Three-Photon-Annihilation Contributions to Positronium Energies at Order mα^{7}

Positronium spectroscopy (n=1 hyperfine splitting, n=2 fine structure, and the 2S-1S 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 mα^{7}. In this Letter, we present th...

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Bibliographic Details
Published in:Physical review letters 2015-12, Vol.115 (23), p.233401-233401
Main Authors: Adkins, Gregory S, Kim, Minji, Parsons, Christian, Fell, Richard N
Format: Article
Language:English
Online Access:Get full text
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Summary:Positronium spectroscopy (n=1 hyperfine splitting, n=2 fine structure, and the 2S-1S 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 mα^{7}. In this Letter, 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)mα^{7}/(nπ)^{3}=11.5/n^{3}  kHz for the spin-triplet S state with principal quantum number n. The corresponding energy shift for true muonium (the μ^{+}μ^{-} bound state) is 2.38/n^{3}  MHz with an additional -5.33/n^{3}  MHz coming from electronic vacuum polarization.
ISSN:1079-7114
DOI:10.1103/PhysRevLett.115.233401