Test of charged baryon interaction with high-resolution vibrational spectroscopy of molecular hydrogen ions

Molecular hydrogen ions are of high interest in fundamental physics and metrology. In particular, the long-range baryon–baryon interaction and the degrees of freedom of baryon rotational and vibrational motion are key features of molecular hydrogen ions. Here we present the measurement of a one-photon transition of HD⁺, a fourth overtone vibrational transition. Through a comparison of experimental and ab initio frequencies of this and previously measured transitions, we implement a test of the low-energy quantum physics of baryon interaction and motion. The results may also be interpreted as a test of Weinberg's quantum mechanics extension. Furthermore, we compare the value of the fundamental constant combination μ/m_e = m_pm_d/(m_p + m_d)m_e determined from our measurement with the value obtained from mass spectrometry experiments. This may also be regarded as a test of the quantum behaviour of baryons, revealing a moderate tension of 1.7 times the combined uncertainty. Combining our measurement result with some previous ones on HD⁺, we obtain a least-squares-adjusted value for μ/m_e as well as a bound for the force between the proton and deuteron in a scenario that is beyond the Standard Model of particle physics. No evidence of a deviation from conventional quantum physics is found.