Searches for B meson decays to purely leptonic final states

The $B^0_{(s)}\to\ell^+\ell^-$ decays are helicity suppressed and process through flavour changing neutral currents. They are extremely rare in the standard model (SM). Thus physics beyond SM could modify their branching ratio up to an observable level. As the theoretical predictions are very precise, these modes are golden channels to probe the SM. The works presented in this thesis have contributed to the establishment of the first evidence of the $B^0_{(s)}\to\mu^+\mu^-$decay. A statistical method has been built to extract and combine limits on the decays branching fraction and to compute signals significance. On the basis of this work, an original method was developed to re-optimised the categories used to classified the candidates which improved the analysis sensitivity by 14%. A study of the interplay between the flavour mixing of the $B^0_s$ and its decay demonstrated that the analysis results are model dependent. Accounting for this dependency allows to improve constraints on new physics. Finally, an inclusive topological reconstruction was developed and tested in particular to reconstruct $B^0_{(s)}\to\tau^+\tau^-$ candidates with $\tau^- \to \pi^+\pi^-\pi^-\nu_\tau$.