Electric dipole moment of $^{199}$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 $^{199}$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 $^{199}$Hg nucleus is $\langle \Psi |\, \sigma_{nz} | \Psi \rangle \approx -0.3$ with an errorbar of less than 20% and that of the proton is limited by $| \langle \Psi |\, \sigma_{pz} | \Psi \rangle | < 0.01$, with a dominant configuration of $p_{1/2}$ orbital neutron. Combined with the results of the hadronic and atomic level calculations, the overall uncertainty of the relation between the CP-odd light quark-electron interaction renormalized at the TeV scale and the EDM of $^{199}$Hg atom is about 30%, which is the most accurately known for this system. We also derive constraints on the CP phases of Higgs-doublet models, supersymmetric models, and leptoquark models from the latest experimental limit $|d_{\rm Hg}| < 7.4 \times 10^{-30}e$ cm.