \overline p $ signal yield. The orange solid curves correspond to the statisticalonly profiles whereas the blue dashed curves include systematic uncertainties. 
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Animated gif made out of all figures. 
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Relative systematic uncertainties contributing to the $ B ^0 _{(s)} \rightarrow p \overline p $ branching fractions. The total corresponds to the sum of all contributions added in quadrature. 
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Created on 11 July 2020.