Nuclear Spin Dependent Parity Violation in Diatomic Molecules

Nuclear spin-dependent parity violation (NSD-PV) effects arise from exchange of the $Z^{0}$ boson between electrons and the nucleus, and from interaction of electrons with the nuclear anapole moment, a parity-odd magnetic moment. The latter scales with nucleon number of the nucleus $A$ as $A^{2/3}, $whereas the $Z^{0}$ coupling is independent of $A$. Thus the former is the dominant source of NSD-PV for nuclei with $A\ge $\textit{20}. We study NSD-PV effects using diatomic molecules, where signals are dramatically amplified by bringing rotational levels of opposite parity close to degeneracy in a strong magnetic field. The NSD-PV interaction matrix element is measured using a Stark-interference technique. We present results that demonstrate statistical sensitivity to NSD-PV effects surpassing that of any previous atomic parity violation measurement, using the test system~$^{\mathrm{138}}$Ba$^{\mathrm{19}}$F. We report our progress on measuring and cancelling systematic effects due to combination of non-reversing stray $E$-fields, $E_{nr}$ with $B$-field inhomogeneities. Short-term prospects for measuring the nuclear anapole moment of $^{\mathrm{137}}$Ba$^{\mathrm{19}}$F are discussed. In the long term, our technique is sufficiently general and sensitive to enable measurements across a broad range of nuclei.