The constraint on the $R$-parity violating supersymmetric interactions is discussed in the light of current experimental data of the electric dipole moment of neutron, $^{129}$Xe , $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules. To inves
tigate the constraints without relying upon the assumption of the dominance of a particular combination of couplings over all the rest, an extensive use is made of the linear programming method in the scan of the parameter space. We give maximally possible values for the EDMs of the proton, deuteron, $^3$He nucleus, $^{211}$Rn, $^{225}$Ra, $^{210}$Fr, and the $R$-correlation of the neutron beta decay within the constraints from the current experimental data of the EDMs of neutron, $^{129}$Xe, $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules using the linear programming method. It is found that the $R$-correlation of the neutron beta decay and hadronic EDMs are very useful observables to constrain definite regions of the parameter space of the $R$-parity violating supersymmetry.
The contribution of the R-parity violating trilinear couplings in the supersymmetric model to the fermion electric dipole moment is analyzed at the two-loop level. We show that in general, the Barr-Zee type contribution to the fermion electric dipole
moment with the exchange of W and Z bosons is not small compared to the currently known photon exchange one with R-parity violating interactions. We will then give new upper bounds on the imaginary parts of R-parity violating couplings from the experimental data of the electric dipole moments of the electron and of the neutron. The effect due to bilinear R-parity violating couplings, which needs to be investigated separately, is not included in our analyses.
