Pseudoscalar Meson Mixing, the Contribution of the Hadronic Continuum to Deviation from Factorization

The contribution of the hadronic continuum in the QCD sum rule calculation of the parameters entering in pseudoscalar meson mixing is evaluated by making use of simple integration kernels tailored in order to practically eliminate the contribution of the hadronic continuum. This approach avoids the arbitrariness and instability inherent to previous sum rule calculations. An independent evaluation of the mixed quark gluon condensate $\left\langle QGC\right\rangle =$$\left\langle g\bar{q}\sigma_{\mu\nu}\frac{\lambda^{a}}{2}G_{\mu\nu}^{a}q\right\rangle$ which enters in the calculation is presented as well as the calculation of the K-meson decay constant $f_{K}$ to five loops.