Electroweak Corrections to the True Muonium Hyperfine Splitting

TL;DR

This paper calculates electroweak $Z$ boson corrections to the hyperfine splitting in true muonium, showing they are experimentally accessible and crucial for precise theoretical predictions that could address the muon problem.

Contribution

It provides the first detailed calculation of electroweak corrections to true muonium hyperfine splitting, including the $Z$ boson effects and a general pseudovector coupling expression.

Findings

$Z$ boson correction is approximately -109 MHz.

Electroweak corrections are experimentally accessible soon.

The work enables more precise tests of muonium physics and the muon problem.

Abstract

In contrast to other atomic systems, in true muonium ($\mu^+\mu^-$) the leading-order $Z$ boson corrections to the hyperfine splitting are shown to be experimentally accessible in the near future. This contribution ($-109$ MHz) constitutes a necessary contribution to a full $\mathcal{O}(m\alpha^7)$ calculation of the true muonium hyperfine splitting. This would enable a number of solutions to the muon problem to be constrained. Additionally, we compute the general expression for a pseudovector coupling to particle-antiparticle bound states at leading order, including the annihilation channel.