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PreprintarXiv licencearXiv

A toy model for the quark pole mass

  • Marcos Marino
  • Maximilian Schwick
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Abstract

We study the pole mass for a heavy quark probe in the Gross--Neveu model, at the first non-trivial order in the 1/N expansion. We show that this mass suffers from a perturbative renormalon ambiguity structurally similar to the one in QCD. The exact large N solution leads however to an explicit expression for the pole mass which can be decoded as a trans-series, and we find that non-perturbative corrections cure the renormalon ambiguity. We also calculate the self-energy of the heavy quark beyond perturbation theory by using the OPE method with condensates, and show that the results are in agreement with the large N solution. The non-perturbative corrections to the pole mass turn out to be determined to a large extent by the condensate corrections to the self-energy. However, there is a class of corrections that has to be reorganized due to on-shell effects and cannot be obtained from the conventional condensate expansion. We discuss possible implications of this toy model for QCD.

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Cite

BibTeXRIS
BibTeX
@misc{marino2026model,
  title = {{A toy model for the quark pole mass}},
  author = {Marcos Marino and Maximilian Schwick},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10059},
  eprint = {2610.10059},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10059},
}
RIS
TY  - UNPB
TI  - A toy model for the quark pole mass
AU  - Marcos Marino
AU  - Maximilian Schwick
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10059
UR  - https://arxiv.org/abs/2610.10059
AB  - We study the pole mass for a heavy quark probe in the Gross--Neveu model, at the first non-trivial order in the 1/N expansion. We show that this mass suffers from a perturbative renormalon ambiguity structurally similar to the one in QCD. The exact large N solution leads however to an explicit expression for the pole mass which can be decoded as a trans-series, and we find that non-perturbative corrections cure the renormalon ambiguity. We also calculate the self-energy of the heavy quark beyond perturbation theory by using the OPE method with condensates, and show that the results are in agreement with the large N solution. The non-perturbative corrections to the pole mass turn out to be determined to a large extent by the condensate corrections to the self-energy. However, there is a class of corrections that has to be reorganized due to on-shell effects and cannot be obtained from the conventional condensate expansion. We discuss possible implications of this toy model for QCD.
ER  -