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Searches for new physics (NP) at particle colliders typically involvemultivariate analysis of kinematic distributions of final state particlesproduced in a decay of a hypothetical NP resonance. Since the pair-productioncross-sections mediated by such resonances are strongly suppressed by the NPscale, this analysis becomes less relevant for NP searches for masses of theBSM resonance above 1 TeV. On the other hand, $t$-channel processes are lesssensitive to the mass of the virtual mediator and therefore larger phase-spacecan be potentially probed as well as the couplings between the NP particles andthe Standard Model fields. The fact that transitions between differentgenerations of quarks and leptons may exist, the potential of the searchpresented in this article can be used, as a reference guide, to enlargesignificantly the scope of searches performed at the LHC to flavouroff-diagonal channels, in a theoretically consistent approach. In this work, westudy non-resonant production of scalar leptoquarks which have been proposed inthe literature to provide a potential avenue for radiative generation ofneutrino masses, accommodating as well the existing flavour physics data. Finalstates involving just two muons at the LHC ($\mu^+, \mu^-$), are used as awell-motivated case study.

Exploring mixed lepton-quark interactions in non-resonant leptoquark production at the LHC