Processes commonly studied at the Large Hadron Collider (LHC) are induced by quarks and gluons inside the protons of the LHC beams. Photons and charged leptons can also appear as constituents in ultra-relativistic hadron beams, and admit a description in terms of a Parton Density Function (PDF). Despite the fact the lepton densities are extremely small, there are cases where lepton initiated processes can be relevant. For example, they can give rise to rare Standard Model (SM) signatures and to new production channels, that, in turn, can enlarge the discovery potential of New Physics at the LHC and future high energy hadronic colliders.
I will discuss how the lepton content of the proton can be precisely determined applying the LUX method, originally proposed for the extraction of the photon density with an unprecedented (few)percent level accuracy target. I will then move to a select collection of phenomenological applications at the LHC. In particular, my focus will be on a novel research strategy for resonant single LeptoQuark (LQ) production in the collisions of leptons and quarks. For the case of minimal first- and second-generation scalar LQs, I will show that, in large parts of the parameter space, the obtained limits represent the most stringent constraints to date on LQs of this type.