High-precision Penning-trap spectroscopy of the ground-state spin structure of HD+

We present high-precision spectroscopy of the ground-state hyperfine structure of HD${}^{+}$ at 4~T. We determine the bound-electron $g$ factor, $g_{e,\mathrm{b}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}}=-2.00227854096(40)$, to a relative uncertainty of $2\times$10${}^{-10}$, the most precise determination of a bound-electron $g$ factor of a molecular ion to date. The experimental value agrees with recently developed ab initio theory that now includes quantum-electrodynamical effects up to order ${\alpha }^5$ and has reduced the theoretical uncertainty by three orders of magnitude [O. Kullie $\mathit{\text{et}}\mathit{\text{al.}}$, Phys. Rev. A 112 052813 (2025)]. In addition, we extract the scalar spin-spin interaction coefficients $E_4$~=~925,395.758(41)$$kHz (electron-proton) and $E_5$~=~142,287.821(22)$$kHz (electron-deuteron), which show a moderate tension with another state-of-the-art theoretical prediction [M. Haidar $\mathit{\text{et}}\mathit{\text{al.}}$, Phys. Rev. A 106 042815 (2022)].