Searching for beyond the Standard Model physics using direct and indirect methods at LHCb

It is known that the Standard Model of particle physics is incomplete in its description of nature at a fundamental level. For example, the Standard Model can neither incorporate dark matter nor explain the matter dominated nature of the Universe. This thesis presents three analyses undertaken using data collected by the LHCb detector. Each analysis searches for indications of physics beyond the Standard Model in dierent decays of B mesons, using dierent techniques. Notably, two analyses look for indications of new physics using indirect methods, and one uses a direct approach. The rst analysis shows evidence for the rare decay $B^{+} \rightarrow D^{+}_{s}\phi$ with greater than 3 $\sigma$ signicance; this also constitutes the rst evidence for a fullyhadronic annihilation-type decay of a $B^{+}$ meson. A measurement of the branching fraction of the decay $B^{+} \rightarrow D^{+}_{s}\phi$ is seen to be higher than, but still compatible with, Standard Model predictions. The CP-asymmetry of the decay is also measured, and its value is precisely in line with the Standard Model expectations. The second analysis claims the rst observations of the decays $B^{+} \rightarrow K^{+}\pi^{+}\pi^{-}\mu^{+}\mu^{-}$ and $B^{+} \rightarrow \phi K^{+}\mu^{+}\mu^{-}$ which are both avour changing neutral currents, forbidden at leading order in the Standard Model. Branching fractions of both these decays are measured, and for the high statistics channel $B^{+} \rightarrow K^{+}\pi^{+}\pi^{-}\mu^{+}\mu^{-}$ the dierential branching fraction, as a function of the invariant mass squared of the dimuon system, is also presented. These rst two analyses both constitute indirect searches for physics beyond the scope of the Standard Model, where the observables are sensitive to contributions from new physics entering at loop-level. In contrast, the third analysis presented in this thesis involves the direct search for a new dark boson, , which is a messenger particle between a dark sector and the Standard Model particles. Using a frequentist technique, the dimuon component of candidates consistent with the decay $B^{+} \rightarrow K^{*}(892)^{0}\mu^{+}\mu^{-}$ is searched for an excess indicative of $\kappa \rightarrow \mu^{+}\mu^{-}$