Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions III -- rovibrational spectrum and the non-minimal SME
Rovibrational transitions in the hydrogen and antihydrogen molecular ions $H_2^+$ and $\overline{H}_2^-$ offer the possibility of testing Lorentz and CPT symmetry to extremely high precision, in principle attaining $O(10^{-17})$. In this paper, the third in a series, we give a comprehensive derivation of the rovibrational spectrum of $H_2^+$ and $\overline{H}_2^-$ in the SME, an effective quantum field theory incorporating Lorentz and CPT violation. New developments described here include a complete analysis of the molecular dynamics from first principles in terms of the spherical tensor representation of the SME couplings, the systematic extension of our previous results to the non-minimal SME, a full description of the quantum number dependence of the rovibrational energy levels in the spherical tensor formalism with both high and low background magnetic fields, and an extended discussion of sidereal and annual variations of transition frequencies arising from both rotations and Lorentz boosts. The resulting sensitivity of the rovibrational spectrum to an extended range of SME couplings, together with the ability to isolate their individual effects using the quantum number dependence of the transition frequencies, enhances the opportunities to detect Lorentz and CPT symmetry breaking through rovibrational spectroscopy of $H_2^+$ and $\overline{H}_2^-$.