Abstract
We calculate the dressed gluon and ghost propagators of Landau gauge Yang-Mills theory in the complex momentum plane from their Dyson-Schwinger equations. To this end, we develop techniques for a direct calculation such that no mathematically ill-posed inverse problem needs to be solved. We provide a detailed account of the employed ray technique and discuss a range of tools to monitor the stability of the numerical calculation. Within a truncation employing model Ans\"atze for the three-point vertices and neglecting effects due to four-point functions, we find a singularity in the gluon propagator in the second quadrant of the complex ${p}^{2}$ plane. Although the location of this singularity turns out to be strongly dependent on the model for the three-gluon vertex, it always occurs at complex momenta for the range of models considered.
Highlights
There are at least two reasons why the analytic structure of Yang-Mills propagators, viz., of the ghost and the gluon propagators, are of great interest
Within a truncation employing model Ansätze for the three-point vertices and neglecting effects due to four-point functions, we find a singularity in the gluon propagator in the second quadrant of the complex p2 plane
As we found that for the given truncation the gluon propagator seems to have a singular point in the complex plane, we wanted to remove its influence on the vertex
Summary
There are at least two reasons why the analytic structure of Yang-Mills propagators, viz., of the ghost and the gluon propagators, are of great interest. Reconstruction methods have to be employed to study the analytic continuation into the complex momentum plane. In this respect, many of the above-mentioned explicit forms have been used as trial functions to describe lattice data at real and spacelike p2 [11,12,13,14]. These reconstruction methods can be applied well to solutions from functional methods, i.e., either DysonSchwinger equations or the functional renormalization group [8,19,20] Such functions can be used to analytically continue results (instead of correlation functions) obtained from Euclidean input to the physical momentum regime. Computational details, the reconstruction from arbitrary rays and the employed threegluon vertex models are explained in Appendices
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
