Three-photon-annihilation contributions to positronium energies at order $m \alpha^7$

TL;DR

This paper calculates the energy shifts in positronium due to three-photon virtual annihilation processes at order m alpha^7, improving theoretical precision to match experimental advances.

Contribution

It provides the first complete calculation of three-photon annihilation contributions to positronium energy levels at order m alpha^7.

Findings

Energy shift for spin-triplet S state: 2.6216(11) m alpha^7/(n pi)^3

Enhances theoretical accuracy for positronium spectroscopy

Supports ongoing high-precision experimental efforts

Abstract

Positronium spectroscopy (n=1 hyperfine splitting, n=2 fine structure, and the 1S-2S interval) has reached a precision of order 1 MHz. Vigorous ongoing efforts to improve the experimental results motivate the calculation of the positronium energy levels at order $m \alpha^7$. In this work we present the result for a complete class of such contributions--those involving virtual annihilation of positronium to three photons in an intermediate state. We find an energy shift of $2.6216(11) m \alpha^7/(n \pi)^3$ for the spin-triplet S state with principal quantum number n.