A search for $CP$ violation in charmless fourbody decays of $\Lambda_b$ and $\Xi_b^0$ baryons with a proton and three charged mesons in the final state is performed. To cancel out production and detection chargeasymmetry effects, the search is carried out by measuring the difference between the $CP$ asymmetries in a charmless decay and in a decay with an intermediate charmed baryon with the same particles in the final state. The data sample used was recorded in 2011 and 2012 with the LHCb detector and corresponds to an integrated luminosity of $3 {\rm fb}^{1}$. A total of 18 $CP$ asymmetries are considered, either accounting for the full phase space of the decays or exploring specific regions of the decay kinematics. No significant $CP$violation effect is observed in any of the measurements.
Distributions of invariant masses of pairs of finalstate particles for the candidates selected in the mass window of $\pm 3\sigma$ around the measured $\Lambda ^0_ b $ mass. Figures (a), (b) and (c) show the twobody invariantmass distributions of baryonic $p\pi^$, $p\pi^+$ pairs from $\Lambda ^0_ b \rightarrow p K ^\pi ^+\pi ^$ decays and $pK^$ pairs from $\Lambda ^0_ b \rightarrow p K ^ K ^+ K ^$ decays, respectively. Structures around known the masses of the $N(1520)$, $\Delta(1232)^{++}$ and $\Lambda(1520)$ baryons are observed. Figures (d), (e) and (f) show the invariantmass distributions of $K^\pi^+$, $K^K^+$ and $\pi^+\pi^$ pairs from $\Lambda ^0_ b \rightarrow p K ^\pi ^+\pi ^$ , $\Lambda ^0_ b \rightarrow p K ^ K ^+ K ^$ and $\Lambda ^0_ b \rightarrow p \pi ^\pi ^+\pi ^$ decays, respectively. Structures corresponding to the $K^*(892)^0$, $\phi $ and $\rho (770)^0 $ resonances are visible. The red lines correspond to the invariantmass requirements applied to the selection of the main quasitwo or threebody decays analysed. 
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Invariant $ p \pi ^\pi ^+\pi ^$ mass distributions with the results of the fit superimposed: (first row) full phase space, (second row) LBM and (third row) $\Lambda ^0_ b \rightarrow (\Lambda ^+_ c \rightarrow p \pi ^\pi ^+)\pi ^$ control channel. The two columns correspond to the chargeconjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit model are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ fivebody legend includes two components: the partially reconstructed $\Lambda ^0_ b \rightarrow p \pi ^\eta ^{\prime} $ and $\Lambda ^0_ b \rightarrow p \pi ^\pi ^+\pi ^\pi ^0$ decays where a $\gamma$ or $\pi^0$ is not reconstructed. The latter has a lowermass endpoint. 
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Invariant $ p \pi ^\pi ^+\pi ^$ mass distributions with the results of the fit superimposed: region of the phase space containing (first row) $\Lambda ^0_ b \rightarrow p a_{1} (1260)^$ , (second row) $\Lambda ^0_ b \rightarrow \Delta(1232)^{++}\pi ^{}\pi ^{}$ and (third row) $\Lambda ^0_ b \rightarrow N(1520)^0\rho (770)^0 $ quasi twobody decays. The two columns correspond to the chargeconjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit model are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ fivebody legend includes two components: the partially reconstructed $\Lambda ^0_ b \rightarrow p \pi ^\eta ^{\prime} $ and $\Lambda ^0_ b \rightarrow p \pi ^\pi ^+\pi ^\pi ^0$ decays where a $\gamma$ or $\pi^0$ is not reconstructed. The latter has a lowermass endpoint. 
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Invariant $ p K ^\pi ^+\pi ^$ mass distributions with the results of the fit superimposed: (first row) full phase space, (second row) LBM and (third row) $\Lambda ^0_ b \rightarrow (\Lambda ^+_ c \rightarrow p K ^\pi ^+)\pi ^$ control channel. The two columns correspond to the chargeconjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ fivebody legend includes two components: the partially reconstructed $\Lambda ^0_ b \rightarrow p K ^\eta ^{\prime} $ and $\Lambda ^0_ b \rightarrow p K ^\pi ^+\pi ^\pi ^0$ decays where a $\gamma$ or $\pi^0$ is not reconstructed. The latter has a lowermass endpoint. 
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Invariant $ p K ^\pi ^+\pi ^$ distributions, with the results of the fit superimposed: region of the phase space containing (first row) $\Lambda ^0_ b \rightarrow p K_{1} (1410)^$ , (second row) $\Lambda ^0_ b \rightarrow \Delta(1232)^{++} K ^{}\pi ^{}$ , (third row) $\Lambda ^0_ b \rightarrow \Lambda(1520)\rho (770)^0 $ and (last row) $\Lambda ^0_ b \rightarrow N(1520)^0 K ^*(892)^{0} $ quasi twobody decays. The two columns correspond to the chargeconjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit are indicated in the legends. 
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Invariant $ p K ^ K ^+ K ^$ mass distributions, with the results of the fit superimposed: (first row) full phase space and (second row) LBM, (third row) $\Lambda ^0_ b \rightarrow \Lambda(1520)\phi $ and (fourth row) $\Lambda ^0_ b \rightarrow ( p K ^{})_\text{ highmass} \phi $ . The two columns correspond to the chargeconjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ fivebody legends includes two decays: partially reconstructed $\Lambda ^0_ b \rightarrow p K ^ K ^+ K ^\gamma $ and $\Lambda ^0_ b \rightarrow p K ^ K ^+ K ^\pi ^0$ , where the $\gamma $ and $\pi^0$ are not reconstructed. 
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Invariant (first row) $ p K ^ K ^+\pi ^$ and (second row) $ p K ^\pi ^+ K ^$ mass distributions, with the results of the fit superimposed. The two bottom plots are the results of the fit to the $\Xi ^0_ b \rightarrow (\Xi ^+_ c \rightarrow p K ^\pi ^+)\pi ^$ control channel. The two columns correspond to the chargeconjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ fivebody legend includes two components where a $\pi^0$ is not reconstructed: the partially reconstructed background $\Lambda ^0_ b \rightarrow p K ^\pi ^+\pi ^\pi ^0$ where a pion is misidentified as a kaon and the partially reconstructed background $\Lambda ^0_ b \rightarrow p K ^ K ^+\pi ^\pi ^0$ . 
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Animated gif made out of all figures. 
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Fourbody charmless and charmed decays considered in this analysis. The difference of $ C P$ asymmetries measured for the charmless modes and for the control channels results in $\Delta {\mathcal{A}}^{ C P } $ measurements. For each observable, the choice of the control channel is aiming at cancelling at first order production and detection asymmetries. Given the data samples at hand, it is not possible to meet both criteria for the signal decay $\Xi ^0_ b \rightarrow p K ^\pi ^+ K ^$ : the choice of the Cabibbofavoured decay $\Xi ^0_ b \rightarrow (\Xi ^+_ c \rightarrow p K ^\pi ^+)\pi ^$ as a control channel requires in turn to correct the corresponding $\Delta {\mathcal{A}}^{ C P } $ for the kaondetection asymmetry. 
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Invariantmass requirements applied for the different phasespace selections for each final state considered. 
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Systematic uncertainties for each decay mode. The uncertainties related to the kaon and proton detection asymmetry, the difference of triggering efficiency, the PID asymmetries and the production asymmetry are respectively reported as $\sigma_K$, $\sigma_p$, $\sigma_{\rm L0}$, $\sigma_{\rm PID}$ and $\sigma_{A_P}$. 
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Signal yields for each decay mode, summed over all trigger configurations and years of data taking. 
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Created on 06 March 2021.