Elastic Scattering of Dirac Dark Matter with Charged Leptons through a Scalar Mediator: Analytical Framework, Numerical Stability, and Direct-Detection Bounds
Abstract
We investigate a leptophilic simplified dark matter model in which a Dirac fermion χinteracts with Standard Model charged leptons \ll through a real scalar mediator S. Starting from the low-energy Yukawa interaction Lagrangian in the fermion mass eigenbasis, we derive closed-form tree-level analytical expressions for the invariant scattering amplitude, the spin-averaged squared matrix element, and the differential and total elastic cross sections. To overcome the numerical loss of significance that arises when evaluating the standard antiderivative difference in the heavy-mediator regime, we rearrange the phase-space integral into positive-definite recoil contributions supplemented by convergent power-series expansions. This analytical formulation smoothly connects the light-mediator and heavy-mediator regimes without relying on Effective Field Theory (EFT) contact approximations, allowing us to establish quantitative validity criteria for the contact limit. Finally, we map the microscopic differential cross section onto the reference electron-scattering cross section and evaluate the resulting coupling constraints using experimental data from SENSEI, DAMIC, SuperCDMS, XENON10, and XENON1T.
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BibTeX
@misc{xuan2026elastic,
title = {{Elastic Scattering of Dirac Dark Matter with Charged Leptons through a Scalar Mediator: Analytical Framework, Numerical Stability, and Direct-Detection Bounds}},
author = {Nguyen Nhu Xuan and Vu Toan Thang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36003},
eprint = {2610.36003},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36003},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Elastic Scattering of Dirac Dark Matter with Charged Leptons through a Scalar Mediator: Analytical Framework, Numerical Stability, and Direct-Detection Bounds
AU - Nguyen Nhu Xuan
AU - Vu Toan Thang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36003
UR - https://arxiv.org/abs/2610.36003
AB - We investigate a leptophilic simplified dark matter model in which a Dirac fermion χinteracts with Standard Model charged leptons \ll through a real scalar mediator S. Starting from the low-energy Yukawa interaction Lagrangian in the fermion mass eigenbasis, we derive closed-form tree-level analytical expressions for the invariant scattering amplitude, the spin-averaged squared matrix element, and the differential and total elastic cross sections. To overcome the numerical loss of significance that arises when evaluating the standard antiderivative difference in the heavy-mediator regime, we rearrange the phase-space integral into positive-definite recoil contributions supplemented by convergent power-series expansions. This analytical formulation smoothly connects the light-mediator and heavy-mediator regimes without relying on Effective Field Theory (EFT) contact approximations, allowing us to establish quantitative validity criteria for the contact limit. Finally, we map the microscopic differential cross section onto the reference electron-scattering cross section and evaluate the resulting coupling constraints using experimental data from SENSEI, DAMIC, SuperCDMS, XENON10, and XENON1T.
ER -