New Minimal Extension of MSSM

We construct a new minimal extension of the Minimal Supersymmetric Standard Model (MSSM) by promoting the $\mu$-parameter to a singlet superfield. The resulting renormalizable superpotential is enforced by a $\mathcal{Z}_5$ $R$-symmetry which is imposed on the non-renormalizable operators as well. The proposed model provides a natural solution to the $\mu$-problem and is free from phenomenological and cosmological problems.Comment: 5 page

Minimal Nonminimal Supersymmetric Standard Model

We review the basic field-theoretic and phenomenological features of the recently introduced Minimal Nonminimal Supersymmetric Standard Model (MNSSM). The introduced model is the simplest and most economic version among the proposed nonminimal supersymmetric models, in which the so-called $\mu$-problem can be successfully addressed. As opposed to the MSSM and the frequently-discussed NMSSM, the MNSSM can naturally predict the existence of a light charged Higgs boson with a mass smaller than 100 GeV. Such a possible realization of the Higgs sector can be soon be tested at the upgraded Run II phase of the Tevatron collider.Comment: 8 pages, 4 figures, talk given at the conference ``Beyond the Desert 2002,'' 2--7 June 2002, Oulu, Finlan

Realizations of Hybrid Inflation in Supergravity with natural initial conditions

We present viable F-term realizations of the hybrid inflationary scenario in the context of supergravity addressing at the same time the well-known problems of the initial conditions and of the adequate suppression of the inflaton mass. An essential role in our construction is played by "decoupled" superheavy fields without superpotential acquiring large vevs due to D-terms associated with "anomalous" U(1) gauge symmetries. The naturalness of the initial conditions is achieved through a "chaotic" inflation starting at energies close to the Planck scale and driven by the "anomalous" D-terms. We discuss two distinct mechanisms leading to such an early "chaotic" D-term inflation which depend on the choice of the K\"ahler potential involving the superheavy fields. The one relies on a choice of the K\"ahler potential of the $SU(1,1)/U(1)$ K\"ahler manifold of the type encountered in no-scale supergravity whereas the other employs a more "conventional" choice for the K\"ahler potential of the $SU(1,1)/U(1)$ or $SU(2)/U(1)$ K\"ahler manifold but invokes rather specific valuesof the Fayet-Iliopoulos $\xi$ term.Comment: 32 pages LATEX, no figure

Hybrid Inflation in Supergravity with (SU(1,1)/U(1))m(SU(1,1)/U(1)) ^{m} Ka¨% \ddot{a}hler Manifolds

In the presence of fields without superpotential but with large vevs through D-terms the mass-squared of the inflaton in the context of supergravity hybrid inflation receives positive contributions which could cancel the possibly negative K$\ddot{a}$hler potential ones. The mechanism is demonstrated using K$\ddot{a}$hler potentials associated with products of $SU(1,1)/U(1)$ K$\ddot{a}$hler manifolds. In a particularly simple model of this type all supergravity corrections to the F-term potential turn out to be proportional to the inflaton mass allowing even for an essentially completely flat inflationary potential. The model also allows for a detectable gravitational wave contribution to the microwave background anisotropy. Its initial conditions are quite natural largely due to a built in mechanism for a first stage of ``chaotic'' D-term inflation.Comment: 16 pages, revtex., version to be published in Phys. Lett.

Stabilized NMSSM without Domain Walls

We reconsider the Next to Minimal Supersymmetric Standard Model (NMSSM) as a natural solution to the $\mu$-problem and show that both the stability and the cosmological domain wall problems are eliminated if we impose a ${\cal {Z}}_2$ $R$-symmetry on the non-renormalizable operators.Comment: 5 page