Spectral representation of lattice gluon and ghost propagators at zero temperature

We consider the analytic continuation of Euclidean propagator data obtained from 4D simulations to Minkowski space. In order to perform this continuation, the common approach is to first extract the Kallen-Lehmann spectral density of the field. Once this is known, it can be extended to Minkowski space to yield the Minkowski propagator. However, obtaining the Kallen-Lehmann spectral density from propagator data is a well known ill-posed numerical problem. To regularisethis problem we implement an appropriate version of Tikhonov regularisationsupplemented with the Morozov discrepancy principle. We will then apply this to various toy model data to demonstrate the conditions of validity for this method, and finally to zero temperature gluon and ghost lattice QCD data. We carefully explain how to deal with the IR singularity of the massless ghost propagator. We also uncover the numerically different performance when using two-mathematically equivalent-versions of the Kallen-Lehmann spectral integral. (C) 2020 The Authors. Published by Elsevier B.V.