Higher Order Corrections to Positronium Energy Levels

Positronium spectroscopy is of continuing interest as a high-precision test of our understanding of binding in QFT. Spectroscopic studies of low-lying states (n = 1 hyperfine splitting, n = 2 fine structure, and the 1S — 2S interval) have reached a precision of order 1MHz, and ongoing experimental efforts give the promise of improved results. Theoretical calculations of positronium energies at order mα ⁶ ∼ 18.7MHz are complete, but only partial results are known at order mα ⁷ ∼ 0.14MHz. We report on the status of the positronium energy calculations and give some details of the methods employed. (paper)