A systematic study of lepton flavor violating dark matter interactions via indirect detection in effective field theories

TL;DR

This work systematically probes LFV interactions between Dark Matter and charged leptons within a dark sector EFT framework, analyzing DM annihilation products to constrain leading operators for scalar, fermion, and vector DM. By computing photon and positron spectra from FSR, radiative decays, and ICS, and comparing with data from INTEGRAL, XMM-Newton, Fermi-LAT, and AMS-02, the authors derive 2σ constraints on the corresponding cross sections and translate them into bounds on EFT Wilson coefficients and effective scales. A key finding is the strong complementarity between INTEGRAL (low DM masses) and AMS-02 (higher DM masses), with s-wave operators typically providing the strongest indirect-detection constraints and p-/d-wave operators generally yielding weaker bounds; some operators exhibit mixed-wave dominance, depending on DM mass. The results supplement existing charged LFV decay constraints and demonstrate that indirect detection can access DM masses above LFV decay thresholds, offering guidance for future collider and cosmological searches. These findings advance the understanding of LFV DM in EFT, quantifying the sensitivity of current gamma-ray and cosmic-ray observations to a broad class of LFV DM–lepton interactions it introduces two potential follow-ups: incorporating realistic astrophysical backgrounds and exploring collider probes at future facilities for LFV DM scenarios.

Abstract

Lepton flavor violating (LFV) interactions involving dark matter (DM) particles remain a largely unexplored area. In this study, we systematically investigate LFV DM interactions within the framework of effective field theories by analyzing astrophysical photons and positrons produced from DM annihilation. Employing the astrophysical photon and positron data collected by Fermi-LAT, INTEGRAL, XMM-Newton, and AMS-02, we place meaningful constraints on all leading-order effective operators involving a DM pair and a flavor violating charged lepton pair. Our analysis covers the three well-known DM candidates: a scalar, a fermion, and a vector particle. For the photon flux, we consider contributions from final-state radiation, radiative decay, and inverse Compton scattering, and examine their respective sensitivity regions across different DM masses and photon energies. We find that for DM masses below $\mathcal{O}(20\,\rm GeV)$, INTEGRAL provides the most stringent constraints on annihilation cross sections and effective operators in all three LFV channels, whereas AMS-02 offers the strongest constraints above $\mathcal{O}(20\,\rm GeV)$.

Figures (10)

• Figure 1: Comparison of $\sigma v_{\text{rel}}$ as a function of $m_{\tt DM}$ between the full calculation (thick gray curve) and the partial-wave components for the operators $\mathcal{O} _{\ell\chi2}^{{\tt V (A)},ij}$. In the plots, we use typical values of $v_{\rm rel}=10^{-3}$ and $\Lambda_{\text{eff}}=100$ GeV. Similar behavior applies to the vector DM operators $\mathcal{O} _{\ell X3}^{{\tt V (A)},ij}$, where the labels 's-wave' and 'p-wave' are replaced by 'p-wave' and 'd-wave', respectively.
• Figure 2: Comparison of normalized FSR spectra across various s-wave operators and different benchmark DM masses for the three LFV annihilation channels. The dashed curves represent the analytical calculation based on \ref{['eq:ana']}.
• Figure 3: Comparison of photon spectra for different annihilation channels, including both LFV and LFC cases. The FSR spectra are shown as solid curves, while the Rad spectra are represented by dashed curves. The left, middle, and right panels correspond to DM masses of 3 GeV, 30 GeV, and 300 GeV, respectively.
• Figure 4: Photon fluxes from FSR (red), Rad (blue), and ICS (green) are shown for the three LFV DM annihilation channels. The solid and dashed curves correspond to $m_{\tt DM}=3\,\rm{GeV}$ and $300\,\rm{GeV}$, respectively. The gray vertical dashed lines denote the energy ranges covered by INTEGRAL and Fermi-LAT. We fix $\langle \sigma v_{\rm rel} \rangle_{ij+ji}$ to $3\times10^{-26}$ and $3\times10^{-24}\,{\rm cm}^3/{\rm s}$ for $m_{\tt DM}=3$ and 300 GeV cases, respectively, and adopt the sky region for the Fermi-LAT dataset ($8^\circ < |b| < 90^\circ$, $0 < l < 360^\circ$).
• Figure 5: Comparison of the constraints on $\langle \sigma v_ {\rm rel} \rangle_{ij+ji}$ from the three photon components: FSR (red), Rad (blue), and ICS (green). The constraints are derived from the INTEGRAL (solid) and Fermi-LAT (dashed) datasets.