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Title: Spectral representation of lattice gluon and ghost propagators at zero temperature
Authors: Dudal, David
Oliveira, Orlando 
Roelfs, Martin
Silva, Paulo 
Issue Date: 16-Jan-2019
Publisher: Elsevier
Serial title, monograph or event: Nuclear Physics B
Volume: 952
Abstract: 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 K\"all\'en-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 K\"all\'en-Lehmann spectral density from propagator data is a well known ill-posed numerical problem. To regularize this problem we implement an appropriate version of Tikhonov regularization supplemented 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 K\"all\'en-Lehmann spectral integral.
Description: 33 pages, 18 figures
ISSN: 05503213
DOI: 10.1016/j.nuclphysb.2019.114912
Rights: openAccess
Appears in Collections:I&D CFis - Artigos em Revistas Internacionais

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