Probing the QCD $\bar θ$ term with paramagnetic molecules

Abstract: The experimental search for CP violation in paramagnetic atomic and molecular systems has made impressive progress in recent years. This has led to strong upper limits on the electron electric dipole moment. The same measurements can also be used to constrain hadronic sources of CP violation through CP-violating interactions between the electrons and the nucleus. We employ heavy-baryon chiral perturbation theory to compute such CP-violating semileptonic electron-nucleus interactions arising from the QCD theta term. We sharpen earlier results by determining the relevant short-distance effects and by an explicit two-loop calculation of meson-photon diagrams. We derive a bound of $|\bar{\theta}| < 1.5 \cdot 10^{-8}$ at $90\%$ confidence, based on HfF$^+$ experiments at JILA. A further experimental improvement of one to two orders of magnitude would make paramagnetic molecular electric dipole moment experiments competitive with the neutron and diamagnetic atom program in constraining strong CP violation and higher-dimensional CP-odd quark-gluon operators.