We present a next-to-leading order accurate simulation of t-channel single-top plus jet production matched to parton showers via the POWHEG method. The calculation underlying the simulation is enhanced with a process-specific implementation of the multi-scale improved NLO (MINLO) method, such that it gives physical predictions all through phase space, including regions where the jet additional to the t-channel single-top process is unresolved. We further describe a tuning procedure for the MINLO Sudakov form factor, fitting the coefficient of the first subleading term in its exponent using an artificial neural-network. The latter tuning, implemented as a straightforward event-by-event reweighting, renders the MINLO simulation NLO accurate for t-channel single-top observables, in addition to those of the analogous single-top plus jet process.
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