Precision computation of the kaon bag parameter

TL;DR

This paper presents a precise lattice QCD calculation of the kaon bag parameter B_K, reducing uncertainties in the Standard Model prediction of CP violation in kaon decays and aiding the search for new physics.

Contribution

The study provides a fully controlled, nonperturbative lattice QCD determination of B_K with multiple lattice spacings and physical pion masses, improving the accuracy over previous estimates.

Findings

Main result: B_K^{RI}(3.5GeV)=0.531(6)_{stat}(2)_{sys}

Converted value: B_K^{MSbar-NDR}(2GeV)=0.564(6)_{stat}(3)_{sys}(6)_{PT}

Results agree with experimental data fits

Abstract

Indirect CP violation in K \rightarrow {\pi}{\pi} decays plays a central role in constraining the flavor structure of the Standard Model (SM) and in the search for new physics. For many years the leading uncertainty in the SM prediction of this phenomenon was the one associated with the nonperturbative strong interaction dynamics in this process. Here we present a fully controlled lattice QCD calculation of these effects, which are described by the neutral kaon mixing parameter B_K . We use a two step HEX smeared clover-improved Wilson action, with four lattice spacings from a\approx0.054 fm to a\approx0.093 fm and pion masses at and even below the physical value. Nonperturbative renormalization is performed in the RI-MOM scheme, where we find that operator mixing induced by chiral symmetry breaking is very small. Using fully nonperturbative continuum running, we obtain our main result B_K^{RI}(3.5GeV)=0.531(6)_{stat}(2)_{sys}. A perturbative 2-loop conversion yields B_K^{MSbar-NDR}(2GeV)=0.564(6)_{stat}(3)_{sys}(6)_{PT}, which is in good agreement with current results from fits to experimental data.