Search for $K_\mathrm{S}^0 \rightarrow \mu^+\mu^-$ and trigger developments at LHCb

The SM is, up to now, a robust model that describes with high accuracy the interactions between elementary particles. However, several processes, like the observation of neutrino oscillations or the presence of dark matter in the universe, constitute signs of physics beyond this model. The LHCb experiment, located at the CERN, aims at contributing to clarify the picture we currently have about particle physics, and to understand the laws that rule our universe. By studying the decays of certain particles produced at the LHC, one can infer the existence of new particles. These new particles might give extra degrees of freedom and, complementing the SM, would allow to explain other processes. This work constitutes a search for physics beyond the SM in $K_\mathrm{S}^0 \rightarrow \mu^+\mu^-$ decays, and the development of reconstruction techniques and trigger configurations to study strange decays in the LHCb experiment. In the first place, an overview to the theory of particle physics is presented. The SM is explained, together with new theoretical proposals, and its relation with strange decays. A description of the LHCb detector follows the previous chapter, emphasizing the features that make this unique detector able to study strange decays. Afterwards, the search for the $K_\mathrm{S}^0 \rightarrow \mu^+\mu^-$ decay at LHCb is presented, whose result constitutes up to date, the most stringent limit on the branching fraction of this mode. To finalize, the upgrade of the LHCb detector is discussed, and a work on new reconstruction techniques for muons in this environment is presented. These results are complemented with preliminary trigger studies for some strange decays of interest, including $K_\mathrm{S}^0 \rightarrow \mu^+\mu^-$.