New calculation of the three-photon-annihilation contribution to the positronium hyperfine interval

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 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.

Hyperfine splitting in positronium to O(α(7)m(e)): one photon annihilation contribution

We present the complete result for the O(α7me) one photon annihilation contribution to the hyperfine splitting of the ground state energy levels in positronium. Numerically it increases the prediction of quantum electrodynamics by 217±1  kHz.

Order alpha(7)ln(1/alpha) contribution to positronium hyperfine splitting

The logarithmically enhanced alpha(7)ln(1/alpha) contribution to the hyperfine splitting of the positronium ground-state energy levels is calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. The correction is negative and amounts to about 1/3 of the leading logarithmic alpha(7)ln (2)(1/alpha) one. The discrepancy between the experimental measurements and the theoretical prediction is reduced.