Relations between matrix elements of different weak interactions and interpretation of the parity-nonconserving and electron electric-dipole-moment measurements in atoms and molecules

The relations between matrix elements of different (P,T)-odd weak interactions are derived. We demonstrate that similar relations hold for parity-nonconserving transition amplitudes and electron electric dipole moments (EDMs) of atoms and molecules. This allows one to express P- and T-odd effects in many-electron systems caused by different symmetry-breaking mechanisms via each other using simple analytical formulas. We use these relations for the interpretation of the anapole moment measurements in cesium and thallium and for the analysis of the relative contributions of the scalar-pseudoscalar $CP$-odd weak interaction and electron EDMs to the EDMs of Cs, Tl, Fr, and other atoms and many polar molecules (YbF, PbO, ThO, etc.). Model-independent limits on electron EDMs and the parameter of the scalar-pseudoscalar $CP$-odd interaction are found from the analysis of the EDM measurements for Tl and YbF.