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.

5 pages, 2 figures

References in corpus (9)

• Production of the Smallest QED Atom: True Muonium (mu^+ mu^-)
• First test of $O({\alpha }^2)$ correction of the orthopositronium decay rate
• First Millimeter-wave Spectroscopy of the Ground-state Positronium
• Observation of positronium annihilation in the 2S state: towards a new measurement of the 1S-2S transition frequency
• Hard Three-Loop Corrections to Hyperfine Splitting in Positronium and Muonium
• Positronium energy levels at order $m{\alpha }^7$: light-by-light scattering in the two-photon-annihilation channel
• Hard Nonlogarithmic Corrections of Order $m{\alpha }^7$ to Hyperfine Splitting in Positronium
• Electroweak Corrections to the True Muonium Hyperfine Splitting
• On the possibility of observable signatures of leptonium from astrophysical sources

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• Hadronic Vacuum Polarization in True Muonium
• $P-$state Positronium for Precision Physics: an Ultrafine Splitting at ${\alpha }^6$
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• 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
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