Improved limits on the hadronic and semihadronic $CP$ violating parameters and role of a dark force carrier in the electric dipole moment of ${}^{199}\mathrm{Hg}$

Combining the recently reported electric dipole moment (EDM) of the ${}^{199}\mathrm{Hg}$ atom due to breaking of parity and time-reversal symmetries with the improved relativistic atomic calculations, precise limits on the tensor-pseudotensor (T-PT) electron-nucleus (e-N) coupling coefficient and the nuclear Schiff moment interactions are determined. Using these limits with the nuclear calculations, we infer limits on the EDMs of the neutron and proton as $d_n<2.2\times {10}^{-26}|e|\mathrm{cm}$ and $d_p<2.1\times {10}^{-25}|e|\mathrm{cm}$, respectively, and on the quantum chromodynamics parameter and the combined up- and down-quark chromo-EDMs as $|\overline{\theta }|<1.1\times {10}^{-10}$ and $|{\tilde{d}}_u-{\tilde{d}}_d|<5.5\times {10}^{-27}|e|\mathrm{cm}$, respectively. These are the best limits to date to probe new sources of $CP$ violation beyond the standard model from a diamagnetic atom. The role of a capable many-body method to account for the electron correlation effects to all orders for inferring the above limits has been highlighted. From this analysis, constraints on the T-PT e-N coupling coefficient with a large range of mass of a possible dark matter carrier $\chi$ between the atomic electrons and nucleus are given.

Figure 1

Behavior of ${\rho }_N^{\chi }$ values with the distance from the origin of the nucleus of ${}^{199}\mathrm{Hg}$ in the uniform charge distribution for different values of $m_{\chi }$ (in $\mathrm{MeV}/c^2$). This is perfectly in agreement with the findings of Ref. [36].

Figure 2

Demonstration of trends in the $d_a^{\chi }$ values (in ${10}^{-18}{C}_T^{\chi }⟨{\sigma }_N⟩|e|\mathrm{cm}$) with $m_{\chi }$ (in $\mathrm{MeV}/c^2$) from the DHF, RPA and CCSD methods. This clearly shows RPA values are far away from the DHF results, while the CCSD results are close to the DHF values. The differences between the RPA and CCSD results are clear indication of strong contributions by the electron pair-correlation effects.

Figure 3

Variation in the $R^{\chi }$ values with $m_{\chi }$ (in $\mathrm{MeV}/c^2$) from the DHF, RPA and CCSD methods. We find that all the methods are predicting almost the same $R^{\chi }$ values irrespective of the fact that the trends in the $d_a^{\chi }$ results are coming out to be completely different from all the three employed methods. However, slight deviations in these results can be observed for smaller values of $m_{\chi }$ as shown in the inset of the figure. This observation does not agree perfectly with the findings in Ref. [36] though earlier it was seen that behavior of ${\rho }_N^{\chi }$ was in perfect agreement between both the works.

Figure 4

The area shown in color is the allowed region of the $C_T^{\chi }$ values with the $m_{\chi }$ values (in $\mathrm{MeV}/c^2$). This range is substantially different than that estimated in Ref. [36].