Discovery Of Rare B decays. First observation of the $B_s \rightarrow \mu^+\mu^-$ decays, first evidence of the $B^0 \rightarrow \mu^+ \mu^-$ decays.

The dissertation describes the search for new physics with the rare $B_s\rightarrow \mu^+ \mu^-$ and $B^0 \rightarrow \mu^+ \mu^-$ decays. The results presented are the most precise up to date. The work is divided into three parts: the first part describes the theoretical framework and the LHCb experiment, the second part the LHCb $B^0_(s)\rightarrow \mu^+ \mu^-$ searches in data collected in 2011 and 2012 and the third the discovery of $B_s\rightarrow \mu^+ \mu^-$ decays and the first evidence of $B^0 \rightarrow \mu^+ \mu^-$ decays with the combined CMS and LHCb analysis. Special emphasis has been placed on describing the improvements to the LHCb trigger efficiency estimation on data with the TISTOS method (Chapter 5), the normalisation procedure (Chapter 7), and the yield extraction with the invariant mass model; both in the LHCb (Chapter 6) and the combined CMS and LHCb analysis (Chapter 10). The impact of the $B_s\rightarrow \mu^+ \mu^-$ and $B^0 \rightarrow \mu^+ \mu^-$ branching fractions measurements on the various new physics models is reviewed in Chapter 10. The measured branching fractions are compatible with the Standard Model predictions within their uncertainties. The latter are still large due to the limited statistics, and could very well accommodate the possible new physics effects as seen in other rare B decays with b-to-s quark transitions. Future studies of the recently measured $B_s\rightarrow \mu^+ \mu^-$ and $B^0 \rightarrow \mu^+ \mu^-$ decays are eagerly awaited. Especially because a complementary observable, the mass eigenstate asymmetry. The mass eigenstate asymmetry could hide various types of new physics and will soon, for the first time, be accessible with the $B_s\rightarrow \mu^+ \mu^-$ decays.