mα7-Order Corrections in the Hydrogen Molecular Ions and Antiprotonic Helium

We present a calculation of the complete set of QED corrections of order m alpha(7) for one-electron two-center systems. Leading corrections of order m alpha(8) are also considered, which allows us to estimate the magnitude of yet uncalculated contributions. The theoretical uncertainty on the frequencies of rovibrational transitions in the hydrogen molecular ions H-2(+) and HD+, and of two-photon transition in antiprotonic helium is reduced by about 1 order of magnitude, down to (3-4) x 10(-11) and 10(-10), respectively. These results open new perspectives for improved determination of the proton- and antiproton-to-electron mass ratios by precision spectroscopy experiments.