  In the chiral limit, the $D=6$ contribution to the Operator Product Expansion
(OPE) of the $\mathrm{VV-AA}$ correlator of quark currents only depends on two
vacuum condensates, which can be related to hadronic matrix elements associated
to CP violation in non-leptonic kaon decays. We use those relations to
determine $\langle(\pi\pi)_{I=2}|\mathcal{Q}_{8}|K\rangle$, using the updated
ALEPH spectral functions. Alternatively, we use those relations in the opposite
direction. Taking the values of the matrix elements from the lattice to obtain
the $D=6$ vacuum elements provides a new short-distance constraint which allows
for an inclusive determination of $f_{\pi}$ and an updated value for the $D=8$
condensate.

High Energy Physics - Phenomenology