Searching for Heavy Neutral Leptons at LHCb and SHiP

Heavy Neutral Leptons are very weakly interacting particles expected in many theories for the extension of the Standard Model. In this thesis two different studies are presented concerning Heavy Neutral Leptons. The first study presents details of the validation of the SHiP detector simulation software. Several models for the simulation of muon production at the beam dump are compared with data collected by the CHARM collaboration. The study shows that the simulation software gives a satisfactory simulation of the geometry of the muonic flux as well as of the energy deposition measurements. The second study is an inclusive search for a Heavy Neutral Lepton decaying at an isolated vertex. The search is performed using a $pp$-collision data sample collected at $\sqrt{s}=7$ and 8 TeV with the LHCb detector, corresponding to integrated luminosities of 1 and 2 fb$^{-1}$ respectively. No significant signal is observed in the mass range $2000 \le m_N \le 6200$ MeV, and therefore model independent limits are placed on the production cross-section times branching ratio as a function of the mass and lifetime of the Heavy Neutral Lepton. The limits are subsequently interpreted as model dependent limits on the mixing between the Heavy Neutral Lepton and the Standard Model muon neutrino as a function of the mass of the Heavy Neutral Lepton.