Electric dipole moment of ${}^{199}\mathrm{Hg}$ atom from $P$, $CP$-odd electron-nucleon interaction

We calculate the effect of the $P$, $CP$-odd electron-nucleon interaction on the electric dipole moment of the ${}^{199}\mathrm{Hg}$ atom by evaluating the nuclear spin matrix elements in terms of the nuclear shell model. It is found that the neutron spin matrix element of the ${}^{199}\mathrm{Hg}$ nucleus is $⟨\mathrm{\Psi }|{\sigma }_{nz}|\mathrm{\Psi }⟩\approx -0.4$ with a dominant configuration of $p_{1/2}$ orbital neutron. We also derive constraints on the $CP$ phases of Higgs-doublet models, supersymmetric models, and leptoquark models from the latest experimental limit $|d_{\text{Hg}}|<7.4\times {10}^{-30}e\mathrm{cm}$.

Figure 1

The energy spectrum of ${}^{199}\mathrm{Hg}$ is given on the right panel (PTSM). The optimized strength parameters of the effective two-body interactions are shown in Table 2. The experimental data (Expt.) on the left panel is taken from Ref. [148].

Figure 2

The next-to-leading order two-nucleon correction to the nucleon operators, with (a) the pion-exchange current and (b) the two-nucleon contact interaction. The solid and dashed lines indicate the nucleon and pion, respectively. The scalar, pseudoscalar, and tensor operators are denoted by $\mathrm{\Gamma }$.

Figure 3

Diagramatic representation of the leading contribution of new physics to the $CP$-odd $e\text{−}N$ interaction. (a) $t$-channel electron-quark interaction, (b) $s$-channel electron-quark interaction, (c) electron-gluon interaction. For (b), the dashed line of the intermediate state may be a scalar or a vector boson. For (c), the particle in the loop can be a quark as well as a colored scalar field.