Best Values for the CP-odd Meson-Nucleon Couplings from Supersymmetry

In the supersymmetric models, the dominant sources of the hadronic flavor-diagonal CP violation at low energy are the theta term and the chromoelectric dipole moments of quarks. Using QCD sum rules, we estimate the preferred range and the best values for the CP-odd meson-nucleon coupling constants induced by these operators. When the theta term is removed by the axion mechanism, the size of the most important isospin triplet pion-nucleon coupling is estimated to be \bar g_{\pi NN}^{(1)} = 2 times 10^{-12}(tilde d_u - tilde d_d), where chromoelectric dipole moments are given in units of 10^{-26} cm.