Revisiting the T,P -odd spin-rotational Hamiltonian of HfF+ for precise electron-electric-dipole-moment measurements

The current constraint on the electron electric dipole moment ($e\mathrm{EDM}$), $|{d}_{\mathrm{e}}|<4.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30} e\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ (90% confidence), was recently established using the trapped $^{180}\mathrm{Hf}^{19}\mathrm{F}^{+}$ molecular ions in the $J=1$ rotational level of its $^{3}\mathrm{\ensuremath{\Delta}}_{1}$ electronic state [T. S. Roussy, L. Caldwell, T. Wright et al., arXiv:2212.11841]. The extensive experimental study of the ${\mathrm{HfF}}^{+}$ cation provides detailed spectroscopy of the $\mathrm{\ensuremath{\Omega}}$-doublet levels in the external rotating electric and magnetic fields. We showed that previously developed theoretical approaches can fully reproduce the latest experimental data. Their justification from the first principles is very important for the examination of both modern molecular theory and possible systematic uncertainties in the interpretation of the experimental data obtained with high accuracy.