Analysis of p-Wave Sommerfeld Resonance Behavior in Finite-Size Dark Matter
Abstract
Different stages of cosmic evolution impose different requirements on the dark matter annihilation cross section. Sommerfeld enhancement provides a possible way to accommodate them. However, in the point-like dark matter scenario, satisfying these requirements with either s-wave or p-wave Sommerfeld enhancement can strongly constrain the dark matter and mediator masses and their coupling. A finite dark matter size introduces an additional parameter and may relax these constraints. Motivated by this possibility, in this work we study the p-wave Sommerfeld resonances of finite-size dark matter (like proton or neutron) without specifying its internal structure. We find that the p-wave contribution can exceed the s-wave contribution. Nevertheless, the finite-size p-wave resonances are weaker than those in the point-like case. Despite this suppression, their velocity dependence remains similar to that of point-like dark matter. We then extend our analysis to nugget dark matter composed of a small number of constituents. In this case, the p-wave Sommerfeld enhancement exhibits behavior similar to that of point-like dark matter.
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BibTeX
@misc{xu2026analysis,
title = {{Analysis of p-Wave Sommerfeld Resonance Behavior in Finite-Size Dark Matter}},
author = {Wu-Long Xu and Jin Min Yang and Rui Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11166},
eprint = {2610.11166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11166},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analysis of p-Wave Sommerfeld Resonance Behavior in Finite-Size Dark Matter
AU - Wu-Long Xu
AU - Jin Min Yang
AU - Rui Zhu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11166
UR - https://arxiv.org/abs/2610.11166
AB - Different stages of cosmic evolution impose different requirements on the dark matter annihilation cross section. Sommerfeld enhancement provides a possible way to accommodate them. However, in the point-like dark matter scenario, satisfying these requirements with either s-wave or p-wave Sommerfeld enhancement can strongly constrain the dark matter and mediator masses and their coupling. A finite dark matter size introduces an additional parameter and may relax these constraints. Motivated by this possibility, in this work we study the p-wave Sommerfeld resonances of finite-size dark matter (like proton or neutron) without specifying its internal structure. We find that the p-wave contribution can exceed the s-wave contribution. Nevertheless, the finite-size p-wave resonances are weaker than those in the point-like case. Despite this suppression, their velocity dependence remains similar to that of point-like dark matter. We then extend our analysis to nugget dark matter composed of a small number of constituents. In this case, the p-wave Sommerfeld enhancement exhibits behavior similar to that of point-like dark matter.
ER -