Update on the improved lattice calculation of direct CP-violation in K decays

TL;DR

This paper updates the lattice calculation of direct CP-violation in kaon decays, emphasizing new statistical methods for analyzing correlated data and improving the accuracy of the results.

Contribution

It introduces a bootstrap-based technique for determining null distributions in correlated data, enhancing the reliability of lattice QCD analyses.

Findings

Development of a bootstrap method for correlated data

Improved statistical error estimation in lattice calculations

Enhanced p-value computation for complex data correlations

Abstract

We discuss the status of the RBC & UKQCD collaboration's lattice determination of $\epsilon'$, the measure of direct CP-violation in kaon decays, focusing in particular on recent developments in statistical techniques for estimating standard errors and goodness-of-fit metrics for large amounts of data that have correlations both in the temporal coordinate and also in molecular dynamics time. A key result is the formulation of a technique for determining the null distribution of a fit using a bootstrap method that is free from the usual assumptions of independence, large-$n$ and/or normal data, that can for instance be applied to compute p-values even for uncorrelated fits.