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Stress in static force fields and the sign of the D-term

  • Adam Freese
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Abstract

The sign of the D-term is negative for a variety of hadrons, including the proton and pion. Speculation that this is the result of a mechanical stability condition has persisted despite counterexamples, including the positive D-term of the hydrogen atom. In this work, I explore how the sign of the D-term is influenced by the stress carried by static abelian force fields, finding the contributions from spin-even fields to be negative and the contributions from spin-odd fields (such as the electromagnetic field) to be positive. These contributions correlate with the signs of the D-terms of the fields' respective quanta. Since fields with different spin can produce identical potentials---thus resulting in equally-stable composite systems with identical wave functions---the sign of the D-term has nothing to do with stability. Since hadrons are bound by spin-one gluons, their negative D-terms appear atypical and require explanation. I briefly speculate on how color flux confinement could produce a negative hadronic D-term.

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Cite

BibTeXRIS
BibTeX
@misc{freese2026stress,
  title = {{Stress in static force fields and the sign of the D-term}},
  author = {Adam Freese},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33151},
  eprint = {2609.33151},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33151},
}
RIS
TY  - UNPB
TI  - Stress in static force fields and the sign of the D-term
AU  - Adam Freese
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33151
UR  - https://arxiv.org/abs/2609.33151
AB  - The sign of the D-term is negative for a variety of hadrons, including the proton and pion. Speculation that this is the result of a mechanical stability condition has persisted despite counterexamples, including the positive D-term of the hydrogen atom. In this work, I explore how the sign of the D-term is influenced by the stress carried by static abelian force fields, finding the contributions from spin-even fields to be negative and the contributions from spin-odd fields (such as the electromagnetic field) to be positive. These contributions correlate with the signs of the D-terms of the fields' respective quanta. Since fields with different spin can produce identical potentials---thus resulting in equally-stable composite systems with identical wave functions---the sign of the D-term has nothing to do with stability. Since hadrons are bound by spin-one gluons, their negative D-terms appear atypical and require explanation. I briefly speculate on how color flux confinement could produce a negative hadronic D-term.
ER  -