Relativistic Elastic Scattering of Cosmic-Ray Boosted Dirac Dark Matter with Charged Leptons through a Scalar Mediator
Abstract
We investigate the relativistic kinematics, spinor-recoil structure, and direct-detection phenomenology of a Dirac dark matter fermion interacting with SM charged leptons through a real scalar mediator within a low-energy effective Lagrangian in the fermion mass basis. Standard halo direct-detection searches lose sensitivity for sub-MeV dark matter, because the maximum recoil energy falls below detector thresholds. When halo dark matter particles are upscattered to relativistic energies by galactic cosmic-ray electrons (CRE), the momentum transfer in both the astrophysical upscattering stage and the terrestrial detection stage can exceed the fermion mass scales. By decomposing the tree-level t-channel cross section into three positive-definite contributions, we separate the static-numerator contribution from the linear and quadratic momentum-transfer spinor-recoil contributions, evaluated via convergent power series that reduce subtractive cancellation at small momentum transfer. For incident large kinetic energies, the spinor-recoil contributions become comparable to and begin to exceed σ0; at substantially higher energies, they enhance the total cross section by several orders of magnitude relative to the static-numerator approximation. Furthermore, retaining the dynamical scalar propagator yields a high-energy cross section that decreases as 1/s and satisfies s-wave helicity partial-wave unitarity, in contrast to the linear 𝒪(s/mS4) growth of the contact approximation. Applying the exact differential recoil spectra within an effective propagation model for cosmic-ray electron boosted dark matter (CRE-BDM), we derive 90% C.L. exclusion bounds in the 1 keV -- 10 MeV mass range from Super-Kamiokande, XENONnT, and PandaX-4T, extending experimental sensitivity into the sub-MeV window.
Related
- Elastic Scattering of Dirac Dark Matter with Charged Leptons through a Scalar Mediator: Analytical Framework, Numerical Stability, and Direct-Detection Bounds
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- Ultra-relativistic freeze-out of fermion dark matter through a heavy scalar mediator
- Inelastic Scattering Effects on Attenuation of Boosted Dark Matter
- Classical gravitational scattering with a massive scalar mediator
BibTeX
@misc{xuan2026relativistic,
title = {{Relativistic Elastic Scattering of Cosmic-Ray Boosted Dirac Dark Matter with Charged Leptons through a Scalar Mediator}},
author = {Nguyen Nhu Xuan and Vu Toan Thang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36004},
eprint = {2610.36004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36004},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relativistic Elastic Scattering of Cosmic-Ray Boosted Dirac Dark Matter with Charged Leptons through a Scalar Mediator
AU - Nguyen Nhu Xuan
AU - Vu Toan Thang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36004
UR - https://arxiv.org/abs/2610.36004
AB - We investigate the relativistic kinematics, spinor-recoil structure, and direct-detection phenomenology of a Dirac dark matter fermion interacting with SM charged leptons through a real scalar mediator within a low-energy effective Lagrangian in the fermion mass basis. Standard halo direct-detection searches lose sensitivity for sub-MeV dark matter, because the maximum recoil energy falls below detector thresholds. When halo dark matter particles are upscattered to relativistic energies by galactic cosmic-ray electrons (CRE), the momentum transfer in both the astrophysical upscattering stage and the terrestrial detection stage can exceed the fermion mass scales. By decomposing the tree-level t-channel cross section into three positive-definite contributions, we separate the static-numerator contribution from the linear and quadratic momentum-transfer spinor-recoil contributions, evaluated via convergent power series that reduce subtractive cancellation at small momentum transfer. For incident large kinetic energies, the spinor-recoil contributions become comparable to and begin to exceed σ_0; at substantially higher energies, they enhance the total cross section by several orders of magnitude relative to the static-numerator approximation. Furthermore, retaining the dynamical scalar propagator yields a high-energy cross section that decreases as 1/s and satisfies s-wave helicity partial-wave unitarity, in contrast to the linear 𝒪(s/m_S^4) growth of the contact approximation. Applying the exact differential recoil spectra within an effective propagation model for cosmic-ray electron boosted dark matter (CRE-BDM), we derive 90% C.L. exclusion bounds in the 1 keV -- 10 MeV mass range from Super-Kamiokande, XENONnT, and PandaX-4T, extending experimental sensitivity into the sub-MeV window.
ER -