Reconstructing QCD Spectral Functions with Gaussian Processes

TL;DR

This paper employs Gaussian process regression to reconstruct ghost and gluon spectral functions in 2+1 flavor QCD, reducing artifacts and systematic errors, and compares results with functional computations to explore real-time QCD properties.

Contribution

It introduces a Gaussian process-based framework for spectral function reconstruction in QCD, integrating lattice data with functional results to improve accuracy and reduce artifacts.

Findings

Effective suppression of reconstruction artifacts.

Reduced systematic errors through combined lattice and functional data.

Agreement with functional computations validates the approach.

Abstract

We reconstruct ghost and gluon spectral functions in 2+1 flavor QCD with Gaussian process regression. This framework allows us to largely suppress spurious oscillations and other common reconstruction artifacts by specifying generic magnitude and length scale parameters in the kernel function. The Euclidean propagator data are taken from lattice simulations with domain wall fermions at the physical point. For the infrared and ultraviolet extensions of the lattice propagators as well as the low-frequency asymptotics of the ghost spectral function, we utilize results from functional computations in Yang-Mills theory and QCD. This further reduces the systematic error significantly. Our numerical results are compared against a direct real-time functional computation of the ghost and an earlier reconstruction of the gluon in Yang-Mills theory. The systematic approach presented in this work offers a promising route towards unveiling real-time properties of QCD.