# Discovering True Muonium at LHCb

## TL;DR

This paper explores the potential for the LHCb experiment to discover the true muonium bound state, a particle composed of a muon and an anti-muon, through specific decay channels involving displaced vertices.

## Contribution

It proposes novel search strategies for true muonium at LHCb, including both inclusive and exclusive methods, and demonstrates their potential to achieve significant discovery significance.

## Key findings

- Displaced vertex search can exceed 5 sigma significance
- Two search strategies: inclusive and exclusive with photon reconstruction
- Potential to discover true muonium at LHCb for the first time

## Abstract

We study the potential of the LHCb experiment to discover, for the first time, the $\mu^+\mu^-$ true muonium bound state. We propose a search for the vector $1^3S_1$ state, $\mathcal{T\!M}$, which kinetically mixes with the photon and dominantly decays to $e^+e^-$. We demonstrate that a search for $\eta \to \gamma \mathcal{T\!M}$, $\mathcal{T\!M}\to e^+e^-$ in a displaced vertex can exceed a significance of 5 standard deviations assuming statistical uncertainties. We present two possible searches: an inclusive search for the $e^+e^-$ vertex, and an exclusive search which requires an additional photon and a reconstruction of the $\eta$ mass.