# Hyperfine Splitting in Muonium: Accuracy of the Theoretical Prediction

## TL;DR

This paper provides a precise theoretical prediction for muonium hyperfine splitting, crucial for upcoming experiments aiming to test the Standard Model and search for new physics.

## Contribution

It clarifies discrepancies in previous theoretical error estimates and delivers an updated, highly accurate prediction for muonium hyperfine splitting.

## Key findings

- Theoretical prediction: 4,463,302,872(515) Hz
- Identified origin of error estimate discrepancies
- Supports future experimental tests of fundamental physics

## Abstract

In the last twenty years, the theory of hyperfine splitting in muonium developed without any experimental input. Finally, this situation is changing and a new experiment on measuring hyperfine splitting in muonium is now in progress at J-PARC. The goal of the MuSEUM experiment is to improve by an order of magnitude experimental accuracy of the hyperfine splitting and muon-electron mass ratio. Uncertainty of the theoretical prediction for hyperfine splitting will be crucial for comparison between the forthcoming experimental data and the theory in search of a possible new physics. In the current literature estimates of the error bars of the theoretical prediction differ roughly by a factor of two. We explain the origin of this discrepancy and obtain the theoretical prediction for the muonium hyperfine splitting $\Delta \nu^{th}_{\scriptscriptstyle HFS}(Mu)=4~463~302~872~(515)~\mbox{Hz},\; \delta=1.2\times 10^{-7}$.