The positronium hyperfine structure: Progress towards a direct measurement of the 2³S₁ rightarrow 2¹S₀ transition in vacuum

We present the current status for the direct measurement of the positronium hyperfine structure using the $\text{2}^\text{3}\text{S}_\text{1} \rightarrow \text{2}^\text{1}\text{S}_\text{0}$ transition. This experiment, currently being commissioned at the slow positron beam facility at ETH Zurich, will be the first measurement of this transition and the first positronium hyperfine splitting experiment conducted in vacuum altogether. This experiment will be free of systematic effects found in earlier experiments, namely the inhomogeneity in static magnetic fields and the extrapolation from dense gases to vacuum. The achievable precision is expected to be on the order of $10\, \mathrm{ppm}$ while the systematic uncertainty is estimated to be within a few $\mathrm{ppm}$. This would allow to check recent bound state QED calculations and a $3$-$\sigma$ discrepancy with earlier experiments.