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PreprintarXiv licencearXiv

Effective Field Theory of Protonium

  • Hans-Werner Hammer
  • Akaki Rusetsky
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Abstract

We investigate the level shifts in protonium using the framework of non-relativistic effective field theory (NREFT). Our study is prompted by the PUMA collaboration's plans to probe the neutron-to-proton ratio in the nuclear density tail using antiprotonic atoms -- a method for which light atoms provide an important benchmark. We calculate the corrections to the Deser-Goldberger-Baumann-Thirring formula for the complex level shift of S-wave states from the unitary cusp and Coulomb photon exchange. Structure dependent corrections enter at the next order. For higher-partial-wave states, they enter already at leading order. Using input from chiral NNbar interactions, we compare to other calculations and measurements from LEAR.

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Cite

BibTeXRIS
BibTeX
@misc{hammer2026effective,
  title = {{Effective Field Theory of Protonium}},
  author = {Hans-Werner Hammer and Akaki Rusetsky},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06624},
  eprint = {2609.06624},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06624},
}
RIS
TY  - UNPB
TI  - Effective Field Theory of Protonium
AU  - Hans-Werner Hammer
AU  - Akaki Rusetsky
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06624
UR  - https://arxiv.org/abs/2609.06624
AB  - We investigate the level shifts in protonium using the framework of non-relativistic effective field theory (NREFT). Our study is prompted by the PUMA collaboration's plans to probe the neutron-to-proton ratio in the nuclear density tail using antiprotonic atoms -- a method for which light atoms provide an important benchmark. We calculate the corrections to the Deser-Goldberger-Baumann-Thirring formula for the complex level shift of S-wave states from the unitary cusp and Coulomb photon exchange. Structure dependent corrections enter at the next order. For higher-partial-wave states, they enter already at leading order. Using input from chiral NNbar interactions, we compare to other calculations and measurements from LEAR.
ER  -