  As an important step towards a complete next-to-leading order (NLO) QCD
analysis of the ratio $\varepsilon'/\varepsilon$ within the Standard Model
Effective Field Theory (SMEFT), we present for the first time the NLO master
formula for the BSM part of this ratio expressed in terms of the Wilson
coefficients of all contributing operators evaluated at the electroweak scale.
To this end we use the common Weak Effective Theory (WET) basis (the so-called
JMS basis) for which tree-level and one-loop matching to the SMEFT are already
known. The relevant hadronic matrix elements of BSM operators at the
electroweak scale are taken from Dual QCD approach and the SM ones from lattice
QCD. It includes the renormalization group evolution and quark-flavour
threshold effects at NLO in QCD from hadronic scales, at which these matrix
elements have been calculated, to the electroweak scale.
