  Recent progress in calculating lepton density functions inside the proton and
simulating lepton showers laid the foundations for precision studies of
resonant leptoquark production at hadron colliders. Direct quark-lepton fusion
into a leptoquark is a novel production channel at the LHC that has the
potential to probe a unique parameter space for large masses and couplings. In
this work, we build the first Monte Carlo event generator for a full-fledged
simulation of this process at NLO for production, followed by a subsequent
decay using the POWHEG method and matching to the parton showers utilizing
HERWIG. The code can handle all scalar leptoquark models with renormalisable
quark-lepton interactions. We then comprehensively study the differential
distributions, including higher-order effects, and asses the corresponding
theoretical uncertainties. We also quantify the impact of the improved
predictions on the projected (HL-)LHC sensitivities and initiate the first
exploration of the potential at the FCC-hh. Our work paves the way toward
performing LHC searches using this channel.
