Search for new physics in rare decays of 𝑩 mesons at the LHCb experiment

In this thesis searches for the purely leptonic decays $B_s^0$ → e${}^{+}$e${}^{-}$ and $B^0$ → e${}^{+}$e${}^{-}$ as well as the lepton-flavour violating decays $B^{+}$ → $K^{+}$ e${}^{\pm }$ μ${}^{\mp }$ are presented. As these decays are rare or forbidden in the Standard Model, these searches allow for null tests of the Standard Model. Measurements of these decays also allow to place constraints on scenarios of physics beyond the Standard Model. The search for the decays $B_s^0$ → e${}^{+}$e${}^{-}$ and $B^0$ → e${}^{+}$e${}^{-}$ uses data collected by the LHCb experiment in the years 2011, 2012, 2015 and 2016, it is the first search for these decays at the LHC. Upper limits on the branching fractions of $B_s^0$ → e${}^{+}$e${}^{-}$ and $B^0$ → e${}^{+}$e${}^{-}$ are set at the order of O(10${}^{-8}$), improving the previous limits by a factor of 30. The search for the lepton-flavour violating decays $B^{+}$ → $K^{+}$e${}^{\pm }$μ${}^{\mp }$ uses the full LHCb dataset, adding to the above the data collected in 2017 and 2018, effectively doubling the amount of $B$ mesons in the analysed dataset. As the analysis is not yet published, the status as of the time of writing is presented.