A search for $C P$ violation in the decay $\Lambda^0_b \to p K^ \mu^+ \mu^$ is presented. This decay is mediated by flavourchanging neutralcurrent transitions in the Standard Model and is potentially sensitive to new sources of $C P$ violation. The study is based on a data sample of protonproton collisions recorded with the LHCb experiment, corresponding to an integrated luminosity of $3$ $\mathrm{fb}^{1}$. The $\Lambda^0_b \to p K^ \mu^+ \mu^$ decay is observed for the first time, and two observables that are sensitive to different manifestations of $C P$ violation are measured, $\Delta\mathcal{A}_{C P} \equiv \mathcal{A}_{C P}(\Lambda^0_b \to p K^ \mu^+ \mu^)\mathcal{A}_{C P}(\Lambda^0_b\to pK^ J/\psi)$ and $a_{C P}^{\widehat{T}odd}$, where the latter is based on asymmetries in the angle between the $\mu^+\mu^$ and $p K^$ decay planes. These are measured to be $\Delta\mathcal{A}_{C P} = (3.5 \pm 5.0(stat) \pm 0.2(syst))\times 10^{2}$, $a_{C P}^{\widehat{T}odd} = (1.2 \pm 5.0(stat) \pm 0.7(syst))\times 10^{2}$, and no evidence for $C P$ violation is found.
Diagrams for the decay $\Lambda ^0_ b \rightarrow p K ^ \mu ^+ \mu ^ $ , in which $V_{bq}$ and $V_{qs}$ are CKM matrix elements and $q$ represents one of the three uptype quarks $u$, $c$ or $t$, the $t$quark contribution being dominant. The $u\overline{u}$ pairs originate from the hadronization process. 
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Diagra[..].pdf [41 KiB] HiDef png [67 KiB] Thumbnail [35 KiB] *.C file 

Definition of the angle $\chi$ for $\Lambda ^0_ b \rightarrow p K ^ \mu ^+ \mu ^ $ decays, in the $\Lambda ^0_ b $ rest frame. 
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Invariant mass distributions of (top) $\Lambda ^0_ b \rightarrow p K ^ \mu ^+ \mu ^ $ and (bottom) $\Lambda ^0_ b \rightarrow p K ^ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $ candidates, with fit results superimposed. Plots refer to the (left) $\Lambda ^0_ b $ and (right) $\overline{\Lambda} {}^0_ b $ subsamples. 
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ACP_Jpsi.pdf [28 KiB] HiDef png [233 KiB] Thumbnail [183 KiB] *.C file 

Invariant mass distributions of the $\Lambda ^0_ b \rightarrow p K ^ \mu ^+ \mu ^ $ subsamples used for the $ A_{\widehat{T}}$ and $\overline{ A}_{\widehat{T}}$ measurements. Plots refer to (top) $\Lambda ^0_ b $ and (bottom) $\overline{\Lambda} {}^0_ b $ decays divided into the subsamples (left) $ C_{\widehat{T}} >0,\overline{ C}_{\widehat{T}} >0$ and (right) $ C_{\widehat{T}} <0,\overline{ C}_{\widehat{T}} <0$. 
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Todd_m[..].pdf [28 KiB] HiDef png [297 KiB] Thumbnail [251 KiB] *.C file 

Animated gif made out of all figures. 
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Supplementary material full pdf 
Supple[..].pdf [110 KiB] 

This ZIP file contains supplemetary material for the publication LHCbPAPER2016059. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in variuous formats 
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Fig2.pdf [17 KiB] HiDef png [132 KiB] Thumbnail [114 KiB] *C file 
Created on 20 February 2021.