Suppressing the μ and neutrino masses by a superconformal force

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 μ 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 ≲O(10-13) for the μ 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 R3 or R6, 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 ≲O(10) TeV so that this sector will be observable at the CERN Large Hadron Collider (LHC). Our models can accommodate a large mixing among neutrinos and give the same upper bound of the lightest Higgs boson mass as the minimal supersymmetric standard model.