Search for New Physics with an angular analysis of $B^0 \to D^\ast \mu \nu$ decays and alignment of the LHCb Vertex Locator

A search for New Physics was performed with an angular analysis of $B^0 \rightarrow D^* \mu \nu$ decays in $pp$ collision data collected by the LHCb experiment during 2011 and 2012, corresponding to an integrated luminostiy of 3 $\rm fb^{-1}$. The signal is extracted using a multidimensional fit to data using templated distributions derived from simulation and from control samples in collision data. New Physics contributions are measured via their corresponding Wilson coefficients (real and imaginary part) and in several fit configurations that allow for different New Physics operators (vector, scalar and tensor). Form factor parameters using three parametrizations (BLPR, CLN and BGL) are measured in a Standard Model scenario. The the New Physics operators Im($V_{\rm qRlL}$), Re($V_{\rm qRlL}$), Im($V_{\rm qLlL}$), Im($S_{\rm qRlL}$), Re($S_{\rm qRlL}$), Im($T_{\rm qLlL}$), Re($T_{\rm qLlL}$) are measured with precision of 1.14e-02, 1.66e-02, 1.18e+00, 3.49e-01, 4.77e-01, 8.70e-03, 1.59e-02, respectively. This is the first full angular analysis of semileptonic $B$ hadron decays at LHCb and is the first measurement of New Physics search using LHCb data in semileptonic decays.The thesis also discusses a suite of alignment studies for the LHCb Vertex Locator (VELO). Thermal properties of the LHCb Vertex Locator (VELO) are studied using the real-time detector alignment procedure where the variation of the position and orientation of the detector elements as a function of the operating temperature of the VELO is presented. This study uses a dataset collected by the LHCb experiment during a VELO temperature scan performed at the end of LHC Run 2 (October 2018). Significant shrinkage of the VELO modules is observed at the operating temperature of $-30^\circ$C compared to the laboratory measurements on a single module taken at a range of temperatures from $+45^\circ$C to $-25^\circ$C. The thermal shrinkage expected from the extrapolation of laboratory measurements to lower temperatures and the results of this alignment study are in good agreement. A study of the VELO alignment for Run 3 is made in order to investigate the alignment performance with the Run 3 VELO detector and to establish the best alignment strategy to ensure the desired physics performance. The VELO detector is aligned using different configurations and degrees of freedom. The results of Run 3 alignment accuracy along with a set of monitoring plots that show sensitivity under different misalignments are presented.