Reconstructing QCD spectral functions with Gaussian processes

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 toward unveiling real-time properties of QCD.

Automated summary

In this study, we reconstruct ghost and gluon spectral functions in 2 + 1 flavor QCD using Gaussian process regression. By specifying generic magnitude and length scale parameters in the kernel function, we are able to suppress spurious oscillations and other common reconstruction artifacts. We utilize results from functional computations in Yang-Mills theory and QCD to further reduce systematic error. Our numerical results are compared against direct real-time functional computations and an earlier reconstruction in Yang-Mills theory, showing the promising potential of this systematic approach in unveiling real-time properties of QCD.