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

Combining the recently reported electric dipole moment (EDM) of $^{199}$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 (NSM) interactions are determined. Using these limits with the nuclear calculations, we infer limits on the EDMs of neutron and proton as $d_n < 2.2 \times 10^{-26} |e| \rm{cm}$ and $d_p < 2.1 \times 10^{-25} |e| \rm{cm}$, respectively, and on the quantum chromodynamics (QCD) parameter and the combined up- and down- quark chromo-EDMs as $|\bar{\theta}| < 1.1 \times 10^{-10}$ and $|\tilde{d}_u - \tilde{d}_d| < 5.5 \times 10^{-27} |e|\rm{cm}$, respectively. These are the best limits till date to probe new sources of CP violation beyond the standard model (SM) from a diamagnetic atom. Role of considering a capable many-body method to account 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.