Prospects for testing Lorentz and CPT symmetry with ${\rm H}^+_2$ and ${\rm \bar{H}}^-_2$

This work presents a model for testing Lorentz and CPT symmetry using rovibrational transitions within the electronic ground state of the molecular hydrogen ion (H$^+_2$). The model is based on the Standard-Model Extension (SME) and incorporates minimal and nonminimal effects. Our analysis concludes that sidereal variation studies of these transitions could establish first bounds on SME proton coefficients. Additionally, the prospects for testing CPT symmetry with the molecular antihydrogen ion are discussed and compared to those of atomic antihydrogen experiments. This comparison highlights that both systems complement each other, as each is better suited to constrain specific types of CPT-violating operators.