Probing the singularities of the LandauGauge gluon and ghost propagators with rational approximants
Abstract
We employ Padé approximants in the study of the analytic structure of the fourdimensional SU(2) Landaugauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, serve as fitting functions for the lattice data. We carefully propagate the uncertainties due to the fitting procedure, taking into account all possible correlations. For the gluonpropagator data, we confirm the presence of a pair of complex poles at p_{pole2} = [(0.37 ± 0.05_{stat}± 0.08_{sys}) ± i (0.66 ± 0.03_{stat}± 0.02_{sys})] GeV^{2}, where the first error is statistical and the second systematic. The existence of this pair of complex poles, already hinted upon in previous works, is thus put onto a firmer basis, thanks to the model independence and to the careful error propagation of our analysis. For the ghost propagator, the Padés indicate the existence of a single pole at p^{2} = 0, as expected. In this case, our results also show evidence of a branch cut along the negative real axis of p^{2}. This is corroborated with another type of approximant, the DLog Padés, which are better suited to studying functions with a branch cut and are applied here for the first time in this context. Due to particular features and limited statistics of the gluonpropagator data, our analysis is inconclusive regarding the presence of a branch cut in the gluon case.
 Publication:

Journal of High Energy Physics
 Pub Date:
 February 2023
 DOI:
 10.1007/JHEP02(2023)144
 arXiv:
 arXiv:2210.10490
 Bibcode:
 2023JHEP...02..144B
 Keywords:

 Correlation Functions;
 Lattice Quantum Field Theory;
 Vacuum Structure and Confinement;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology
 EPrint:
 36 pages, 12 figures. Small changes in the text, references added, results unchanged. Accepted for publication in JHEP