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Charged lepton flavor violating decays with a pair of light dark matter and muonium invisible decay

Sahabub Jahedi, Yi Liao, Xiao-Dong Ma

Abstract

In this paper, we initiate the study of lepton flavor violating (LFV) dark matter (DM) interactions, expanding our focus beyond the flavor-conserving DM interactions typically considered in conventional direct and indirect detections. We work in an effective field theory (EFT) framework, focusing on the leading-order local operators of the form, $\bar \ell_j Γ\ell_i\,{\tt DM}^2$, where $(ij)=(eμ, eτ, μτ)$ and the DM includes the three well-known scenarios: a scalar, a fermion, and a vector. We derive the invariant-mass distribution for the three-body decay $\ell_i \to \ell_j +{\tt DM+DM}$ and demonstrate that it can be used to distinguish between different operator structures and to determine the DM mass. By utilizing current experimental bounds on the charged muon LFV decay involving neutrinos and the ratio of tau leptonic decay widths, we establish stringent limits on the effective scale associated with each operator. Additionally, for the $eμ$ flavor combination, we investigate the muon four-body radiative decay ($μ\to e +{\tt DM+DM}+γ$) to complement our probe of such interactions. Finally, we examine muonium invisible decays based on the derived bounds on the effective operators and find that the branching ratios can be significantly enhanced compared to the predictions of the standard model. In particular, any future observation of the para-muonium invisible decay serves as a compelling signature for these flavored DM interactions.

Charged lepton flavor violating decays with a pair of light dark matter and muonium invisible decay

Abstract

In this paper, we initiate the study of lepton flavor violating (LFV) dark matter (DM) interactions, expanding our focus beyond the flavor-conserving DM interactions typically considered in conventional direct and indirect detections. We work in an effective field theory (EFT) framework, focusing on the leading-order local operators of the form, , where and the DM includes the three well-known scenarios: a scalar, a fermion, and a vector. We derive the invariant-mass distribution for the three-body decay and demonstrate that it can be used to distinguish between different operator structures and to determine the DM mass. By utilizing current experimental bounds on the charged muon LFV decay involving neutrinos and the ratio of tau leptonic decay widths, we establish stringent limits on the effective scale associated with each operator. Additionally, for the flavor combination, we investigate the muon four-body radiative decay () to complement our probe of such interactions. Finally, we examine muonium invisible decays based on the derived bounds on the effective operators and find that the branching ratios can be significantly enhanced compared to the predictions of the standard model. In particular, any future observation of the para-muonium invisible decay serves as a compelling signature for these flavored DM interactions.

Paper Structure

This paper contains 14 sections, 15 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Lepton-DM interactions in the DSEFT
  3. Three-body LFV decays $\ell_i \to \ell_j +\tt{ DM+DM}$
  4. The $q^2$-distribution
  5. Constraints from $\mu^- \to e^-\nu_{e} \bar{\nu}_{\mu}$
  6. Constraints from $\tau \to e+\rm inv.$
  7. Constraints from $\tau \to \mu+\rm inv.$
  8. Muon four-body radiative decay $\mu\to e+\tt{DM+DM}+\gamma$
  9. Event distributions
  10. Constraints from the four-body radiative decay
  11. Implications on muonium invisible decay
  12. Summary
  13. Matrix elements
  14. Differential distributions

Figures (11)

  • Figure 1: Left: Variation of normalized differential decay rate for the process $\tau \to \mu \chi \chi$ considering the operators $\mathcal{O}^{{\tt S}, \mu \tau}_{\ell \chi 1}$ (solid) and $\mathcal{O}^{{\tt P}, \mu \tau}_{\ell \chi 1}$ (dashed) with different DM masses. Note that the distribution for $m_{\chi}=0.8$ MeV is scaled by 0.1 along $y$-axis for better visibility. Right: Variation of normalized differential decay rate for a fixed DM mass, comparing different processes for operators $\mathcal{O}^{{\tt S}, ji}_{\ell \chi1}$ (solid) and $\mathcal{O}^{{\tt P}, ji}_{\ell \chi1}$ (dashed). The inset is for $\mu\to e\chi\chi$ due to much smaller $q^2$.
  • Figure 2: Differential decay rate distribution for the process $\mu \to e +{\tt DM+DM}$ with a fixed DM mass of 26 MeV, from different DSEFT operators. The darker dot-dashed black line represents the differential rate for the SM process $\mu^- \to e^- \bar{\nu}_e \nu_{\mu}$, which contributes at leading order.
  • Figure 3: Same as \ref{['fig:diff.dist.mu2e']} but for the process $\tau \to \mu + {\tt DM + DM}$ with a DM mass of 418 MeV. The darker dot-dashed black line represents the decay rate for the SM process $\tau^- \to \mu^- \bar{\nu}_{\mu} \nu_{\tau}$.
  • Figure 4: Constraints on the effective scale $\Lambda$ as a function of the DM mass $m$ for different sets of DSEFT operators from the process $\mu \to e + {\tt DM+DM}$.
  • Figure 5: Same as \ref{['fig:const.mu2e']} but for the process $\tau \to e +{\tt DM+DM}$.
  • ...and 6 more figures