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We have calculated all contributions to the energy levels of parapositroniumat order $m \alpha^7$ coming from vacuum polarization corrections to processesinvolving virtual annihilation to two photons. This work is motivated byongoing efforts to improve the experimental determination of the positroniumground-state hyperfine splitting.

Positronium energy levels at order $m \alpha^7$: vacuum polarization corrections in the two-photon-annihilation channel