Extraction of spin-averaged rovibrational transition frequencies in HD⁺ for the determination of fundamental constants

We present a comprehensive analysis of all currently available high-accuracy frequency measurements of rotational and rovibrational transitions in the hydrogen molecular ion (Formula presented.). Our analysis utilises the theoretically calculated hyperfine structure to extract the values of three spin-averaged transition frequencies through a global linear least-squares adjustment that takes into account theory-induced correlations between the different transitions. We subsequently use the three spin-averaged transition frequencies as input data in a second adjustment which employs precise theoretical expressions for the transition frequencies, written as a function of the proton, deuteron and electron relative atomic masses, the Rydberg constant, and the proton and deuteron charge radii. Our analysis shows that the (Formula presented.) data may significantly improve the value of the electron relative atomic mass and the proton-electron mass ratio, in particular if combined with recent high-precision measurements of particle atomic masses and mass ratios obtained from Penning traps.