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

TL;DR

This paper improves QCD sum rule calculations for pseudoscalar meson mixing by using tailored integration kernels to reduce hadronic continuum contributions, providing more stable and less arbitrary results.

Contribution

It introduces a novel method with integration kernels to minimize hadronic continuum effects in sum rule calculations, enhancing accuracy and stability.

Findings

Reduced hadronic continuum contribution in sum rule calculations.

Independent evaluation of the mixed quark-gluon condensate.

Calculation of the K-meson decay constant to five loops.

Abstract

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.