Abstract
We present a detailed description of the calculation of radiative-recoil corrections to the ground-state hyperfine splitting in muonium and positronium to order , the results of which were previously reported. All these corrections involve two-photon exchanges with one-loop radiative corrections to either a photon or a lepton. The QED vacuum polarization corrections are evaluated completely analytically to the order of interest. The hadronic contributions are estimated and found to be very small. As a preliminary to the lepton line calculation, a compact expression is derived for the radiative correction to such lines. This factor is then applied in a number of different contexts: the recalculation of the old nonrecoil result, which is known analytically; the analytic evaluation of terms of order , which arise from the electron leg; and the nonlogarithmic terms from both lines, which require numerical calculations. The muonium results are and those for positronium are , where for positronium does not include the annihilation contribution.
- Received 7 December 1983
DOI:https://doi.org/10.1103/PhysRevD.29.2290
©1984 American Physical Society