Predictions of SUSY masses in the minimal supersymmetric grand unified theory

The Minimal Supersymmetric Standard Model (MSSM) distinguishes itself from other GUT's by a successful prediction of many unrelated phenomena with a minimum number of parameters. Among them: a) Unification of the gauge couplings constants; b) Unification of the b-quark and τ-lepton masses; c) Proton stability; d) Electroweak symmetry breaking at a scale far below the unification scale and the corresponding relation between the gauge boson masses and the top quark mass. A combined fit of the free parameters in the MSSM to these low energy constraints shows that the MSSM model can satisfy these constraints simultaneously. From the fitted parameters the masses of the as yet unobserved superpartners of the SM particles are predicted, the top mass is constrained to a range between 140 and 200 GeV, and the second order QCD coupling constant is required to be between 0.108 and 0.132. The complete second order renormalization group equations for the gauge and Yukawa couplings are used and analytical solutions for the neutral gauge boson, the Higgs masses and the sparticle masses are derived, taking into account the one-loop corrections to the Higgs potential.     

Gauge-invariant inflaton in the minimal supersymmetric standard model

We argue that all the necessary ingredients for successful inflation are present in the flat directions of the Minimally Supersymmetric Standard Model. We show that out of many gauge-invariant combinations of squarks, sleptons, and Higgs bosons, there are two directions, LLe and udd, which are promising candidates for the inflaton. The model predicts more than 10(3) e-foldings, with an inflationary scale of H(inf) approximately O(1-10) GeV, provides a tilted spectrum with an amplitude of delta(H) approximately 10(-5) and a negligible tensor perturbation. The temperature of the thermalized plasma could be as low as T(rh) approximately O(1-10) TeV. Parts of the inflaton potential can be determined independently of cosmology by future particle physics experiments.     

Composite quarks and leptons in supersymmetric grand unification

Chirality under SUSY-GUT is suggested as a sufficient condition for composites to be massless, in addition to the necessary anomaly matching á la 't Hooft. This results in a very stringent set of self-consistency requirements, which dictates also the number and structure of the generations. As an illustration I present an [SU(3)]³×[SUSY] model. It involves three generations (2 light + 1 heavy) and some other realistic features.     

A non-commutative version of the minimal supersymmetric standard model

A minimal supersymmetric standard model on non-commutative space-time (NC MSSM) is proposed. The model fulfills the requirements of non-commutative gauge invariance and the absence of anomaly. The existence of supersymmetry with a scale of its breaking lower than the non-commutative scale is crucial in order to achieve consistent gauge symmetry breaking.     

Charged current universality in the minimal supersymmetric standard model

We compute the complete one-loop contributions to low-energy charged current weak interaction observables in the minimal supersymmetric standard model (MSSM). We obtain the constraints on the MSSM parameter space which arise when precision low-energy charged current data are analyzed in tandem with measurements of the muon anomaly. While the data allow the presence of at least one light neutralino, they also imply a pattern of mass splittings among first and second generation sleptons and squarks which contradicts predictions of widely used models for supersymmetry-breaking mediation.     

Neutrino charge radius in the minimal supersymmetric standard model

As recently suggested by Degrassi, Marciano, and Sirlin, the electromagnetic form factor of the neutrino extracted from low energy elastic scattering cross sections ofv e and can be used to define the neutrino charge radius in the Standard Model in a gauge-invariant way. The complete one-loop contributions to the form factor consist not only the induced vertex but also the Z vertex corrections and theW andZ propagators arise from the counterterm diagrams, and theWW andZZ box diagrams. We show that the neutrino charge radius is a finite and gauge independent quantity in the Minimal Supersymmetric Standard Model. We consider only the oblique corrections to the neutrino charge radius in our numerical work, because the vertex and box contributions are small. The dependence of the oblique corrections on the supersymmetric parameters in each of the three sectors: Higgs, scalar matter and gaugino sectors are studied by taking into account of the current experimental bounds from LEP.     

Mechanisms of supersymmetry breaking in the minimal supersymmetric standard model

We provide a bird’s eyeview of current ideas on supersymmetry breaking mechanisms in the MSSM. The essentials of gauge, gravity, anomaly and gaugino/higgsino mediation mechanisms are covered briefly and the phenomenology of the associated models is touched upon. A few statement are also made on braneworld supersymmetry breaking.