Higher-order corrections to spin-spin scalar interactions in HD$^+$ and H$_2^+$

Abstract

The largest hyperfine interaction coefficients in the hydrogen molecular ion HD + , i.e. the electronproton and electron-deuteron spin-spin scalar interactions, are calculated with estimated uncertainties slightly below 1 ppm. The (Zα) 2 EF relativistic correction, for which a detailed derivation is presented, QED corrections up to the order α 3 ln 2 (α) along with an estimate of higher-order terms, and nuclear structure corrections are taken into account. Improved results are also given for the electron-proton interaction coefficient in H + 2 , in excellent agreement with RF spectroscopy experiments. In HD + , a 4σ difference is found in the hyperfine splitting of the (v, L) = (0, 3) → (9, 3) two-photon transition that was recently measured with high precision. The origin of this discrepancy is unknown.