Exploring the 0-bound state with dressed quarks in Minkowski space

The Bethe-Salpeter equation for a pseudoscalar bound-system, with i) a ladder kernel with massive gluons, ii) dynamically-dressed quark mass function and iii) an extended quark-gluon vertex, is solved in Minkowski space by using the Nakanishi integral representation of the Bethe-Salpeter amplitude. The quark dressing is implemented through a phenomenological ansatz, which was tuned by lattice QCD calculations of the quark running mass. The latter were also used for assigning the range of the gluon mass and the parameter featuring the extended color density. This framework allows to investigate the gluon dynamics that manifest itself in the quark dressing, quark-gluon vertex and the binding, directly in the physical space. We present the first results for low-density pseudoscalar systems in order to elucidate the onset of the interplay between the above mentioned gluonic phenomena, and we discuss both static and dynamical quantities, like valence longitudinal and transverse distributions.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

The Bethe-Salpeter equation for a pseudoscalar bound-system is solved in Minkowski space using the Nakanishi integral representation of the Bethe-Salpeter amplitude, with a ladder kernel featuring massive gluons, dynamically-dressed quark mass function, and an extended quark-gluon vertex. Quark dressing is implemented through a phenomenological ansatz tuned by lattice QCD calculations. The framework allows investigating gluon dynamics in the physical space. The first results for low-density pseudoscalar systems are presented to understand the interplay between gluonic phenomena.