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

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.

Comments: 5 pages, 2 figures