Exotic particles at the LHC: production via the Higgs portal and FIMP dark matter searches

This thesis addresses two different aspects of the search for Physics Beyond the Standard Model at the Large Hadron Collider (LHC). First, and motivated by the recent discovery of a new interaction mediated by the Higgs boson, we systematically analyze the impact of the Higgs interaction on the production of new particles at the LHC. Second, we investigate the collider signatures of long-lived particles decaying into leptons and invisible energy, and which are predicted to exist in a class of neutrino mass models with a feebly interacting dark matter particle.