Vacuum polarization corrections to $\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ spectrum

Abstract

The energy levels of the $n=1$ and $n=2$ bound states of the $\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ atom (true muonium) are calculated starting from a previously derived potential that correctly describes positronium to order $\hat{I}{\pm }^5$ supplemented by the known $\hat{I}{\pm }^6$ contributions. All electron vacuum polarization corrections on the true muonium levels are computed to order $\hat{I}{\pm }^6$ order. The second order perturbative contributions from all of the $\hat{I}{\pm }^4$ and $\hat{I}{\pm }^5$ terms in the potential are also included. Additional order $\hat{I}{\pm }^6$ contributions from the two photon and three photon annihilation processes are included in the evaluation of the ground state ($1^3{S}_1-1^1{S}_0$) hyperfine splitting.

7 pages, 2 Tables, additional contributions and references