Using Rare Decays to Probe the Standard Model at LHCb

The Large Hadron Collider beauty Experiment (LHCb) detector is one of the four main particle detectors on the Large Hadron Collider (LHC). It is dedicated to the study of physics processes involving b quarks. This thesis presents three analyses of data collected by LHCb. The first measures the photoelectron yield of the Ring Imaging Cherenkov Detector (RICH) detector subsystem, which distinguishes between pions, kaons and protons. The yield is seen to be 15% (19%) less than that in the simulation for the $\rm C_4 F_{10}$ ($\rm CF_4$) radiator medium. The result is a Particle Identication (PID) performance which is sufficient for the physics goals of LHCb, albeit slightly less than expected from simulation. No evidence is found for the deterioration of the Hybrid Photon Detector (HPD) quantum efficiency, mirror reflectivity or RICH medium transparency over the course of 2011 and 2012 data collection. The second analysis measures the dependence of the $b \to \Lambda^0_b$ to $b \to B^0$ hadronisation ratio on the $p_{\rm T}$ and $\eta$ of the $\Lambda^0_b$ and $B^0$. An exponential function with a plateau provides the best fit for the $p_{\rm T}$ dependence. A linear dependence of the ratio to $\eta$ is also observed. These observations are substantial improvements on previous measurements of the dependencies that can aid the development of QCD models and simulation frameworks that describe b quark hadronisation. The third analysis presents the world's first search for the decays $B^0_s \to \mu^+\mu^-\mu^+\mu^-$ and $B^0 \to \mu^+\mu^-\mu^+\mu^-$. Upper limits are set on the branching fractions of both decays that are 2 orders of magnitude above Standard Model (SM) expectations. These limits begin to exclude the phase-space of supersymmetric models where the decays are mediated by S and P sgoldstinos.