# Current and future perspectives of positronium and muonium spectroscopy as dark sectors probe

## TL;DR

This paper assesses how current and future positronium and muonium spectroscopy can detect new physics beyond the Standard Model, highlighting the potential and challenges of these methods in probing dark sectors.

## Contribution

It provides a comprehensive analysis of the sensitivity of positronium and muonium spectroscopy to new physics, outlining experimental targets and technological challenges.

## Key findings

- Positronium spectroscopy needs five orders of magnitude improvement for competitive sensitivity.
- Muonium experiments like Mu-MASS can explore new dark force parameter spaces.
- Current technology faces significant challenges in achieving the required precision.

## Abstract

Positronium and Muonium are purely leptonic atoms and hence free of an internal sub-structure. This qualifies them as potentially well suited systems to probe the existence of physics beyond the Standard Model. We hence carry out a comprehensive study of the sensitivity of current Positronium and Muonium precision spectroscopy to several new physics scenarios. By taking properly into account existing experimental and astrophysical probes, we define clear experimental targets to probe new physics via precise spectroscopy. For Positronium we find that, in order for the spectroscopy bounds to reach a sensitivity comparable to the electron gyromagnetic factor, an improvement of roughly five orders of magnitude from state-of-the-art precision is required, which would be a challenge based on current technology. More promising is instead the potential reach of Muonium spectroscopy: in the next few years experiments like Mu-MASS at PSI will probe new regions of the parameter space testing the existence of medium/short range (MeV and above) spin-dependent and spin-independent dark forces between electrons and muons.