Triplication of SU(5) Monopoles

We investigate all spherically symmetric fundamental monopole solutions with fixed topological charge in the SU(5)-->[SU(3) x SU(2) x U(1)]/Z(3) x Z(2) symmetry breaking. We find that there are three solutions that are gauge equivalent but, as we argue, would correspond to physically distinct degrees of freedom in the dualized version of the model. The triplication of monopoles could help us understand the observed family structure of standard model particles.     

Supersymmetric flipped SU(5) revitalized

We describe a simple N = 1 supersymmetric GUT based on the group SU(5)×U(1) which has the following virtues: the gauge group is broken down to the SU(3)_C×SU(2)_L×U(1)_Y of the standard model using just 10, $\text{10}$ Higgs representations, and doublet-triplet mass splitting problem is solved naturally by a very simple missing-partner mechanism. The successful supersymmetric GUT prediction for sin²θ_w can be maintained, whilst there are no fermion mass relations. The gauge group and representation structure of the model may be obtainable from the superstring.     

SU(2)L×SU(2)R×U(1) gauge model

We determine here the most general electroweak interaction based on the groupSU(2)_L×SU(2)_R×U(1). When we rotate theZ ₁,Z ₂ basis to theZ,D basis such that the total interaction ofZ with the right-handed current is zero, we obtain an interaction that is free of triangle anomalies. This condition enables us to know the angle through whichZ ₁,Z ₂ basis is to be rotated. We show that the triangle anomaly free interaction obtained by others is contained here as a special case. We also determine the triangle anomaly free weak interaction whenever the neutral (Z,D) bosons are mass eigenstates and show that it reduces to the neutral sector of the standard model whenever g _R ² goes to infinity. The charged sector is also developed here. The most general elements of the masssquared matrix of theZ,D bosons are evaluated. The masses of the left- and right-handed charged bosons are also determined.     

Supersymmetric SU C (4) × SU L (2) × SU R (2) and spontaneous breakdown of symmetries

A supersymmetric version of the left right symmetric partial unification group SU _C (4) × SU _L (2) × SU _R (2) is presented. The spontaneous breakdown of gauge symmetry in a favourable chain of descent has been studied in detail. The mass spectra have been calculated. The method of O’Raifeartaigh has been used to break supersymmetry. The lifting of degeneracy of mass levels between physical multiplets has been shown to occur due to radiative corrections.     

SU(3)×SU(2)×U(1) next-to-leading corrections for proton decay in the SU(5) model

We compute in the standard model of SU(3)^c×(SU(2)×U(1)) with massless quarks and leptons the two-loop anomalous dimensions of the four-fermion operators relevant to proton decay in process involving (u, d, e, ν_e). The calculation is carried out by the use of dimensional reduction, a variant of dimensional regularization. Our aim is to give a complete calculation within the SU(5) GUT model of the next-to-leading enhancement-suppression factor for nucleon decay due to renormalization effects arising from hard gluons, W's and B's in process which involve (u, d, e, ν_e). It turns out that the result is sensitive to the ratios x_(i) = M_{H (i)}/M_X where M_H(i) are the masses of the twelve superheavy Higgs scalars in the $\text{24}$ multiplet which breaks SU(5) → SU(3)×SU(2)×U(1).     

Nonlinear local supersymmetric SU(5)-model

We construct a realistic nonlinear supersymmetric SU(5) model without superpartner particles in curved space and investigate the Higgs sector in the limit of flat space. We need at least an adjoint-, a quintuplet- and an antiquintuplet-Higgs multiplet. In order to obtain a realistic breakdown of SU(5) to SU(3) × U(1) at tree level we have to modify the vacuum structure of the adjoint representation in comparison to other SU(5)-models. This model requires an “elegant” fine-tuning. We determine the mass spectrum of the electroweak Higgs sector.     

SUSY SU(5) and hybrid inflation

We consider a scenario of hybrid inflation in the framework of the minimal supersymmetric SU(5) model, compatible, for a quite wide range of initial conditions for inflation scalar fields, with inflation efficiency, monopole dilution and perturbation constraints.     

Hierarchical fermion masses in SU(5)

Rediative masses are generated for the first and the second fermion families by exploiting the idea that their chirality is a symmetry of the “low-energy” SU(3) × SU(2) × U(1) approximation of SU(5), broken only by including the effects of superheavy particles. With only 5's of Higgs coupled to fermions and getting a non-zero vacuum expectation value, we unavoidably get (i) $\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{m}{}_{\mathrm{\mu }}\text{3}$ at the grand unification scale; (ii) the charm quark needing a direct mass as the third family; (iii) neutrino masses of size $\text{? (}\text{α}\text{π}\text{)}\text{M}{}_{\mathrm{W}}{}^2\text{M}$.     

Symmetry breaking of supersymmetric SU(5)

Numerous inequivalent ground states are shown to exist in the supersymmetric SU(5) model. We derive necessary conditions for an explicit breaking of supersymmetry to yield a potential bounded from below and to select the phenomenologically desired vacuum. These requirements are fulfilled in an example.     

Softly broken supersymmetry and SU(5)

We construct an explicit realistic SU(5) model in which softly broken supersymmetry is used to protect the Higgs doublets from quadratic mass renormalization. The model requires one natural but incredibly accurate adjustment of parameters. We argue that such an adjustment will be required in any supersymmetric GUT in which baryon number is not conserved.     

SU(5) at very high energies

By exhibiting the relationship between the fullSU(5) theory in the unitary gauge and the underlying Higgs-Goldstone system in thet'Hooft-Feynman gauge the high energy limits of amplitudes (involving gauge and Higgs bosons) can be calculated easily. As an application tree unitarity bounds on Higgs parameters and masses are discussed.