Abstract
Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Pad\'e approximants, identify the poles and zeros for each approximant and map them into the analytic structure of the propagators. For the Landau gauge gluon propagator the Pad\'e analysis identifies a pair of complex conjugate poles and a branch cut along the negative real axis of the Euclidean ${p}^{2}$ momenta. For the Landau gauge ghost propagator the Pad\'e analysis shows a single pole at ${p}^{2}=0$ and a branch cut also along the negative real axis of the Euclidean ${p}^{2}$ momenta. The method gives precise estimates for the gluon complex poles that agree well with other estimates found in the literature. For the branch cut the Pad\'e analysis gives, at least, a rough estimate of the corresponding branch point.
Highlights
AND MOTIVATIONQuantum chromodynamics (QCD) is a non-Abelian gauge theory associated with the SU(3) color group that describes the interactions between quarks and gluons [1,2,3]
This negative result suggests that the single particle states associated with quarks and gluons do not belong to the Hilbert space of the physical states
Quarks and gluons can only exist as components of the physical states, identified as the color singlet states, a statement that is normally phrased saying that quarks and gluons are confined particles
Summary
Quantum chromodynamics (QCD) is a non-Abelian gauge theory associated with the SU(3) color group that describes the interactions between quarks and gluons [1,2,3]. The presence of complex poles in the Argand plane make the usual Wick rotation impractical but not the analytical extension of the correlation functions [12] It has been argued by some authors that the use of integral representations can solve the problem of accessing Minkowski space correlation functions from the corresponding Euclidean functions [13,14]. In [38,39,40] there has been a tentative to identify the branch cut for the gluon and ghost propagators relying on its Källen-Lehmann representation by measuring directly, from the lattice data, its spectral function at zero temperature All these studies suggest that the gluon and ghost propagators have a nontrivial analytic structure that requires to be understood. VI we summarize our results, discuss its meaning and look for future work
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