Non-perturbative strong coupling at timelike momenta

TL;DR

This paper calculates the strong coupling constant in Landau gauge QCD across the full complex momentum plane using spectral reconstruction and direct methods, validating the approaches with lattice and functional QCD data.

Contribution

It introduces a spectral reconstruction method for the coupling constant in complex momenta and compares it with direct calculations, providing a non-perturbative benchmark.

Findings

Spectral representation of the coupling is established.

Spectral reconstruction agrees well with direct calculations.

Method proves reliable for non-perturbative QCD analysis.

Abstract

We compute the strong coupling constant of Landau gauge QCD in the full complex momentum plane, both directly and via spectral reconstruction. In particular, we consider the Taylor coupling given by the product of ghost and gluon dressing functions. Assuming spectral representations for the latter, we first show that also the coupling obeys such a representation. The subsequent spectral reconstruction of the coupling data, obtained from 2+1 flavour lattice QCD results for the ghost and gluon, is based on a probabilistic inversion of this representation using Gaussian process regression with analytically enforced asymptotics. In contradistinction, our direct calculation relies on earlier reconstruction results for the ghost and gluon spectral functions themselves, as well as data obtained in functional QCD. Apart from its relevance for studies of resonances or scattering processes, the calculation also serves as a non-trivial benchmark of our reconstruction approach. The results show remarkable agreement, testifying to the reliability of the method.