Split-even approach to the rare kaon decay $K \to \pi \ell^+ \ell^-$

TL;DR

This paper explores a split-even estimator method to improve the calculation of rare kaon decay processes, addressing stochastic noise issues in lattice QCD computations.

Contribution

It introduces and investigates the split-even approach as a variance reduction technique for rare kaon decay calculations.

Findings

Split-even estimator reduces variance in kaon decay calculations.

Potential for more precise lattice QCD results.

Addresses stochastic noise from quark loops.

Abstract

In recent years the rare kaon decay has been computed directly at the physical point. However, this calculation is currently limited by stochastic noise stemming from a light and charm quark loop GIM subtraction. The split-even approach is an alternative estimator for such loop differences, and has shown a large variance reduction in certain quantities. We present an investigation into the use of the split-even estimator in the calculation of the rare kaon decay.