The causal structure of the quark propagator
We study the causal structure of the quark propagator with the spectral DSE. The spectral gap equation is solved with the input of the spectral representation of the gluon and a causal STI-construction for the quark-gluon vertex. The latter includes a potential infrared enhancement of the vertex str...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
11 September 2025
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| In: |
The European physical journal. C, Particles and fields
Year: 2025, Volume: 85, Issue: 9, Pages: 1-13 |
| ISSN: | 1434-6052 |
| DOI: | 10.1140/epjc/s10052-025-14683-z |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1140/epjc/s10052-025-14683-z
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| Author Notes: | Jan M. Pawlowski, Jonas Wessely |
| Summary: | We study the causal structure of the quark propagator with the spectral DSE. The spectral gap equation is solved with the input of the spectral representation of the gluon and a causal STI-construction for the quark-gluon vertex. The latter includes a potential infrared enhancement of the vertex strength of the classical tensor structure that accommodates for the physical strength of chiral symmetry breaking. We find a critical vertex strength, below which the quark has a Källén-Lehmann representation. While the nature of the first singularity does not change above the critical strength, we find that the quark propagator features at least two additional pairs of complex conjugate poles that are located approximately at the sum of quark pole mass and peak position of the quark-gluon coupling. These additional poles lead to violations of causality, if they persist in S-matrix elements. While the vertex strength of the classical tensor structure in full QCD is below the critical one, that of commonly used vertex models, which rely solely on the classical vertex structure, is typically above it. Finally, we discuss how these additional poles could be avoided in full QCD, where part of chiral symmetry breaking is generated by the other tensor structures in the quark-gluon vertex. |
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| Item Description: | Gesehen am 20.01.2026 |
| Physical Description: | Online Resource |
| ISSN: | 1434-6052 |
| DOI: | 10.1140/epjc/s10052-025-14683-z |