Treatment of systematic uncertainties in $b$-jet identification and measurement of Higgs boson decays to $b$-quarks with the ATLAS detector

The Higgs boson was discovered in 2012, and since then the ATLAS and CMS collaborations have been analyzing an ever increasing number of collisions from the LHC collider to pin down the properties of this particle as precisely as possible. Among the measurements performed, especially interesting is the measurement of the Higgs boson decays to two $b$-quarks. However, this decay mode is hard to observe because of the large background from multi-jet production. To measure the Higgs boson decaying to two $b$-quarks, the best Higgs boson production channel is the associated production with a vector boson (VH) where one vector boson, either the W or Z boson, is produced in association with a Higgs boson. If the vector boson decays leptonically into neutrinos or changed leptons, the leptons will provide a handle to reduce the large multi-jet background. This thesis work involves multiple efforts on increasing the signal significance of the VH, H$\rightarrow$bb analysis including optimizing the event selection, adding a new control region for the top background and using machine learning methods to purify the W+jets background in a dedicated control region and ultimately to get a better constraint on the normalization factor for this background. Each attempt increases the signal significance of the analysis by several percent. Apart from the H$\rightarrow$bb analysis work, the thesis work also involves inventing two new approaches to treat systematic uncertainties related to $b$-jet identification, which plays a crucial role in enabling the H$\rightarrow$bb measurement and also in many other ATLAS analyses. The first allows for the correct correlation of b-jet identification systematic uncertainties across multiple analyses. The second new treatment provides an estimate of the systematic uncertainties on identifying b-jets with especially large transverse momentum. This is particularly relevant for events in the "boosted" VH, H$\rightarrow$bb analyses