Distributions of the $p K ^- \pi ^+ \pi ^- $ invariant mass in the four samples defined by the $\Lambda ^0_ b $ ( $\overline{\Lambda} {}^0_ b $ ) flavour and the sign of $ C_{\widehat{T}}$ ( $\overline{ C}_{\widehat{T}}$ ). The results of the fit are overlaid as described in the legend. The contribution of the cross-feeds to the fit results is barely visible but is found to be nonnegligible.

Distributions of the $p K ^- K ^+ K ^- $ invariant mass in the four samples defined by the $\Lambda ^0_ b $ ( $\overline{\Lambda} {}^0_ b $ ) flavour and the sign of $ C_{\widehat{T}}$ ( $\overline{ C}_{\widehat{T}}$ ). The results of the fit are overlaid as described in the legend. The contribution of the cross-feeds to the fit results is barely just visible but is found to be nonnegligible.

Distributions of the $p K ^- K ^- \pi ^+ $ invariant mass in the four samples defined by the $\Xi ^0_ b $ ( $\overline \Xi {}_ b ^0$ ) flavour and the sign of $ C_{\widehat{T}}$ ( $\overline{ C}_{\widehat{T}}$ ). The results of the fit are overlaid as described in the legend. The contribution of the $ B ^0 \rightarrow K ^- K ^+ K ^+ \pi ^- $ cross-feed to the fit results is barely visible but is found to be nonnegligible.

The asymmetries using binning schemes (left) A and (right) B for the $\Lambda ^0_ b \rightarrow p K ^- \pi ^+ \pi ^- $ decay. For $ a_P^{\widehat{T}\text{-odd}}$ ( $ a_ C P ^{\widehat{T}\text{-odd}}$ ), the values of the $\chi^2$ /ndf for the $P$-symmetry ( $ C P$ -symmetry) hypothesis, represented by a dashed line, are quoted.

The asymmetries using binning schemes (left) C and (right) D for $\Lambda ^0_ b \rightarrow p K ^- K ^+ K ^- $ decay. For $ a_P^{\widehat{T}\text{-odd}}$ ( $ a_ C P ^{\widehat{T}\text{-odd}}$ ), the values of the $\chi^2$ /ndf for the $P$-symmetry ( $ C P$ -symmetry) hypothesis, represented by a dashed line, are quoted.

The left (right) plot shows the distribution of the $\pi^+\pi^-$ ($K^{+}K^{-}_{\textrm{fast}}$) reconstructed invariant mass for $\Lambda ^0_ b $ candidates selected within $\pm2\sigma$ of the $\Lambda ^0_ b $ mass peak. The results of the fit for different signal and background components are overlaid as described in the legend.

Background-subtracted distributions of $\Lambda ^0_ b $ ( $\overline{\Lambda} {}^0_ b $ ) candidates in different regions of phase space of the $\Lambda ^0_ b \rightarrow p K ^- \pi ^+ \pi ^- $ decay for different values of $ C_{\widehat{T}}$ ( $\overline{ C}_{\widehat{T}}$ ). The background subtraction is performed using the $sPlot$ technique [27].

Background-subtracted distributions of $\Lambda ^0_ b $ ( $\overline{\Lambda} {}^0_ b $ ) candidates in different regions of phase space of the $\Lambda ^0_ b \rightarrow p K ^- \pi ^+ \pi ^- $ decay for different values of $ C_{\widehat{T}}$ ( $\overline{ C}_{\widehat{T}}$ ). The background subtraction is performed using the $sPlot$ technique [27].

Background-subtracted distributions of $\Lambda ^0_ b $ ( $\overline{\Lambda} {}^0_ b $ ) candidates in different regions of phase space of the $\Lambda ^0_ b \rightarrow p K ^- K ^+ K ^- $ decay for different values of $ C_{\widehat{T}}$ ( $\overline{ C}_{\widehat{T}}$ ). The background subtraction is performed using the $sPlot$ technique [27].

Background-subtracted distributions of $\Lambda ^0_ b $ ( $\overline{\Lambda} {}^0_ b $ ) candidates in different regions of phase space of the $\Lambda ^0_ b \rightarrow p K ^- K ^+ K ^- $ decay for different values of $ C_{\widehat{T}}$ ( $\overline{ C}_{\widehat{T}}$ ). The background subtraction is performed using the $sPlot$ technique [27].

Animated gif made out of all figures.

Selection window for control samples used to assess systematic uncertainties and for selection criteria optimization.

Measurements of the $ C P$ - and $P$-violating observables $ a_ C P ^{\widehat{T}\text{-odd}}$ and $ a_P^{\widehat{T}\text{-odd}}$ , together with their statistical and systematic uncertainties.

Sources of systematic uncertainty and their relative contributions to the total uncertainty. Where present, the value in brackets shows the systematic uncertainty assigned to the measurement in specific phase-space regions.

Definition of the 14 regions that form scheme A for the $\Lambda ^0_ b \rightarrow p K ^- \pi ^+ \pi ^- $ decay. Bins $1-4$ focus on the region dominated by the $\Delta(1232)^{++}\rightarrow p\pi ^+ $ resonance. The other 10 bins are defined to study regions where $p K ^- $ resonances are present on either side of the $f_0(980)\rightarrow \pi ^+ \pi ^- $ or $\overline{ K }{} {}^{*}(892)^{0} \rightarrow K ^- \pi ^+ $ resonances. Further splitting depending on $|\Phi|$ is performed to reduce potential dilution of asymmetries, as suggested in Ref. [14]. Masses are in units of $ {\mathrm{ Ge V /}c^2}$ .

Measurements of $ a_P^{\widehat{T}\text{-odd}}$ and $ a_ C P ^{\widehat{T}\text{-odd}}$ in specific phase-space regions for the $\Lambda ^0_ b \rightarrow p K ^- \pi ^+ \pi ^- $ decay. Each value is obtained through an independent fit to the candidates in the corresponding region of the phase space. Scheme A is defined in Table 4 and divides the phase space according to dominant resonant contributions, while scheme B consists of twelve non-overlapping bins of width $\pi/12$ in $|\Phi|$.

Definition of the seven regions that form scheme C for the $\Lambda ^0_ b \rightarrow p K ^- K ^+ K ^- $ decay. The scheme is defined to study regions where $ p K_{\rm slow}^-$ resonances are present ($1-3$) on either side of the $\Phi\rightarrow K ^+ K ^- $ resonances. Masses are in units of $ {\mathrm{ Ge V /}c^2}$ .

Measurements of $ a_P^{\widehat{T}\text{-odd}}$ and $ a_ C P ^{\widehat{T}\text{-odd}}$ in specific phase-space regions for the $\Lambda ^0_ b \rightarrow p K ^- K ^+ K ^- $ decay. Each value is obtained through an independent fit to the candidates in the corresponding region of the phase space. Scheme C is defined in Table 6 and divides the phase space according to dominant resonant contributions, while scheme D consists of ten non-overlapping bins of width $\pi/10$ in $|\Phi|$.