Probing lepton flavor violating dark matter scenarios via astrophysical photons and positrons

In this Letter we explore, for the first time, the constraints on lepton flavor violating (LFV) dark matter (DM) scenarios via the astrophysical photons and positrons, including both the annihilation and decay modes, ${\tt DM(+DM)}\to e^\pm μ^\mp, e^\pm τ^\mp, μ^\pm τ^\mp$. Given the presence of LFV interactions in various DM models and the challenge of probing such interactions at terrestrial facilities, such as DM direct detection and collider experiments, indirect detection offers a unique approach to investigating them. We utilize the currently available photon datasets from the XMM-Newton, INTEGRAL, and Fermi-LAT telescopes, along with the positron datasets from the AMS-02 satellite, to establish stringent bounds on the relevant annihilation cross sections or decay widths. In particular, we include contributions to the photon spectrum from final state radiation, radiative decays, and inverse Compton scattering. We find that the INTEGRAL (AMS-02) provides the most stringent bound on the annihilation cross sections and decay widths for DM mass below (above) approximately 20 GeV, which are comparable to those of their lepton flavor conserving counterparts.

💡 Research Summary

In this work the authors present the first comprehensive indirect‑detection study of dark‑matter (DM) models that violate lepton‑flavour (LFV). They consider both s‑wave annihilation (DM + DM → ℓ_i ℓ_j) and single‑particle decay (DM → ℓ_i ℓ_j) for the three mixed‑flavour final states e±μ∓, e±τ∓ and μ±τ∓. Because LFV interactions are extremely difficult to probe with direct‑detection experiments or collider searches – the kinetic energy of halo DM is insufficient to overcome the mass gap between different charged leptons, and there is no dedicated e‑μ or e‑τ collider – indirect detection offers a unique window.

Theoretical framework
The observable photon flux from DM is split into three contributions: (i) final‑state radiation (FSR), (ii) radiative decays of the primary leptons (Rad), and (iii) inverse‑Compton scattering (ICS) of the high‑energy e± on the Galactic radiation fields (CMB, infrared dust emission and optical starlight). For FSR the authors adopt a normalized spectrum derived from the dimension‑six operator (\bar\ell_i\gamma^\mu\ell_j\bar\chi\gamma_\mu\gamma_5\chi) for a Majorana DM particle; they argue that the spectrum is only weakly dependent on the detailed operator structure when the DM mass is well above the lepton thresholds. Radiative photons from μ and τ decays are taken from analytic formulas for μ→eννγ and from Pythia8 simulations for τ decays, including hadronic contributions. The ICS component is computed using the “on‑the‑spot’’ approximation, i.e. the e± are assumed to scatter where they are produced; the authors verify that this reproduces full Galprop calculations within a factor of two.

The positron flux is built from primary e± (when the final state contains an electron) and secondary e± from μ and τ decays. The authors include energy‑loss processes through a total loss function (b_{\rm tot}(E_e,r)) and propagate the injected spectrum with a Green’s function (I(E_e,\tilde E_e,r)) that encodes diffusion and energy loss. The DM density is modeled with a standard Navarro‑Frenk‑White (NFW) profile; the line‑of‑sight integral appears as (\int\rho^2) for annihilation and (\int\rho) for decay.

Datasets
Four astrophysical data sets are employed:

• INTEGRAL/SPI (27 keV–1.8 MeV) with latitude cuts and central bins removed to avoid strong background contamination.
• XMM‑Newton (0.2–20 keV) all‑sky observations divided into 30 concentric rings; the authors explicitly use the exposure‑weighted response matrices, correcting a common mistake in earlier works that led to overly strong limits.
• Fermi‑LAT (4 MeV–10 GeV) with 8° < |b| < 90° to minimise Galactic‑plane background.
• AMS‑02 positron spectrum above 20 GeV, where solar modulation effects are small.

Statistical method
A conservative χ² is defined as (\chi^2=\sum_i