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

TL;DR

This paper explores lepton flavor violating dark matter interactions within an effective field theory framework, deriving decay distributions, setting experimental bounds, and proposing muonium invisible decay as a potential signature.

Contribution

It introduces a systematic EFT approach to LFV dark matter interactions, analyzing decay distributions, and linking experimental bounds to potential observable signatures like muonium invisible decay.

Findings

Invariant-mass distributions can distinguish operator structures and determine DM mass.

Current experimental bounds impose stringent limits on effective operators.

Muonium invisible decay could be significantly enhanced, serving as a signature for flavored DM interactions.

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, $\bar \ell_j \Gamma \ell_i\,{\tt DM}^2$, where $(ij)=(e\mu, e\tau, \mu\tau)$ 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 $e\mu$ flavor combination, we investigate the muon four-body radiative decay ($\mu\to e +{\tt DM+DM}+\gamma$) 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.