  The idea of Nelson and Strassler to obtain a power law suppression of
parameters by a superconformal force is applied to understand the smallness of
the $\mu$ parameter and neutrino masses in R-parity violating supersymmetric
standard models. We find that the low-energy sector should contain at least
another pair of Higgs doublets, and that a suppression of $\lsim O(10^{-13})$
for the $\mu$ parameter and neutrino masses can be achieved generically. The
superpotential of the low-energy sector happens to possess an anomaly-free
discrete R-symmetry, either $R_3$ or $R_6$, which naturally suppresses certain
lepton-flavor violating processes, the neutrinoless double beta decays and also
the electron electric dipole moment. We expect that the escape energy of the
superconformal sector is $\lsim$ O(10) TeV so that this sector will be
observable at LHC. Our models can accommodate to a large mixing among neutrinos
and give the same upper bound of the lightest Higgs mass as the minimal
supersymmetric standard model.
