# One More Hard Three-Loop Correction to Parapositronium Energy Levels

## TL;DR

This paper calculates a specific three-loop quantum correction to parapositronium energy levels, providing a precise nonlogarithmic contribution important for high-precision theoretical predictions.

## Contribution

It presents the first calculation of a nonlogarithmic three-loop correction of order mα^7 to parapositronium energy levels, focusing on photon propagator insertions in two-photon annihilation diagrams.

## Key findings

- Energy shift ΔE=0.03297(2)(mα^7/π^3) calculated.
- Provides a key correction for high-precision parapositronium energy level predictions.
- Advances theoretical understanding of quantum electrodynamics corrections.

## Abstract

A hard three-loop correction to parapositronium energy levels of order $m\alpha^7$ is calculated. This nonlogarithmic contribution is due to the insertions of one-loop photon propagator in the fermion lines in the diagrams with virtual two-photon annihilation. We obtained $\Delta E=0.03297(2)(m\alpha^7/\pi^3)$ for this energy shift.