# Discovering True Muonium in $K_L\rightarrow (\mu^+\mu^-) \gamma$

## TL;DR

This paper predicts the rare decay rate of $K_L$ into true muonium and a photon, suggesting that upcoming experiments could detect true muonium and differentiate between theoretical models.

## Contribution

It provides the first detailed predictions of $K_L$ decay into true muonium, highlighting the potential for experimental discovery and model discrimination.

## Key findings

- Predicted branching ratio ~7×10^{-13} for $K_L$ decay into true muonium.
- Decay rates are within reach of current and near-future experiments.
- Detection could distinguish between different form factor models.

## Abstract

Theoretical and phenomenological predictions of $\mathcal{BR}(K_L\rightarrow (\mu^+\mu^-) \gamma)\sim7\times10^{-13}$ are presented for different model form factors $F_{K_L\gamma\gamma^*}(Q^2)$. These rates are comparable to existing and near-term rare $K_L$ decay searches at J-PARC and CERN, indicating a discovery of true muonium is possible. The model uncertainties are sufficiently small that detection of true muonium could discriminate between the form factor models. Further discussion of potential backgrounds is made.