https://doi.org/10.1140/epjc/s10052-023-12058-w
Regular Article - Theoretical Physics
Schwinger poles of the three-gluon vertex: symmetry and dynamics
1
Institute of Physics “Gleb Wataghin”, University of Campinas-UNICAMP, 13083-859, Campinas, São Paulo, Brazil
2
Department of Theoretical Physics and IFIC, University of Valencia and CSIC, 46100, Valencia, Spain
Received:
3
July
2023
Accepted:
19
September
2023
Published online:
3
October
2023
The implementation of the Schwinger mechanism endows gluons with a nonperturbative mass through the formation of special massless poles in the fundamental QCD vertices; due to their longitudinal character, these poles do not cause divergences in on-shell amplitudes, but induce detectable effects in the Green’s functions of the theory. Particularly important in this theoretical setup is the three-gluon vertex, whose pole content extends beyond the minimal structure required for the generation of a gluon mass. In the present work we analyze these additional pole patterns by means of two distinct, but ultimately equivalent, methods: the Slavnov–Taylor identity satisfied by the three-gluon vertex, and the nonlinear Schwinger–Dyson equation that governs the dynamical evolution of this vertex. Our analysis reveals that the Slavnov–Taylor identity imposes strict model-independent constraints on the associated residues, preventing them from vanishing. Approximate versions of these constraints are subsequently recovered from the Schwinger–Dyson equation, once the elements responsible for the activation of the Schwinger mechanism have been duly incorporated. The excellent coincidence between the two approaches exposes a profound connection between symmetry and dynamics, and serves as a nontrivial self-consistency test of this particular mass generating scenario.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
