# Variance Reduction and Cluster Decomposition

## TL;DR

This paper introduces a method based on the cluster decomposition principle to reduce statistical noise in lattice QCD calculations, significantly improving the precision of hadron mass and CP violation measurements.

## Contribution

It demonstrates that the cluster decomposition principle can effectively reduce noise in lattice QCD calculations, leading to more accurate results for various physical quantities.

## Key findings

- Statistical errors reduced by a factor of 3 to 4.
- Systematic errors comparable to statistical errors for strangeness content.
- Overall error decreased by 2 to 3 times.

## Abstract

It is a common problem in lattice QCD calculation of the mass of the hadron with an annihilation channel that the signal falls off in time while the noise remains constant. In addition, the disconnected insertion calculation of the three-point function and the calculation of the neutron electric dipole moment with the $\theta$ term suffer from a noise problem due to the $\sqrt{V}$ fluctuation. We identify these problems to have the same origin and the $\sqrt{V}$ problem can be overcome by utilizing the cluster decomposition principle. We demonstrate this by considering the calculations of the glueball mass, the strangeness content in the nucleon, and the CP violation angle in the nucleon due to the $\theta$ term. It is found that for lattices with physical sizes of 4.5 - 5.5 fm, the statistical errors of these quantities can be reduced by a factor of 3 to 4. The systematic errors can be estimated from the Akaike information criterion. For the strangeness content, we find that the systematic error is of the same size as that of the statistical one when the cluster decomposition principle is utilized. This results in a 2 to 3 times reduction in the overall error.