Measurement of the $\Lambda_{b}$ Polarization with $pp$ Collisions at 7 TeV

This thesis presents a measurement of the $\Lambda_{b}$ baryon polarization with proton-proton collisions at a center-of-mass energy $\sqrt{s} =$ 7 TeV. The analysis is performed with the CMS detector at the Large Hadron Collider at CERN. The results are based on data collected in 2011 corresponding to an integrated luminosity $\mathcal{L} = 5.1$ fb$^{-1}$. $\Lambda_{b}$ candidates are reconstructed in the decay mode $\Lambda_{b} \rightarrow J/\psi(\mu^{+}\mu^{-}) \Lambda(p\pi^{-})$. The selected signal yield is $911 \pm 38$ and $845 \pm 37$ candidates for $\Lambda_{b}$ and $\overline{\Lambda}_{b}$, respectively. The polarization is extracted through the angular correlations between the daughter particles in the decay by a multi-dimensional likelihood fit. A production polarization of \begin{equation*} P^{+} = 0.03 \pm 0.09 \text{ (stat.)} \pm 0.03 \text{ (syst.)}\text{ for $\Lambda_{b}$} \end{equation*} and \begin{equation*} P^{-} = 0.02 \pm 0.08 \text{ (stat.)} \pm 0.05 \text{ (syst.)}\text{ for $\overline{\Lambda}_{b}$} \end{equation*} is measured. The parity violating asymmetry parameter characterizing the decay $\Lambda_{b} \rightarrow J/\psi\,\Lambda$ is measured to be 0.47 $\pm$ 0.24 (stat.) $\pm$ 0.17 (syst.). A key detector system for the presented polarization analysis is the silicon pixel detector of CMS. It allows precise reconstruction of primary and displaced vertices as well as particle momentum measurements. Due to the presence of combined electric and magnetic fields, the charge carriers in the silicon pixel sensors experience the Lorentz force and their drift direction is deviated at the so-called $\textit{Lorentz angle}$. This leads to a shift in the measured hit position which needs to be corrected for. Measurements of the Lorentz angle for the barrel pixel detector are presented, performed with cosmic ray data and collision data and utilizing two independent measurement techniques. For a nominal magnetic field of 3.8 T and a bias voltage of 150 V, the measured Lorentz angle is $21.7^{\circ}$ with a systematic uncertainty of less than 5$\%$.