Abstract
We reconstruct the gluon spectral function in Landau gauge QCD from numerical data for the gluon propagator. The reconstruction relies on two novel ingredients: Firstly we derive analytically the low frequency asymptotics of the spectral function. Secondly we construct a functional basis from a careful consideration of the analytic properties of the gluon propagator in Landau gauge. This allows us to reliably capture the non-perturbative regime of the gluon spectrum. We also compare different reconstruction methods and discuss the respective systematic errors.
Highlights
In the present work we argue that the low frequency asymptotics is determined by the infrared (IR) limit in the Euclidean domain using only rather general assumptions
In the present context it entails that the Goldstone contributions to the gluon in Landau gauge are an additional source of the p2 ln p2 running of the gluon propagator, that can turn the sign of zG: this follows from the similarity of the Higgs-gluon vertex to that of the ghost-gluon vertex and a respective perturbative analysis
Decoupling-type propagators have been computed in both Dyson-Schwinger equations (DSE) and in functional renormalization group (FRG) calculations in good agreement with the corresponding lattice results, see e.g. [28,69,70] and [18,28], respectively
Summary
Real-time correlation functions play a pivotal role for the theoretical understanding of heavyion collisions and the hadron spectrum. Non-perturbative Euclidean first principles methods such as Euclidean functional approaches and lattice simulations have been extensively used to obtain numerical results for QCD correlation functions When analytically continuing these to the real-time regime or equivalently reconstructing their spectral function by means of solving an inverse integral transformation, one encounters large systematic uncertainties as in the case of single particle spectral functions [1,2,3,4,5,6,7,8] or the energy momentum tensor (EMT) [9,10,11,12,13,14], to name another pertinent correlator.
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