Remarks about weighted energy integrals over Minkowski spectral functions from Euclidean lattice data

TL;DR

This paper discusses how to extract weighted averages of Minkowski spectral densities from Euclidean lattice data, demonstrating the potential to determine spectral features like the rho pole with reasonable precision.

Contribution

It provides a simple method for deriving weighted energy averages of spectral functions from Euclidean correlators measured in lattice simulations, with a focus on the vector current correlator.

Findings

Weighted averages near the rho pole can be determined at the 5% level from lattice data.

The approach simplifies the connection between Euclidean correlators and Minkowski spectral densities.

Potential for applying this method to other spectral features in lattice QCD.

Abstract

I make some simple observations about the calculation of weighted averages over energy of Minkowski space spectral densities from weighted averages over time of Euclidean space correlation functions, measured in latice simulations. The correlator of two vector currents is used as an example, where it appears that a determination of a weighted average of the spectral function near the rho pole at the five per cent level is possible from lattice simulations.