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

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.

9 pages, 1 figure

References in corpus (2)

• Precision Study of Positronium: Testing Bound State QED Theory
• Hard Nonlogarithmic Corrections of Order $m{\alpha }^7$ to Hyperfine Splitting in Positronium

Cited by in corpus (5)

• Electroweak Corrections to the True Muonium Hyperfine Splitting
• The QED four-photon amplitudes off-shell: part 2
• One More Hard Three-Loop Correction to Parapositronium Energy Levels
• $P-$state Positronium for Precision Physics: an Ultrafine Splitting at ${\alpha }^6$
• Hyperfine Splitting in True Muonium to $\mathcal{O}(m_{\mu }{\alpha }^6)$: Two Photon Annihilation Contribution from Other Flavors