Standard-model prediction for direct CP violation in $K\to\pi\pi$ decay

TL;DR

This paper presents the first lattice QCD calculation of the complex kaon decay amplitude $A_0$, providing insights into direct CP violation in $K o\pi\pi$ decays and testing the Standard Model's predictions.

Contribution

It introduces a novel lattice QCD computation of $A_0$ with physical kinematics, enabling direct comparison with experimental CP violation measurements.

Findings

Re$(A_0)$ is approximately consistent with experimental data.

Calculated Re$(rac{ ext{CP violation ratio}}{ ext{expected}})$ is below experimental value.

Results serve as a test of the Standard Model's CP violation predictions.

Abstract

We report the first lattice QCD calculation of the complex kaon decay amplitude $A_0$ with physical kinematics, using a $32^3\times 64$ lattice volume and a single lattice spacing $a$, with $1/a= 1.3784(68)$ GeV. We find Re$(A_0) = 4.66(1.00)(1.26) \times 10^{-7}$ GeV and Im$(A_0) = -1.90(1.23)(1.08) \times 10^{-11}$ GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re$(A_0) = 3.3201(18) \times 10^{-7}$ GeV while the second can be used to compute the direct CP violating ratio Re$(\varepsilon'/\varepsilon)=1.38(5.15)(4.59)\times 10^{-4}$, which is $2.1\sigma$ below the experimental value $16.6(2.3)\times 10^{-4}$. The real part of $A_0$ is CP conserving and serves as a test of our method while the result for Re$(\varepsilon'/\varepsilon)$ provides a new test of the standard-model theory of CP violation, one which can be made more accurate with increasing computer capability.