Ro-vibrational spin-averaged transitions in the hydrogen molecular ions

Abstract: We reconsider the calculation of rovibrational transition frequencies in hydrogen molecular ions. Some previously neglected contributions, such as the deuteron polarizability, are included into consideration in comparison with our previous work. In particular, one-loop and two-loop QED corrections at $m\alpha^7$ and $m\alpha^8$ orders are recalculated in the framework of the adiabatic approximation, with systematic inclusion of corrections associated with vibrational motion. Improved theoretical transitions frequencies are obtained and found to be in very good agreement with recent high-precision spectroscopy experiments in HD$^+$. New values for the $m_p/m_e$ and $m_d/m_p$ mass ratios are determined.