# Decay of the dimuonium into a photon and a neutral pion

## TL;DR

This paper calculates the decay rate of dimuonium into a photon and a neutral pion, finding a rare decay channel and exploring its implications for hyperfine splitting and muon magnetic moment.

## Contribution

It provides the first detailed computation of the dimuonium decay into a photon and a neutral pion, linking this process to hyperfine splitting and muon g-2.

## Key findings

- Approximately 1 in 10^5 ortho-dimuonia decays via this channel.
- Quantitative contribution of virtual photon-pion loops to hyperfine splitting.
- Reproduction of the leading effect of this loop in muon anomalous magnetic moment.

## Abstract

We compute the decay rate of dimuonium into a neutral pion and a photon. We find that approximately one in 10^5 ortho-dimuonia decays into this channel. We also determine the contribution of the virtual photon-pion loop to the hyperfine splitting in dimuonium and reproduce its leading effect in the anomalous magnetic moment of the muon.