⚛️ phenomenology

Revisiting the limits on dark matter annihilation cross-section and decay lifetime in light of electron and positron fluxes

This paper revises the upper bounds on dark matter annihilation cross-sections and lower bounds on decay lifetimes across a wide mass range by analyzing electron, positron, and gamma-ray fluxes from multiple experiments, finding that AMS-02 and HESS provide the most stringent constraints for masses below and above 2 TeV, respectively, while electron-positron flux data offer the strongest limits for decaying dark matter in the $10^3$ – $10^9$ GeV range.

Original authors: Nagisa Hiroshima, Kazunori Kohri, Partha Kumar Paul, Narendra Sahu

Published 2026-07-08

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Nagisa Hiroshima, Kazunori Kohri, Partha Kumar Paul, Narendra Sahu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is filled with a ghostly, invisible substance called Dark Matter. We know it's there because it holds galaxies together with its gravity, but we can't see it, touch it, or smell it. Scientists have two main theories about what this ghost might be doing:

The Party Theory (Annihilation): Dark matter particles are bumping into each other and crashing, turning into regular particles like electrons and positrons (the antimatter twin of an electron).
The Slow Leak Theory (Decay): Dark matter particles are unstable and slowly breaking apart over billions of years, leaking out regular particles.

The paper you provided is like a team of cosmic detectives trying to figure out how "active" these ghosts are. They are looking for the "smoke" (electrons and positrons) that these theories predict should be floating around our solar system.

The Detective Tools: Cosmic Messengers

The researchers used data from several high-tech "ears" listening to the universe:

CALET, DAMPE, AMS-02: These are instruments on satellites or the International Space Station that catch electrons and positrons directly.
H.E.S.S., HAWC, GRAPES-3, CASA-MIA: These are ground-based telescopes that look for high-energy gamma rays. Interestingly, these telescopes can't always tell the difference between a gamma ray and an electron/positron pair, so they act as a safety net, catching any "extra" energy that shouldn't be there.

The Investigation: Searching for the "Excess"

The scientists calculated how many electrons and positrons should be in space just from normal cosmic events (like supernovas exploding or pulsars spinning). This is the "background noise."

Then, they asked: "If Dark Matter is crashing or decaying, would we see more electrons than the background noise?"

They tested five different ways Dark Matter could turn into particles:

Turning into heavy particles (like W bosons or bottom quarks).
Turning into lighter particles (like muons, taus, or electrons).

They ran the numbers for Dark Matter particles ranging from 500 GeV (about the weight of a heavy atom) all the way up to 10,000,000,000,000 GeV (a mass so heavy it's hard to imagine, like a tiny black hole).

The Findings: Who Caught the Ghost?

The paper found that different "detectives" are best at catching the ghost at different weights:

The Lighter Ghosts (Below 2 TeV): The AMS-02 satellite (listening to positrons) is the sharpest detective here. It set the strictest rules on how much Dark Matter can be crashing or decaying in this weight range.
The Heavy Ghosts (Above 2 TeV): The H.E.S.S. telescope (listening to high-energy rays) takes the lead. It found that for very heavy Dark Matter, the limits on how much it can decay are incredibly strict. In fact, for a 10 TeV particle, the universe must be incredibly stable, with a lifetime longer than $10^{30}$ seconds (that's a number with 30 zeros!).

The Big Picture: Why Electrons Matter

One of the paper's main discoveries is that looking at electrons and positrons is actually a better way to hunt for very heavy Dark Matter than looking at gamma rays or neutrinos (ghostly particles that rarely interact).

For Annihilation: If Dark Matter is crashing into itself, the electron data is the most powerful tool for masses between 3 TeV and 100 TeV.
For Decay: If Dark Matter is slowly leaking, the electron data is the strongest tool for masses between 1,000 GeV and 1,000,000,000 GeV.

The Conclusion

The paper doesn't say, "We found Dark Matter!" Instead, it says, "We looked very hard, and here is exactly how quiet the universe must be."

They have set a "speed limit" on how fast Dark Matter can crash and a "minimum age" for how long it must last before decaying. If Dark Matter were doing anything wilder than these limits, our telescopes would have seen it by now. Since we haven't, we know that Dark Matter is either very heavy, very stable, or just very shy.

In short: The universe is a quiet place. If Dark Matter is crashing or decaying, it's doing so at a rate so slow and rare that our best instruments can barely detect it, but we now have much better maps of exactly where to look next.

Technical Summary: Revisiting Limits on Dark Matter Annihilation and Decay via Electron and Positron Fluxes

Problem Statement
Dark matter (DM) remains a fundamental mystery in particle physics and cosmology, with its nature (mass, spin, interactions) undetermined. While indirect detection via cosmic rays is a primary search strategy, constraints on heavy dark matter ( $M_{DM} \gtrsim 500$ GeV) have historically relied heavily on gamma-ray and neutrino observations. Previous studies have constrained DM properties up to masses of $\sim 10^{11}$ GeV using these channels, but the regime $M_{DM} \gtrsim 10^{11}$ GeV remains largely unexplored with limited available literature. Furthermore, while electron and positron ( $e^\pm$ ) fluxes are sensitive to DM, a comprehensive re-evaluation of upper bounds on the annihilation cross-section ( $\langle \sigma v \rangle$ ) and lower bounds on the decay lifetime ( $\tau_{DM}$ ) using the latest high-energy $e^\pm$ data across a broad mass range ( $500 \text{ GeV} - 10^{16} \text{ GeV}$ ) is necessary.

Methodology
The authors analyze two scenarios: stable DM annihilation and unstable DM decay into Standard Model (SM) final states ( $W^+W^-$ , $b\bar{b}$ , $\mu^+\mu^-$ , $\tau^+\tau^-$ , and $e^+e^-$ ). The analysis focuses on the production and propagation of $e^\pm$ in the Galactic medium.

Propagation Modeling: The $e^\pm$ flux at Earth is calculated by solving the diffusion equation in a steady state. The authors adopt the "SLIM" propagation model with the "MIN" benchmark configuration (characterized by a smaller diffusive halo height $L$ and diffusion coefficient $K_0$ ) combined with an NFW dark matter halo profile. This choice is conservative, ensuring limits are robust against astrophysical uncertainties regarding the DM distribution in the Galactic center.
Source Terms: The injection spectra for annihilation and decay are derived using HDMSpectra, which incorporates complete electroweak corrections essential for heavy DM.
Data Integration: The study utilizes observed fluxes and upper limits from multiple experiments covering a wide energy range:
- $e^\pm$ Flux: CALET, DAMPE, H.E.S.S., and AMS-02 (positron only).
- Gamma-ray Flux (used as $e^\pm$ proxies): HAWC, GRAPES-3, and CASA-MIA (noting these experiments cannot distinguish gamma-rays from $e^\pm$ pairs).
Statistical Analysis:
- For experiments with measured fluxes (CALET, AMS-02, DAMPE, H.E.S.S.), a $\chi^2$ analysis is performed to determine the 95% Confidence Level (C.L.) limits on $\langle \sigma v \rangle$ and $\tau_{DM}$ .
- For experiments providing only upper limits (HAWC, GRAPES-3, CASA-MIA), the constraint is imposed such that the predicted total flux (DM signal + astrophysical background) does not exceed the experimental upper limit in any energy bin.
- Background fluxes for primary and secondary electrons/positrons are parameterized based on established models [61] and specific experimental fits.

Key Contributions and Results
The paper derives 95% C.L. limits on $\langle \sigma v \rangle$ and $\tau_{DM}$ for DM masses ranging from 500 GeV to $10^{16}$ GeV.

Annihilation Constraints ( $\langle \sigma v \rangle$ ):
- Low Mass ( $< 2$ TeV): The AMS-02 positron data provides the most stringent constraints.
- High Mass ( $\gtrsim 2$ TeV): H.E.S.S. data yields the strongest limits, extending up to $M_{DM} \sim 10^{14}$ GeV.
- Comparison with Other Channels: For DM masses in the range $10^5 - 10^{11}$ GeV, limits derived from $e^\pm$ flux are competitive with those from gamma-ray and neutrino observations. Beyond $10^{11}$ GeV, the $e^\pm$ constraints become the most stringent available.
Decay Constraints ( $\tau_{DM}$ ):
- Low to Intermediate Mass ( $10^3 - 10^9$ GeV): The $e^\pm$ flux provides the strongest constraints on the DM lifetime.
- High Mass: For $M_{DM} \gtrsim 10^9$ GeV, gamma-ray data generally lead the constraints.
- Specific Limits: For a 10 TeV DM particle decaying to $\mu^+\mu^-$ , the H.E.S.S. data excludes lifetimes $\tau_{DM} \lesssim \mathcal{O}(10^{30})$ s.
Uncertainty Analysis: The authors quantify the impact of propagation model uncertainties (comparing MIN, MED, and MAX benchmarks). They find that while the DM signal flux varies by a factor of 2–3 between models at low energies, the total flux (signal + background) varies by less than $\sim 10\%$ . Consequently, the inferred limits on $\langle \sigma v \rangle$ and $\tau_{DM}$ are robust, with uncertainties less than $\sim 10\%$ .

Significance and Claims
The paper claims to be the first to derive limits on dark matter up to $M_{DM} = 10^{16}$ GeV using electron and positron observations. By synthesizing data from CALET, DAMPE, H.E.S.S., AMS-02, HAWC, GRAPES-3, and CASA-MIA, the study fills a gap in the high-mass regime where previous constraints were sparse. The authors emphasize that for very heavy dark matter ( $M_{DM} \gtrsim 10^{11}$ GeV), $e^\pm$ flux observations offer superior sensitivity compared to traditional gamma-ray and neutrino channels. The results provide updated, robust exclusion regions for heavy DM models, particularly those involving annihilation or decay into leptonic and hadronic channels, and highlight the complementary nature of multi-messenger data in probing the heavy DM parameter space.

The Detective Tools: Cosmic Messengers

The Investigation: Searching for the "Excess"

The Findings: Who Caught the Ghost?

The Big Picture: Why Electrons Matter

The Conclusion

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