Implications of tau data for CP violation in K decays

Abstract

The \bm{D=6}𝐃=6 contribution of the Operator Product Expansion (OPE) of the \bm{\mathrm{VV-AA}}VV−AA correlator of quark currents can be related to hadronic matrix elements associated to CP violation in non-leptonic kaon decays. We use those relations to find an updated value for \bm{\langle(\pi\pi)_{I=2}|\mathcal{Q}_{8}|K\rangle}⟨(𝛑𝛑)𝐈=2|𝒬8|𝐊⟩ in the chiral limit using the updated ALEPH spectral function. Taking instead values of the matrix elements from the lattice to obtain the \bm{D=6}𝐃=6 vacuum elements provides a new short-distance constraint that allows for an inclusive determination of \bm{f_{\pi}}𝐟𝛑 and an updated value for the \bm{D=8}𝐃=8 condensate.