  We compute the hadronic matrix elements of the four-quark operators needed
for the study of $K^0-{\bar K^0}$ mixing beyond the Standard Model. We have
used $n_f=2+1$ flavours of domain wall fermion (DWF) at two values of the
lattice spacing ($a\approx0.08$ and $a\approx0.11\text{fm}$) and with lightest
unitary pion mass of $\approx300\,\text{MeV}$. Renormalisation is performed
non-perturbatively and the impact of different intermediate momentum schemes is
investigated.
