NPR step-scaling across the charm threshold

Matching Non-Perturbative Renormalisation on the lattice and perturbative renormalisation would benefit from higher matching scales, which are needed for observables entering their permile era such as BK. In this work we lay down a strategy, within the Rome-Southampton framework, to push this scale higher across the charm threshold, and apply it to an exploration of the BK running from 3 GeV to 9 GeV. This is done on Nf = 2+1+1 ensembles generated by the RBC-UKQCD collaboration, and features a close study of the discretisation effects.