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

Abstract

Ongoing improvements in the measurement of positronium transition intervals motivate the calculation of the $O(m{\alpha }^7)$ corrections to these intervals. In this work we focus on corrections to the spin-singlet parapositronium energies involving virtual annihilation to two photons in an intermediate state. We have evaluated all contributions to the positronium S-state energy levels that can be written as the product of a one-loop correction on one side of the annihilation event and another one-loop correction on the other side. These effects contribute $\Delta E=-0.561971(25)m{\alpha }^7/{\pi }^3$ to the parapositronium ground state energy.

11 pages, 4 figures

References in corpus (8)

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• Production of the Smallest QED Atom: True Muonium (mu^+ mu^-)
• First Millimeter-wave Spectroscopy of the Ground-state Positronium
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Cited by in corpus (7)

• One More Hard Three-Loop Correction to Parapositronium Energy Levels
• Three-Loop Corrections to Lamb Shift in Muonium and Positronium
• $P-$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
• Astrophysical signatures of leptonium
• Fifth Force and Hyperfine Splitting in Bound Systems
• Measurement of the ${\text{1}}^{\text{3}}{\text{S}}_{\text{1}}\to {\text{2}}^{\text{3}}{\text{S}}_{\text{1}}$ interval in positronium using field-ionization of Rydberg states