  We present for the first time a master formula for
$\varepsilon'/\varepsilon$, the ratio probing direct CP violation in $K \to
\pi\pi$ decays, valid in any theory beyond the Standard Model (BSM). The
formula makes use of hadronic matrix elements of BSM operators calculated
recently in the Dual QCD approach and the ones of the SM operators from lattice
QCD. We emphasize the large impact of several scalar and tensor BSM operators
in the context of the emerging $\varepsilon'/\varepsilon$ anomaly. We have
implemented the results in the open source code flavio.
