# Frequency-splitting estimators of single-propagator traces

## TL;DR

This paper introduces a new family of stochastic estimators for single-propagator traces in lattice QCD, significantly reducing computational costs and variance compared to traditional methods, with promising applications in physics calculations.

## Contribution

The paper proposes a novel frequency splitting and hopping expansion-based estimator for fermion traces, improving efficiency and variance reduction in lattice QCD computations.

## Key findings

- Cost reduction by one to two orders of magnitude for certain diagrams
- Effective computation of disconnected contributions in two-flavor QCD
- Potential large gains for higher-point correlation functions

## Abstract

Single-propagator traces are the most elementary fermion Wick contractions which occur in numerical lattice QCD, and are usually computed by introducing random-noise estimators to profit from volume averaging. The additional contribution to the variance induced by the random noise is typically orders of magnitude larger than the one due to the gauge field. We propose a new family of stochastic estimators of single-propagator traces built upon a frequency splitting combined with a hopping expansion of the quark propagator, and test their efficiency in two-flavour QCD with pions as light as 190 MeV. Depending on the fermion bilinear considered, the cost of computing these diagrams is reduced by one to two orders of magnitude or more with respect to standard random-noise estimators. As two concrete examples of physics applications, we compute the disconnected contributions to correlation functions of two vector currents in the isosinglet omega channel and to the hadronic vacuum polarization relevant for the muon anomalous magnetic moment. In both cases, estimators with variances dominated by the gauge noise are computed with a modest numerical effort. Theory suggests large gains for disconnected three and higher point correlation functions as well. The frequency-splitting estimators and their split-even components are directly applicable to the newly proposed multi-level integration in the presence of fermions.