Abstract
We present new theoretical results for the transition energies of the hydrogen isotope molecular ions and antiprotonic helium atoms. Our consideration includes corrections at the mα 7 order in the nonrecoil limit such as the one-loop self-energy, one-loop vacuum polarization, Wichman-Kroll, and complete two-loop contributions. That allowed to get transition energies for the fundamental transition \((v = 0,L = 0)\rightarrow (1,0)\) in the hydrogen molecular ion with the relative theoretical uncertainty of ∼7⋅10−12 that corresponds to a fractional precision of 1.5⋅10−11 in determination of the electron-to-proton mass ratio, m p /m e . Correspondingly, for the two-photon transitions in the antiprotonic helium we have 4.7⋅10−11 as a relative uncertainty for the \((33,32)\rightarrow (31,30)\) transition frequency and a fractional precision of 3.6⋅10−11 for an inferred antiproton-to-electron mass ratio.
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Proceedings of the International Conference on Exotic Atoms and Related Topics (EXA 2014), Vienna, Austria, 15-19 September 2014
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Korobov, V.I., Hilico, L. & Karr, JP. Bound-state QED calculations for antiprotonic helium. Hyperfine Interact 233, 75–82 (2015). https://doi.org/10.1007/s10751-015-1149-5
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DOI: https://doi.org/10.1007/s10751-015-1149-5