EFT Approaches to Sommerfeld Enhancement and Bound States in Singular Potentials
Abstract
The Sommerfeld enhancement (SE) from long-range interactions, and the related bound state formation rate, can be important non-perturbative inputs to dark matter (DM) annihilation signals. In the presence of singular interaction potentials, the conventional boundary conditions of the Schrödinger equation fail, obfuscating the computation of SE, its physical origin, and its relation to bound states in such potentials. In this work, we clarify the origin of SE in singular potentials in a two-fold manner: using the framework of velocity power counting in non-relativistic effective field theory (NREFT), and via position-space regularization of singular potentials at short distances to compute SE and bound states. We illustrate our findings through the case of pseudoscalar mediators interacting with massive Dirac DM. We find that when such a system arises from a UV-complete theory at weak coupling, no SE is generated. However, in the case of a derivatively coupled pseudoscalar, where the interaction is described by a higher-dimension operator in an effective theory, SE (and bound states) can occur for weak couplings if there is a large hierarchy between the cutoff scale of the effective theory and the dark matter mass. This SE is sensitive to the choice of the UV completion of the potential at short distances, but a non-negligible SE can persist even when the UV physics alone would not generate any SE; we elucidate the interplay of UV and IR physics in this case.
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BibTeX
@misc{bhattacharya2026approaches,
title = {{EFT Approaches to Sommerfeld Enhancement and Bound States in Singular Potentials}},
author = {Arindam Bhattacharya and Rashmish K. Mishra and Tracy R. Slatyer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10690},
eprint = {2609.10690},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10690},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - EFT Approaches to Sommerfeld Enhancement and Bound States in Singular Potentials
AU - Arindam Bhattacharya
AU - Rashmish K. Mishra
AU - Tracy R. Slatyer
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10690
UR - https://arxiv.org/abs/2609.10690
AB - The Sommerfeld enhancement (SE) from long-range interactions, and the related bound state formation rate, can be important non-perturbative inputs to dark matter (DM) annihilation signals. In the presence of singular interaction potentials, the conventional boundary conditions of the Schrödinger equation fail, obfuscating the computation of SE, its physical origin, and its relation to bound states in such potentials. In this work, we clarify the origin of SE in singular potentials in a two-fold manner: using the framework of velocity power counting in non-relativistic effective field theory (NREFT), and via position-space regularization of singular potentials at short distances to compute SE and bound states. We illustrate our findings through the case of pseudoscalar mediators interacting with massive Dirac DM. We find that when such a system arises from a UV-complete theory at weak coupling, no SE is generated. However, in the case of a derivatively coupled pseudoscalar, where the interaction is described by a higher-dimension operator in an effective theory, SE (and bound states) can occur for weak couplings if there is a large hierarchy between the cutoff scale of the effective theory and the dark matter mass. This SE is sensitive to the choice of the UV completion of the potential at short distances, but a non-negligible SE can persist even when the UV physics alone would not generate any SE; we elucidate the interplay of UV and IR physics in this case.
ER -