Speaker
Description
Muonium and positronium, the $e^-\mu^+$ and $e^-e^+$ bound systems, are described almost completely within quantum electrodynamics. Their energy levels can be calculated to high precision, and these systems are also subject to high precision measurements. Recent developments include intense experimental work on muonium by the MuSEUM collaboration at J-PARC and the MuMASS collaboration at PSI, along with measurements of the positronium fine structure by the Cassidy group at UCL and the positronium 1S-2S interval at ETH Zurich. In order to match the uncertainties of projected experimental results the calculation of additional higher order corrections will need to done.
In this talk I will describe progress on a calculation of a set of radiative-recoil corrections to the energy levels of muonium and positronium at order $\alpha^7$. These are terms involving two-loop radiative corrections to the exchange of two photons between the bound fermions, one-loop radiative corrections to the exchange of three photons between the bound fermions, and the exchange of four photons between the bound fermions. Integration by parts identities have been used to reduce the problem to the calculation of a (relatively) few ``master integrals''. The three-loop master integrals with up to eight photon and fermion propagators are now being evaluated using recently developed techniques. This talk will give a report on the progress of this work.