Unitarity violation and restoration in radiative bound-state formation

Abstract

State-of-the-art calculations motivated by dark matter exhibit severe violation of partial-wave unitarity in the non-relativistic regime in radiative bound-state-formation processes. It has been recently shown, in a model-independent fashion, that unitarity is restored by the proper resummation of the inelastic contributions to the self-energy of the incoming state. In this work, we first derive Kramers-like formulae for individual partial waves, demonstrating that existing calculations of bound-state formation severely violate unitarity. We then discuss how unitarity is restored through the resummation of the absorptive contributions to the incoming-state self-energy, generated by bound-state formation processes, taking into account their analytic structure in the complex momentum plane. Our results can be generalized in a variety of theories and employed in phenomenological studies, such as dark-matter freeze-out, indirect detection and self-interactions.

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BibTeX RIS

BibTeX

@article{flores2026unitarity,
  title = {{Unitarity violation and restoration in radiative bound-state formation}},
  author = {Marcos M Flores and Kalliopi Petraki},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = jun,
  doi = {10.1007/jhep06(2026)231},
  eprint = {2602.20243},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05546005v1},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Unitarity violation and restoration in radiative bound-state formation
AU  - Marcos M Flores
AU  - Kalliopi Petraki
PY  - 2026
DA  - 2026/06/22
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep06(2026)231
UR  - https://hal.science/hal-05546005v1
AB  - State-of-the-art calculations motivated by dark matter exhibit severe violation of partial-wave unitarity in the non-relativistic regime in radiative bound-state-formation processes. It has been recently shown, in a model-independent fashion, that unitarity is restored by the proper resummation of the inelastic contributions to the self-energy of the incoming state. In this work, we first derive Kramers-like formulae for individual partial waves, demonstrating that existing calculations of bound-state formation severely violate unitarity. We then discuss how unitarity is restored through the resummation of the absorptive contributions to the incoming-state self-energy, generated by bound-state formation processes, taking into account their analytic structure in the complex momentum plane. Our results can be generalized in a variety of theories and employed in phenomenological studies, such as dark-matter freeze-out, indirect detection and self-interactions.
SN  - 1126-6708
SN  - 1029-8479
ER  -

Abstract

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