Reconstructing QCD spectral functions with Gaussian processes

Jan Horak,Jonas Turnwald,Julian M Urban,José Rodríguez-Quintero,Jan M Pawlowski,Nicolas Wink,Savvas Zafeiropoulos

doi:10.1103/physrevd.105.036014

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.

Highlights

IntroductionThe resolution of many open questions in QCD requires the knowledge of timelike observables and the computation of real-time correlation functions
The Euclidean propagator data are taken from lattice simulations with domain wall fermions at the physical point
We extend the lattice input data for the dressing function into the deep IR and simultaneously fix the low-frequency asymptotics of the spectral function using a direct real-time result in Yang-Mills theory obtained via the spectral ghost DSE [12]

Summary

Introduction

The resolution of many open questions in QCD requires the knowledge of timelike observables and the computation of real-time correlation functions. The computation of the glueball spectrum via Bethe-Salpeter equations relies on the timelike propagators for gluon and ghost, both of which are reconstructed in the present work. QCD transport coefficients used in hydrodynamic simulations can be computed diagrammatically from the real-time gluon propagator. Phenomenological QCD transport models with their underlying assumption of a quasiparticle nature of the gluon can hugely benefit in multiple ways from the present results.

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Conclusion