Reconstruction of the vector meson propagator using a generalized eigenvalue problem

TL;DR

This paper presents a method to reconstruct the vector meson propagator at large Euclidean times by resolving two-pion contributions using a generalized eigenvalue problem, reducing noise in lattice QCD calculations.

Contribution

The authors introduce an efficient approach to measure two-pion propagators and reconstruct the vector meson propagator with reduced noise using GEVP in lattice QCD.

Findings

Successful reconstruction of the vector meson propagator at large Euclidean times.

Reduced noise in the vector correlator signal.

Effective measurement of two-pion propagators in lattice simulations.

Abstract

For long distances in the euclidean time the vector-vector correlator ($\rho$) has an exponentially decreasing signal-to-noise ratio. However, the vector correlator not only consists of the vector meson but also receives contributions from a two-pion system with the same quantum numbers. We measure all two-pion propagators with an energy lower than the mass of the resting vector meson and employ a generalized eigenvalue problem (GEVP) to resolve the different contributing energy states. Using those we can reconstruct the propagator with a much smaller noise at large euclidean time distances. In this work we present an efficient way to measure two-pion propagators and our results on reconstruction of the vector meson propagator with staggered fermions in a $(6^3\times 8.5)\,\textrm{fm}^4$ box.