Search for $CP$ violation in charmless three-body decays of strange-beauty baryons

Studies of charmless three-body decays of the $\Xi^-_b$ and $\Omega^-_b$ baryons to $p h^{-}h^{\prime -}$ final states, where $h^{(\prime)}$ denotes a kaon or pion, are presented. The first part of the analysis is based on a sample of proton-proton collision data collected by the $\mbox{LHCb}$ experiment at centre-of-mass energies $\sqrt{s} = 7$ & $8 {\mathrm{\,Te\kern -0.1em V}}$, corresponding to an integrated luminosity of $3~ {\mbox{fb}^{-1}}$. In this analysis, the decay $\Xi^-_b {\rightarrow} p K^-K^-$ is observed with a significance of $8.7$ standard deviations, and evidence at the level of $3.4$ standard deviations is found for the $\Xi^-_b {\rightarrow} p K^-\pi^-$ decay. The results are reported, relative to the $B^- {\rightarrow} K^+K^-K^-$ normalisation channel, for the products of branching fractions and $b$-hadron production fractions. The branching fractions of $\Xi^-_b {\rightarrow} p K^-\pi^-$ and $\Xi^-_b {\rightarrow} p \pi^-\pi^-$ relative to $\Xi^-_b {\rightarrow} p K^-K^-$ decays are also measured. In the second part of the analysis, an amplitude analysis of $\Xi^-_b {\rightarrow} p K^-K^-$ decays is presented. This analysis is based on a data sample corresponding to integrated luminosities of $1 ~{\mbox{fb}^{-1}}$, $2~ {\mbox{fb}^{-1}}$, $0.3~ {\mbox{fb}^{-1}}$ and $1.7~ {\mbox {fb}^{-1}}$ collected by $\mbox{LHCb}$ during 2011 $({\sqrt{s}} = 7 {\mathrm{\,Te\kern -0.1em V}})$, 2012 (${\sqrt{s}} = 8 {\mathrm{\,Te\kern -0.1em V}}$), 2015 (${\sqrt{s}} = 13 {\mathrm{\,Te\kern -0.1em V}}$) and 2016 (${\sqrt{s}} = 13 {\mathrm{\,Te\kern -0.1em V}}$) respectively. Sensitivity to the $CP$ violation parameters in $\Xi^-_b {\rightarrow} p K^-K^-$ decays is also presented. An updated search for the previously unobserved charmless decay $\Omega^-_b {\rightarrow} p K^-K^-$ is also conducted.