Distributions of invariant masses of pairs of final-state 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 two-body invariant-mass 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 invariant-mass 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 invariant-mass requirements applied to the selection of the main quasi-two- or three-body decays analysed.

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 charge-conjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit model are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ five-body 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 lower-mass endpoint.

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 two-body decays. The two columns correspond to the charge-conjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit model are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ five-body 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 lower-mass endpoint.

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 charge-conjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ five-body 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 lower-mass endpoint.

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 two-body decays. The two columns correspond to the charge-conjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit are indicated in the legends.

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{ high-mass} \phi $ . The two columns correspond to the charge-conjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ five-body 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.

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 charge-conjugate final states: (left) baryon, (right) antibaryon. The different components employed in the fit are indicated in the legends. The $\Lambda ^0_ b \rightarrow $ five-body 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 $\Lambda ^0_ b \rightarrow p K ^- K ^+\pi ^-\pi ^0$ .

Animated gif made out of all figures.

Four-body 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 Cabibbo-favoured 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 kaon-detection asymmetry.

Invariant-mass requirements applied for the different phase-space selections for each final state considered.

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 $\sigma_{A_P}$.

Signal yields for each decay mode, summed over all trigger configurations and years of data taking.