Kaon Weak Matrix Elements with Wilson Fermions

TL;DR

This paper reports on lattice QCD calculations of kaon weak matrix elements using Wilson fermions, providing preliminary results for B_K and K->pi pi matrix elements relevant for understanding CP violation and kaon decays.

Contribution

The study introduces new lattice QCD computations of kaon matrix elements with Wilson fermions, including B_K and K->pi pi amplitudes, extrapolated to the continuum and physical kinematics.

Findings

Preliminary B_K(2 GeV)=0.66(7)

K->pi pi matrix elements: <pi pi|O_7|K>=0.14(1)(1) GeV^3

<pi pi|O_8|K>=0.69(6)(6) GeV^3

Abstract

We present results of several numerical studies with Wilson fermions relevant for kaon physics. We compute the B_K parameter by using two different methods and extrapolate to the continuum limit. Our preliminary result is B_K(2 GeV)=0.66(7). Delta I=3/2 K->pi pi matrix elements are obtained by using the next-to-leading order expressions derived in chiral perturbation theory in which the low energy constants are determined by the lattice results computed at unphysical kinematics. From the simulation at beta=6.0 our (preliminary) results read: <pi pi|O_7(2 GeV)|K>_{I=2}=0.14(1)(1) GeV^3 and <pi pi|O_8(2GeV)|K>_{I=2}=0.69(6)(6) GeV^3.