Abstract
We compute the next-to-leading $O(m{\ensuremath{\alpha}}^{5})$ contribution to the hyperfine splitting in positronium within the framework of nonrelativistic QED (NRQED). When applied to the ground state, our calculation reproduces the known result, providing a further test of NRQED techniques. In addition to providing a very simple method of calculation of this standard result, we also obtain new expressions for excited states of positronium with negligible additional effort. Our calculation requires the complete next-to-leading matching of the lowest-dimension NRQED four-Fermi couplings.
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