Enhanced nuclear-spin-dependent parity-violation effects using the ${}^{199}\mathrm{HgH}$ molecule

Electron interactions with the nuclear-spin-dependent (NSD) parity-nonconserving (PNC) anapole moment are strongly enhanced within heteronuclear diatomic molecules. A low-energy optical rotation experiment is being proposed with the aim of observing NSD PNC interactions in HgH. Based on the relativistic coupled cluster method we present a sophisticated numerical calculation of the circular polarization parameter $P=2\mathrm{Im}\left(E{1}_{\mathrm{PNC}}\right)/M1\approx 3\times {10}^{-6}\kappa$ for the ${}^2\mathrm{\Sigma }_{1/2}\to {}^2\mathrm{\Pi }_{1/2}$ optical transition of HgH, where $\kappa$ is a dimensionless constant determined by the nuclear anapole moment. This provides an improvement in sensitivity to NSD PNC by 2–3 orders of magnitude over the leading atomic Xe, Hg, Tl, Pb, and Bi optical rotation experiments. Therefore we show that the proposed measurement should be sensitive enough to extract the ${}^{199}\mathrm{Hg}$ anapole moment and shed light on the underlying theory of hadronic parity violation.

Figure 1

Ratio of weak interaction constant $W_a$ to relativistic factor $R_W$ plotted against $Z$ of the heavy nucleus for $Z=30$, 48, and 80, which corresponds to ZnH, CdH, and HgH, respectively. [$W_a\left({}^2\mathrm{\Sigma }_{1/2}\right)$ values for each molecule can be found in the first and second column of Table 1.] Circles, solid line of best fit: ground state ${}^2\mathrm{\Sigma }_{1/2}$; diamonds, dashed line of best fit: excited state ${}^2\mathrm{\Pi }_{1/2}$. Calculated using the DHF method (see text).