Cosmic-ray positrons have long been considered a powerful probe of dark matter annihilation. In particular, myriad studies of the unexpected rise in the positron fraction have debated its dark matter or pulsar origins. In this paper, we instead examine the potential for extremely precise positron measurements by AMS-02 to probe hard leptophilic dark matter candidates that do nothave spectral features similar to the bulk of the observed positron excess. Utilizing a detailed cosmic-ray propagation model that includes a primary positron flux generated by Galactic pulsars in addition to a secondary component constrained by He and proton measurements, we produce a robust fit to the local positron flux and spectrum. We find no evidence for a spectral bump correlated with leptophilic dark matter, and set strong constraints on the dark matter annihilation cross-section that fall below the thermal annihilation cross-section for dark matter masses below 60 GeV and 380 GeV for annihilation into τ⁺τ^- and e⁺e^-, respectively, in our default model.

Pulsars are considered to be the leading explanation for the excess in cosmic-ray positrons. A notable feature of standard pulsar models is the sharp spectral cutoff produced by the increasingly efficient cooling of very-high-energy electrons by synchrotron and inverse-Compton processes. This spectral break has been used to argue that many pulsars contribute to the positron flux and that spectral features cannot distinguish between dark matter and pulsar models. We prove that this feature does not exist-it appears due to approximations that treat inverse-Compton scattering as a continuous, instead of as a discrete and catastrophic, energy-loss process. Astrophysical sources do not produce sharp spectral features via cooling, reopening the possibility that such a feature would provide evidence for dark matter.

The annihilation of TeV-scale leptophilic dark matter into electron-positron pairs (hereafter e⁺e⁻) will produce a sharp cutoff in the local cosmic-ray e⁺e⁻ spectrum at an energy matching the dark matter mass. At these high energies, e⁺e⁻ cool quickly due to synchrotron interactions with magnetic fields and inverse-Compton scattering with the interstellar radiation field. These energy losses are typically modeled as a continuous process. However, inverse-Compton scattering is a stochastic energy-loss process where interactions are rare but catastrophic. We show that when inverse-Compton scattering is modeled as a stochastic process, the expected e⁺e⁻ flux from dark matter annihilation is about a factor of ∼2 larger near the dark matter mass than in the continuous model. This greatly enhances the detectability of heavy dark matter annihilating to e⁺e⁻ final states.