Lorentz and CPT violation and the (anti-)hydrogen molecular ion II -- hyperfine-Zeeman spectrum

Fundamental principles of quantum field theory such as Lorentz invariance, CPT symmetry and locality may be tested to extremely high precision in atomic and molecular spectroscopy. The narrow natural linewidth of rovibrational states in the hydrogen molecular ion $H_2^+$ and its antimatter counterpart $\bar{H}_2^-$, make these ideal candidates, and give $O(m_p/m_e)$ increased sensitivity to Lorentz and CPT violation in the proton sector compared to $H$ and $\bar{H}$ atoms. In a previous paper, we presented a detailed analysis of the rovibrational spectrum of $H_2^+$ and $\bar{H}_2^-$ in an effective QFT encoding Lorentz and CPT violation, focusing on spin-independent effects. Here, we extend this analysis to include the full hyperfine-Zeeman spectrum and include spin-dependent Lorentz and CPT violating operators in the effective theory. The results demonstrate how constraints on these symmetry-violating couplings may be extracted from specific rovibrational transitions between hyperfine-Zeeman states in the presence of an applied magnetic field.