New approach to $K^{0}-\bar{K^{0}}$ mixing

TL;DR

This paper introduces a novel QCD method using polynomial kernels to accurately compute the B parameter for $K^{0}-ar{K^{0}}$ mixing, reducing uncertainties from unknown continuum contributions.

Contribution

It presents a new approach with polynomial kernels for sum rules, improving stability and eliminating arbitrariness compared to previous exponential kernel methods.

Findings

Calculated B parameter with reduced continuum uncertainty

Determined mixed quark-gluon condensate value

Computed K-meson decay constant to five-loop accuracy

Abstract

A new QCD calculation of the B parameter of $K^{0}-\bar{K^{0}}$ mixing is presented. It makes use of polynomial kernels in dispersion integrals in order to practically eliminate the contributions of the unknown pseudoscalar strange continuum. This approach avoids the arbitrariness and instability inherent to the Borel exponential kernels used in previous sum rules calculations. A simultaneous calculation of the mixed quark gluon condensate $\langle g\bar{q}\sigma_{\mu\nu}\frac{\lambda^{a}}{2}\sigma_{\mu\nu}^{a}q\rangle$ which enters in the expression for B is presented. Finally the K-meson decay constant $f_{K}$ is calculated to five loop