Radiative symmetry breaking is studied in a superstring-inspired supersymmetric model which is extended with a low energy extra U(1) symmetry. In this model the µ-problem is radiatively solved in an automatic way. The right-handed neutrino can be heavy and the seesaw mechanism will produce the small neutrino mass which makes the MSW solution applicable to the solar neutrino problem. We search a parameter region which has the favorable feature for the radiative symmetry breaking at the weak scale. Rather wide parameter region is found to be allowed. The upper bound of the extra Z boson mass is estimated as M Z 2 ≤ 2000 GeV for a top mass range 150 GeV ≤ m t ≤ 190 GeV. Some phenomenological features of the extra Z boson are also presented. * 1There are other solutions than the present one for the µ-problem [6,7]. However, in the models with extra gauge symmetries in the observable sector as the E 6 models, other solutions do not work so easily because it is difficult to construct a necessary term in the gauge invariant way. In this paper we will not consider them.

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 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 ՇO(10 Ϫ13 ) for the 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 ՇO(10) TeV so that this sector will be observable at the CERN Large Hadron Collider ͑LHC͒. 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.

The radiative neutrino mass model with an inert doublet scalar has been considered as a promising candidate which can explain neutrino masses, dark matter abundance and baryon number asymmetry if dark matter is identified with the lightest neutral component of the inert doublet. We reexamine these properties by imposing all the data of the neutrino oscillation, which are recently suggested by the reactor experiments. We find that the sufficient baryon number asymmetry seems not to be easily generated in a consistent way with all the data of the neutrino masses and mixing as long as the right-handed neutrinos are kept in TeV regions. Two possible modifications of the model are examined. 1

The neutral member of a Majorana fermion triplet (Σ + , Σ 0 , Σ − ) is proposed as a candidate for the dark matter of the Universe. It may also serve as the seesaw anchor for obtaining a radiative neutrino mass.

We reexamine relic abundance of a singlet fermion as a CDM candidate, which contributes to the neutrino mass generation through radiative seesaw mechanism. We search solutions for Yukawa couplings and the mass spectrum of relevant fields to explain neutrino oscillation data. For such solutions, we show that an abundance of a lightest singlet fermion can be consistent with WMAP data without conflicting with both bounds of µ → eγ and τ → µγ. This reconciliation does not need any modification of the original radiative seesaw model other than by specifying flavor structure of Yukawa couplings and taking account of coannihilation effects. *

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We study soft scalar masses comparing with gaugino masses in 4-dimensional string models. In general non-universal soft masses are derived in orbifold models. We give conditions on modular weights to lead to the large non-universality in the soft scalar masses. This non-universality is applied to the unification of the gauge coupling constants in the minimal string model. *

The radiative seesaw model with an inert doublet has been shown to be attractive from a viewpoint of both neutrino masses and cold dark matter. However, if we apply this model to the explanation of the positron excess in the cosmic ray observed by PAMELA, a huge boost factor is required although it can be automatically explained that no anti-proton excess has been observed there. We consider an extension of the model to enhance the thermally averaged annihilation cross section without changing the features of the model favored by both the neutrino oscillation and the relic abundance of dark matter. It is shown that the data of PAMELA and Fermi-LAT can be well explained in this extended model. Constraints from gamma ray observations are also discussed. *