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Three-photon-annihilation contributions to positronium energies at order $m \alpha^7$

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arxiv 1507.07841 v1 pith:AOPI7UDG submitted 2015-07-28 hep-ph

classification hep-ph
keywords positroniumalphaorderenergystateannihilationcalculationclass
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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