Positronium energy levels at order $m \alpha^7$: light-by-light scattering in the two-photon-annihilation channel

TL;DR

This paper calculates a three-loop correction to positronium energy levels involving light-by-light scattering, providing precise energy shifts relevant for ongoing experimental tests of quantum electrodynamics.

Contribution

It presents the first detailed calculation of light-by-light scattering effects at order $m \, \alpha^7$ in positronium energy levels, improving theoretical precision.

Findings

Energy shift of 1.58377(8) m alpha^7 / pi^3 for n=1 singlet state

Correction of -6.95 kHz to ground state hyperfine splitting

More precise light-by-light scattering correction to parapositronium decay

Abstract

Recent and ongoing experimental work on the positronium spectrum motivates new efforts to calculate positronium energy levels at the level of three loop corrections. We have obtained results for one set of such corrections involving light-by-light scattering of the photons produced in a two-photon virtual annihilation process. Our result is an energy shift $1.58377(8) m \alpha^7/\pi^3$ for the n=1 singlet state, correcting the ground state hyperfine splitting by -6.95 kHz. We also obtained a new and more precise result for the light-by-light scattering correction to the real decay of parapositronium into two photons.