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Electron interactions with the nuclear-spin-dependent (NSD) paritynon-conserving (PNC) anapole moment are strongly enhanced within heteronucleardiatomic molecules. A novel, low-energy optical rotation experiment is beingproposed with the aim of observing NSD PNC interactions in HgH. Based on therelativistic coupled cluster method we present a complete calculation of thecircular polarization parameter $P = 2\,\textrm{Im}(E1_{PNC})/M1 \approx 3\times 10^{-6}\; \kappa$ for the $^2\Sigma_{1/2} \to ^2\Pi_{1/2}$ opticaltransition of HgH, where $\kappa$ is a dimensionless constant determined by thenuclear anapole moment. This provides an improvement in sensitivity to NSD PNCby 2 -- 3 orders of magnitude over the leading atomic Xe, Hg, Tl, Pb and Bioptical rotation experiments, and shows that the proposed measurement will besensitive enough to extract the $^{199}$Hg anapole moment and shed light on theunderlying theory of hadronic parity violation.

Enhanced nuclear spin dependent parity violation effects using the 199HgH molecule