Transition from SU(2)L × SU(2)R × U(1)B-L representation to SU(2)L × U(1)Y by q-deformation and the corresponding classical breaking term of chiral U(2)

The minimal Standard Model exhibits a nontrivial chiral U(2) symmetry if the VEV and the hypercharge splitting Δ = (y-y)/2 of right-handed leptons (quarks) in a family vanish and Q = T₀ + Y independently in each helicity sector. As a generalization, we start with SU(2)_L × SU(2)_R × U(1)_(B-L) and introduce Δ as a continuous parameter which is a measure of explicit symmetry breakdown. Values 0 ? Δ ? 1/2 take the neutral generator of the isospin ½ representation to the singlet representation, i.e. ‘deformes’ the LR representation into the minimal Standard one. The corresponding classical O(3)-breaking term is a magnetic field perpendicular to the x₃-axis. A simple mapping on the fundamental Drinfeld-Jimbo q-deformed SU(2) representation is given.     

Discrete symmetries in SO(N) grand unified groups and the survival hypothesis

The possibility of introducing the discrete symmetry D is studied, which along with SU^c(3) × SU_L(2) × U(1)-symmetry, remains after the breaking of SO(N) grand unified symmetry by the Higgs fields vevs ～ 10¹⁵ GeV. The D quantum number distinguishes the fermions coupled with W-bosons via left and right currents. As a result, the presence of low-mass fermions in the theory is provided.     

Supersymmetric models of weak and electromagnetic interactions

General method of spontaneous supersymmetry breaking is developed. On its basis a number of unified lepton models is analyzed. Examples of realistic lepton models based on the groups SU(2) × U(1) and SU(2) × SU(2) × U(1) are considered.     

A supersymmetricSU(5)×U(1) model with natural gauge hierarchy

We present a supersymmetricSU(5)×U(1) model. This model has the following features. The gauge hierarchy is naturally generated by the quadratically divergent nature of the Fayet-IliopoulosD term. TheSU(5)×U(1) gauge symmetry breaks uniquely intoSU(3) _W ×SU(2) _c ×U(1) _y at an energy scale of 10^17–18GeV. The non-vanishing vacuum expectation value of an auxiliary field component ofU(1) gauge vector multiplet induces the breaking ofSU(2) _W ×U(1) _y . It gives a mass of 10^2–3GeV to scalar quarks and scalar leptons at the tree level. The renormalization group analysis shows that the color fine structure constant α _C (M _W ) becomes somewhat small and the Weinberg angle sin²θ _W (M _W ) somewhat too large in a simple version of the model.     

Phase portrait ofSU(5) model. II intermediate phasesSU(3)×[U(1)]2 and [SU(2)]2×[U(1)]2

The effective potential of the scalar field in theSU(5) model has extrema with symmetry:SU(5),SU(4)×U(1),SU(3)×SU(2)×U(1),SU(3)×[U(1)]², [SU(2)]²×[U(1)]². In our recent paper it was shown that theSU(4)×U(1) phase as well asSU(3)×SU(2)×U(1) phase were stable at the nonzero temperature in a vast region of parameters. In the present paper it is found that the [SU(2)]²×[U(1)]² symmetric vacuum is unstable and theSU(3)×[U(1)]² symmetric vacuum can be metastable in the certain interval of the temperature. Domains of the three phases:SU(4)×U(1),SU(3)×SU(2)×U(1),SU(3)×[U(1)]²-could co-exist in the early. Universe.     

Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges

Starting with the definition of quaternion gauge theory, we have undertaken the study of SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m in terms of the simultaneous existence of electric and magnetic charges along with their Yang-Mills counterparts. As such, we have developed the gauge theory in terms of four coupling constants associated with four-gauge symmetry SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m . Accordingly, we have made an attempt to obtain the abelian and non-Abelian gauge structures for the particles carrying simultaneously the electric and magnetic charges (namely dyons). Starting from the Lagrangian density of two SU(2)×U(1) gauge theories responsible for the existence of electric and magnetic charges, we have discussed the consistent theory of spontaneous symmetry breaking and Higgs mechanism in order to generate the masses. From the symmetry breaking, we have generated the two electromagnetic fields, the two massive vector W ^± and Z ⁰ bosons fields and the Higgs scalar fields.     

The construction of vector-like supersymmetric gauge models of weak and electromagnetic interactions

Despite great efforts and partial successes the situation with respect to spontaneously broken supersymmetric unified gauge models of weak, electromagnetic and strong interactions has remained quite unsatisfactory up to now. Starting from the most simple SU(2) × U(1) cases we exploit possible extensions. This naturally leads to a consideration of vector-like models with—in the first instance—a larger number of multiplets. Although the later can be made massive without spoiling the conservation of fermion number, the additional massive fermions only show parity conserving interactions with all the intermediate vector fields. Therefore models with larger gauge groups are considered: SU(2) × SU(2) × U(1) with two quartets, SU(3) × U(1) with four triplets, and finally SU(3) × SU(2) × U(1) with two sextets of matter fields. None of these can be accepted yet as a true model for physical particles, but it is shown how different negative features in the simple theories may be avoided in the more complicated ones. Thus our results may be considered as an encouraging starting point for investigations of larger gauge groups in supersymmetric models.     

A minimalSU(2)×U(1)×U(1) electroweak model with mirror fermions

We present a minimal extension of the standard electroweak model, which accommodates mirror fermions, based onSU(2)×U(1)×U(1). Mirror mixing happens through sterile neutrino states and induces radiative mixing for charged leptons. Quarks and mirror quarks are not mixed with each other, consistent with the suppression of flavour changing neutral currents. Higgs sector, fermion masses and neutral currents are discussed. In this scheme there can be a secondZ boson as light as 0.2TeV.     

Phenomenology ofSO(10) unified superstring models with intermediate scaleSU R(2) breaking

Electroweak breaking and the supersymmetric particle spectrum are discussed in superstring theories where the gauge group after compactification isSO(10)×E _s ^′ , and where the gauge symmetry after flux breaking isSU(3)×SU(2)×SU(2)×U(1).     

The SU(5) potential in desitter space

The one-loop effective potential for a minimal SU(5) theory is calculated on a curved DeSitter background spacetime. The stability of its extrema in the following subgroups is investigated: SU(4) × U(1), SU(3) × SU(2) × U(1), SU(3) × U(1) × U(1), SU(2) × SU(2) × U(1) × U(1). A combination of analytic and numerical methods is used to obtain phase diagrams for the model. In the inflationary universe, the curvature effects do not prevent a slide into the SU(4) × U(1) extremum.     

The symmetry breaking patternSU(5)→SU(3)×U(1) including one loop radiative corrections

We derive conditions on the Higgs parameters of the minimalSU(5) model under which the phenomenologically desired symmetry breaking patternSU(5)→SU(3)×U(1) persists at the one loop level.     

A low composite scale preon model with complementarity

We have constructed the first “realistic candidate” preon model with low composite scale satisfying complementarity between the Higgs and confining phases. The model is based onSU(4) metacolor and predicts four generations of ordinary quarks and leptons together with heavy neutrinos at the level of the standard gauge groupSU(3) _c ×SU(2) _L ×U(1) _Y . There are no exotic massless fermions. The global family group isSU(2)×U(1).     

Supersymmetric non-linear σ model onE 8/SO(10)×SU(3)×U(1)

We calculate the Kähler potential of theE ₈/SO(10)×SU(3)×U(1) homogeneous space. Some quasi Nambu-Goldstone fermions living in the corresponding supersymmetric non-linear σ model are identified with the usual three families of quarks and leptons, and one mirror family. We also show that the dynamical breakdown of supersymmetry does not occur in this model.     

Is hypercharge U(1) in Weinberg's model redundant?

The U₁ × U₁(loc) × SU₂(loc) invariant Weinberg lagrangian can be reduced to a U₁ × SU₂(loc) invariant lagrangian without hypercharge group involving only a single left-handed Weyl spinor field and an isotriplet gauge vector field. Spontaneous symmetry breakdown is induced by condensation of fermion pairs. Charge appears simply as “isospin charge”.     

Phase portrait ofSU(5) grand unified model

The one-loop effective potential of theSU(5) model is investigated both in high and low temperature approximation. We find the regions of values of coupling constants and temperatures where theSU(5), theSU(4)×U(1) and theSU(3)×SU(2)×U(1) symmetric states are metastable. A general method of such an investigation is proposed. We observe that the domain structure of the Universe with the simultaneous existence of the gauge symmetriesSU(4)×U(1) andSU(3)×SU(2)×U(1) in different domains could take place.     

Regge Couplings From SU(2) × SU(2) Saturation Schemes

For any saturation scheme of the chiral SU(2) × SU(2) charge algebra we develop a simple algebraic method of calculating the couplings of ϱ and f trajectories to all particles involved. The information on these coupling is shown to be directly contained in the chiral mass splittings among the different isospin multiplets.     

Gravitational anomaly and fundamental forces

I present an argument, based on the topology of the universe, why there are three generations of fermions. The argument implies a preferred unified gauge group of SU(5), but with SO(10) representations of the fermions. The breaking pattern SU(5) → SU(3) × SU(2) × U(1) is preferred over the pattern SU(5) → SU(4) × U(1). On the basis of the argument one expects an asymmetry in the early universe microwave data, which might have been detected already.     

Hierarchy of symmetry breakings and neutral currents in anSU(6) grand unification model

In anSU(6) grand unification model with eight quarks and eight leptons belonging to 15-plet and singlet representations, the symmetry is spontaneously broken by the sequenceSU(6)SU(3) ^c ×SU(2)×U(1)×U(1)SU(3) ^c ×U(1). Fror two cases of symmetry breakings the effective weak neutral current coupling constants are compared with experiment. For theSU(3) ^c ×SU(2)×U(1)×U(1)×SU(3) ^c ×U(1) symmetry breaking, the coupling constants reproduce the Weinberg-Salam model with a small correction term. Agreement with the experimental mean values is improved with the correction term. Parity violation in atomic physics is also discussed.     

TheR-symmetry violation inN=2 supersymmetric models and the properties of lightest SUSY particle

The present paper discusses the spontaneousR-symmetry violation in theN=2 SUSYSU(4)×U(1) model [1] with soft SUSY breaking terms preserving finiteness. In particular, the mechanism producing a light photino (as a probable candidate for LSP) of a mass of up to some GeV is suggested. InR-odd versions of this model the mechanism of enhancement of the photino decay is discussed.     

Fermion masses and mixing angles in anSU(2) L ×U(1) model with horizontal interactions

AnSU(2) _L ×U(1) horizontal model is presented, in which fermions mass splitting, quark and lepton family mixing is attributed to the presence of the horizontal interactions. In the quark sector, the Cabibbo angle and the Cabibbo-like angles are evaluated. In the lepton sector, the neutrinos mixing angles, which orginate from the charged leptons mixing, are calculated, the scale of the horizontal interactions is related to the neutrino oscillation length.