Measurement of the Time Reversal Asymmetry for the Decay $\bar{B}^{0}\rightarrow\Lambda\bar{p}\pi^{+}$ and Observation of the Decay $\bar{B}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+}$ with the LHCb Experiment

This Analysis presents the measurement of the time reversal asymmetry in the decay $\bar{B}{}^{0}\rightarrow\Lambda\bar{p}\pi^{+}$ based on a triple product given by \begin{equation*} \mathcal{O} = \vec{s}_{\Lambda} \cdot \left( \vec{p}_\Lambda \times \vec{p}_\pi \right) \quad , \end{equation*} where $\vec{s}_{\Lambda}$ is the \Lambda spin vector, $\vec{p}_\Lambda$ and $\vec{p}_\pi$ are the momentum vectors of the $\Lambda$ and $\pi$, respectively. The triple product is evaluated in the $\bar{B}{}^{0}$ rest frame. The Time reversal asymmetry is determined to be \begin{equation*} \mathcal{A}_T = (7.6 \pm 27.0(\mathrm{stat} )\pm 1.1(\mathrm{syst}))\% \quad . \end{equation*} Allowing for CP violation in the $\Lambda$ decay, the asymmetry is determined to be \begin{equation*} \mathcal{A}_T^{\rm CPV} = ({4.3}^{22.1}_{22.0}(\mathrm{stat}) \pm 1.2(\mathrm{syst}))\% \quad . \end{equation*} Both are in agreement with the theoretical predictions but also with $\mathcal{A}_T = 0$. The decays $\bar{B}{}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+}$ and ${B}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+}$ are observed for the first time and their combined statistical significance corresponds to $17.2$ Gaussian standard deviations. The branching fraction for the sum of $\bar{B}{}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+}$ and ${B}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+}$ is measured to be \begin{equation*} \mathcal{B}(\bar{B}{}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+})+\mathcal{B}({B}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+}) = \left[{4.75}^{0.53}_{0.49}(\mathrm{stat})\pm 0.20(\mathrm{syst}) \pm 0.28({f_s}/{f_d})\pm0.44(\mathcal{B})\right]\times 10^{-6} \quad. \end{equation*} For each result the first uncertainty is statistical and the second systematic, further additional external uncertainties are labelled accordingly. In addition to these results, the Dalitz plot for $\bar{B}{}^{0}\rightarrow\Lambda\bar{p}\pi^{+}$ and $\bar{B}{}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+}$ has been studied and shows the familiar behaviour with a pronounced enhancement at the threshold of the invariant baryon antibaryon mass. Finally, the angular distribution for the proton from the $\bar{B}{}^{0}$ and $\Lambda$ decays have been studied. For the $\bar{B}{}^{0}\rightarrow\Lambda\bar{p}\pi^{+}$ the first shows a large asymmetry not expected from naive meson pole models. The angular distribution for the $\bar{B}{}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+}$ and ${B}{}^{0}_{s}\rightarrow\Lambda\bar{p}K^{+}$ exhibit no significant asymmetry. The angular distribution of the proton from the $\Lambda$ decay allows to determine the $\Lambda$ polarisation in these decays and its dependence on the $\Lambda$ energy in the $\bar{B}{}^{0}$ rest frame was investigated. No significant polarisation was found for either decay mode.