mα(7)-order corrections in the hydrogen molecular ions and antiprotonic helium.

We present a calculation of the complete set of QED corrections of order mα7 for one-electron two-center systems. Leading corrections of order mα8 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 H2+ and HD+, and of two-photon transition in antiprotonic helium is reduced by about 1 order of magnitude, down to (3-4)×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.