Study of stochastic estimates of quark loops with unbiased subtraction

TL;DR

This paper investigates variance reduction techniques for stochastic estimates of quark loops in lattice QCD, demonstrating improved accuracy through unbiased subtraction with complex Z2 noise on a specific lattice setup.

Contribution

It introduces an unbiased subtraction method using hopping parameter expansion to reduce variance in stochastic quark loop calculations.

Findings

Variance decreases with more subtraction terms.

Optimal noise number improves estimate precision.

Method effective for point-split vector current.

Abstract

Stochastic noise estimator method is a powerful tool to calculate the disconnected insertion involving quark loops. We study the variance reduction technique with unbiased subtraction. We use the complex $Z_2$ noise to calculate the quark loops on a $16^3 \times 24$ lattice with $\beta = 6.0$ and $\kappa$ = 0.154. Unbiased subtraction method is performed by using hoping parameter expansion. We report on the variance reduction for the point-split vector current as a function of the number of subtraction terms and the number of noise used.