Journal Article

GSI-2025-00293

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Nonlinear Schwinger mechanism in QCD, and Fredholm alternatives theorem

Ferreira, M. N. (Corresponding author) ; Papavassiliou, J.GSI*

2024
Springer Heidelberg

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Please use a persistent id in citations: doi:10.1140/epjc/s10052-024-13223-5  doi:10.15120/GSI-2025-00293

Report No.: arXiv:2407.04392

Abstract: We present a novel implementation of the Schwinger mechanism in QCD, which fixes uniquely the scale of the effective gluon mass scale and streamlines considerably the procedure of multiplicative renormalization. The key advantage of this method stems from the nonlinear nature of the dynamical equation that generates massless poles in the longitudinal sector of the three-gluon vertex. An exceptional feature of this approach is an extensive cancellation involving the components of the integral expression that determines the gluon mass scale; it is triggered once the Schwinger–Dyson equation of the pole-free part of the three-gluon vertex has been appropriately exploited. It turns out that this cancellation is driven by the so-called Fredholm alternatives theorem, which operates among the set of integral equations describing this system. Quite remarkably, in the linearized approximation this theorem enforces the exact masslessness of the gluon. Instead, the nonlinearity induced by the full treatment of the relevant kernel evades this theorem, allowing for the emergence of a nonvanishing mass scale. The numerical results obtained from the resulting equations are compatible with the lattice findings, and may be further refined through the inclusion of the remaining fundamental vertices of the theory.

Note: This article is licensed under a Creative Commons Attribution 4.0 International License. Founded by SCOAP3

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Contributing Institute(s):

1. ExtreMe Matter Institute, EMMI (EXM)

Research Program(s):

1. 612 - Cosmic Matter in the Laboratory (POF4-612) (POF4-612)
2. DFG project G:(GEPRIS)491382106 - Open-Access-Publikationskosten / 2025-2027 / GSI Helmholtzzentrum für Schwerionenforschung (491382106) (491382106)

Experiment(s):

1. no experiment theory work (theory)

Appears in the scientific report 2024

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