A Computational Investigation of Hydronium (H₃O⁺) for 𝜇 Variation Searches

Polyatomic molecules, with their richer internal structure, provide an attractive platform for precision measurements that can probe physics beyond the Standard Model. In this work, we propose using the inversion-transition spectrum of hydronium (H₃O⁺), an ammonia-like symmetric-top molecule that is abundant in the interstellar medium, to search for spatial and temporal variations of the electron-to-proton mass ratio, μ. To enable such measurements, we theoretically design a quantum logic spectroscopy (QLS) scheme for precision determination of H₃O⁺ inversion-transition frequencies. We present a detailed theoretical study of the relevant molecular structure, including inversion–rotational splittings, Zeeman shifts, spin–rotation couplings, and AC Stark shifts. We also evaluate two-photon Rabi rates to inform QLS-based state-preparation protocols. In addition, we examine nuclear-spin statistics arising from the indistinguishability of the hydrogen nuclei to account more fully for symmetry considerations. We expect the protocols developed here to be broadly applicable to precision measurements in other polyatomic systems, including chiral molecules proposed for parity-violation searches.