# Multi-level integration for meson propagators

## TL;DR

This paper introduces multi-level Monte Carlo techniques for lattice QCD to improve the computation of meson correlation functions by factorizing fermion propagators and determinants, reducing noise and enhancing efficiency.

## Contribution

The paper presents new strategies for estimating factorized contributions to meson two-point functions, including an improved estimator for disconnected diagrams using frequency-splitting.

## Key findings

- Preliminary results in quenched theory demonstrate the effectiveness of the two-level integration scheme.
- New estimators improve the calculation of connected and disconnected meson correlators.
- Factorization techniques facilitate multi-level Monte Carlo integration in lattice QCD.

## Abstract

The computation of many correlation functions in lattice QCD is severely hindered by a signal-to-noise problem. Recent developments in the factorization of both the fermion propagator and determinant pave the way for the implementation of multi-level Monte Carlo integration techniques for lattice QCD. In these proceedings we introduce new strategies for the estimation of the factorized contribution to the connected and disconnected diagrams for meson two-point functions. An estimator for the factorized connected diagram is constructed sequentially for a two-level integration scheme. For the disconnected diagram, we introduce an improved estimator by performing a frequency-splitting of traces, applicable with or without multi-level integration. Preliminary results in the quenched theory with a two-level integration scheme are presented.