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Relativistic many-body methods at different levels of approximations areemployed to gain insights into the passage of the electron correlations fromlower to higher levels in the accurate determination of the electric dipolepolarizability ($\alpha_d$) and electric dipole moment (EDM) due to theelectron-nucleus tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM)interactions of the $^{199}$Hg ground state. Moreover, plausible reasons forthe differences in the previous calculations are pointed out. Comparisonbetween the calculated and experimental results of $\alpha_d$ indicates thatour EDM calculations are about 3\% accurate which in combination with themeasured value of $^{199}$Hg EDM yield limits for the T-PT coupling constant$C_T < 2.31 \times 10^{-9}$ and the NSM $S<1.55 \times 10^{-12}|e|fm^3$. Fromthis limit of $S$ and the latest nuclear structure calculation, we get improvedlimits for the strong CP violating parameter $\theta_{QCD} < 2.12 \times10^{-10}$ and the combined up and down quark chromo-EDMs $(-0.004 \tilde{d}_u +0.020 \tilde{d}_d) < 1.15 \times 10^{-27} |e| cm$.

Rigorous limits for hadronic and semi-leptonic CP-violating coupling constants from the electric dipole moment of $^{199}$Hg