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Spectral densities from the lattice
We discuss a method to extract the K\"all\'{e}n-Lehmann spectral density of a
particle (be it elementary or bound state) propagator by means of 4d lattice
data. We employ a linear regularization strategy, commonly known as the
Tikhonov method with Morozov discrepancy principle. An important virtue over
the popular maximum entropy method is the possibility to also probe unphysical
spectral densities, as, for example, of a confined gluon. We apply our proposal
to the SU(3) glue sector.Comment: 7 pages, 9 figures, talk given at the 31st International Symposium on
Lattice Field Theory (LATTICE 2013), July 29-August 3 2013, Mainz, German
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 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.Comment: 33 pages, 18 figure
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