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

TL;DR

This paper calculates high-order vacuum polarization corrections to positronium energy levels, specifically focusing on the two-photon-annihilation channel, to aid in refining experimental measurements of hyperfine splitting.

Contribution

It provides the first comprehensive calculation of $m \, \alpha^7$ order vacuum polarization effects in parapositronium energy levels involving virtual two-photon annihilation.

Findings

Calculated all relevant vacuum polarization corrections at order $m \alpha^7$

Enhanced theoretical precision for positronium energy level predictions

Supports ongoing experimental efforts to measure hyperfine splitting more accurately

Abstract

We have calculated all contributions to the energy levels of parapositronium at order $m \alpha^7$ coming from vacuum polarization corrections to processes involving virtual annihilation to two photons. This work is motivated by ongoing efforts to improve the experimental determination of the positronium ground-state hyperfine splitting.