Beyond antihydrogen: testing CPT with the molecular antihydrogen ion

Measurements of Zeeman, Zeeman-hyperfine and ro-vibrational transitions in (bar {H}_{2}^{-}(bar {p}e^{+}bar {p})) compared to (H_{2}^{+}) have the potential for more precise tests of CPT than can be obtained from antiprotons and antihydrogen. In particular, measurements of ro-vibrational transitions have a potential sensitivity to a difference between antiproton and proton mass three orders of magnitude higher than antihydrogen/hydrogen. Methods are outlined for precision measurements on a single (bar {H}_{2}^{-}) or ({H}_{2}^{+}) ion in a cryogenic Penning trap, with non-destructive state identification using the continuous Stern-Gerlach effect or changes in mass. (bar {H}_{2}^{-}) can be produced using the (bar {H}^{+}+bar {p} rightarrow bar {H}_{2}^{-} + e^{+}) reaction.