Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: theory and application to H${}_2^{+}$

We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $m{\alpha }^7\ln (\alpha )$-order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the $m{\alpha }^6$-order relativistic correction, for the case of H${}_2^{+}$. The theoretical uncertainty is reduced by more than one order of magnitude with respect to the Breit-Pauli level, down to a few ppm. We also compare our results with available rf spectroscopy data.