Positronium energy levels at order $m \alpha^7$: Product contributions in the two-photon-annihilation channel

TL;DR

This paper calculates high-order quantum corrections to positronium energy levels, specifically focusing on two-photon annihilation contributions, to match the precision of ongoing experimental measurements.

Contribution

It provides the first complete evaluation of product-type one-loop correction contributions to positronium S-state energies at order $m \, \alpha^7$, including virtual annihilation effects.

Findings

Contributes approximately -0.562 m α^7/π^3 to the parapositronium ground state energy.

Completes the calculation of all product contributions at this order for the two-photon-annihilation channel.

Enhances theoretical predictions to support high-precision positronium spectroscopy.

Abstract

Ongoing improvements in the measurement of positronium transition intervals motivate the calculation of the $O(m \alpha^7)$ corrections to these intervals. In this work we focus on corrections to the spin-singlet parapositronium energies involving virtual annihilation to two photons in an intermediate state. We have evaluated all contributions to the positronium S-state energy levels that can be written as the product of a one-loop correction on one side of the annihilation event and another one-loop correction on the other side. These effects contribute $\Delta E = -0.561971(25) m \alpha^7/\pi^3$ to the parapositronium ground state energy.