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).     

General description of new physics in t,b and boson interactions and its unitarity constraints

We list all possible dim = 6 CP conserving and SU(3) × SU(2) × U(1) gauge invariant interactions, which could be generated in case no new particles would be reachable in the future Colliders, and the only observable New Physics would be in the form of new interactions affecting the scalar sector and the quarks of the third family. These interactions are described by operators involving the standard model scalar field, the quarks of the third family and the gauge bosons. Subsequently, we identify those operators which do not contribute to LEP1 (and lower energy) observables at tree level and are not purely gluonic. Since present measurements do not strongly constrain the couplings of these operators, we derive here the unitarity bounds on them. Finally, in order to get a feeling on the possible physical meaning of the appearance of any of these operators, we identify the operators generated in a class of renormalizable dynamical models which at the TeV scale, are fully described by the SU(3) × SU(2) × U(1) gauge group.     

Octonionic Non-Abelian Gauge Theory

We have made an attempt to describe the octonion formulation of Abelian and non-Abelian gauge theory of dyons in terms of 2×2 Zorn vector matrix realization. As such, we have discussed the U(1) _e ×U(1) _m Abelian gauge theory and U(1)×SU(2) electroweak gauge theory and also the SU(2) _e ×SU(2) _m non-Abelian gauge theory in term of 2×2 Zorn vector matrix realization of split octonions. It is shown that SU(2) _e characterizes the usual theory of the Yang Mill’s field (isospin or weak interactions) due to presence of electric charge while the gauge group SU(2) _m may be related to the existence of ’t Hooft-Polyakov monopole in non-Abelian Gauge theory. Accordingly, we have obtained the manifestly covariant field equations and equations of motion.     

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 Unified SU(2) × U(1) × U′(1)-models of Electroweak Interaction of Leptons

The possible variants of the unified models of electroweak interaction of leptons in the framework of the broken gauge SU(2) × U(1) × U′(1)-symmetry are constructed. In the first part analysis of SU(2) × U(1) × U′(1)-symmetry breaking by the different combinations of two types of Goldstone-Higgs fields: isodoublet φ and isosinglet Φ complex isovector ξ and Φ φ and ξ is considered. The second part is devoted to the construction of the feasible leptonic models in which the masses of the introduced leptons can be generated by symmetry breaking due to the fields considered in the first part. In the third part acceptability of these models from the point of view of available experimental data of cross-sections of muonic neutrino and antineutrino scattering on electron has been investigated.     

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.     

Baryon number non-conservation as a low-scale phenomenon

We analyse Baryon number non-conservation as a result of scalar boson mediated interactions characterised by a low mass scale (in the TeV region) in the framework of the standardSU(3)×SU(2)×U(1) gauge group.     

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.     

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.     

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.     

Restrictions on realistic superstring models from renormalization group equations

The renormalization group equations for supersymmetric models are re-examined considering the normalization factor of the hypercharge as a free parameter. This possibility has recently been raised in the context of superstring theories. Very important (and simple) restrictions for the phenomenological viability of the models are obtained. Several examples (some of them with great physical relevance) are given in order to illustrate how the analysis of an important class of SU(3)×SU(2)×U(1)_Ysuperstring constructions can be carried out. Many models can be ruled out in this way, which is welcome for the predictive power of the theory.     

A model for the u-d mass difference

Extending the conditions which lead to natural symmetries we show that m_d?m_u can be made positive in an SU(2)_L × SU(2)_R × U(1) gauge model for the weak and electromagnetic interactions.     

The supersymmetric Higgs mechanism—Quartet decoupling and nondoubled Goldstone bosons

A complete quantum field theoretic analysis of the supersymmetric Higgs mechanism is presented, in the general case where the Goldstone bosons may be either doubled or nondoubled. If gauge fields are coupled to nondoubled Goldstone bosons, it is found that supersymmetry is spontaneously broken not just by the masses but also by the spins of the physical particles. The spectrum reveals no supersymmetry multiplet structure. The decoupling of unphysical degrees of freedom is carefully discussed, and the quartet decoupling mechanism for gauged Goldstone bosons is extended to supersymmetry theories. The results are illustrated with an SU(2) × U(1) model.     

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).     

Signals of new gauge bosons at futuree + e − colliders

We analyze possible indirect signals of additional neutral gauge bosons at futuree ⁺ e ^? colliders, concentrating onSU(2) _L ×U(1) _y ×U(1) _y , andSU(2) _L ×SU(2) _R ×U(1) effective theories. We develop a simple formalism to describe these effects and make a careful study of radiative corrections, in particular initial state radiation, which will be shown to have important implications. To make realistic estimates of the sensitivity to the new gauge boson effects, we use a model detector fore ⁺ e ^? annihilation at a center of mass energy of 500 GeV. Using a number of selected physical observables we then show that masses considerably higher than the total energy (up to a factor of 6) can be probed and that distinction between various theoretical models is possible.     

B^0 - \bar B^0 mixing in a supersymmetric model without at-quark

A model based on a low energySU(3)_c×SU(2)₁×SU(2)₂×U(1) _H gauge group is considered. Theb-quark couples mainly to thec-quark via a new heavyW-boson and thet-quark is omitted altogether. The model is shown to be compatible with low energy charged current data. \(B_d^0 - \bar B_d^0 \) mixing occurs through the exchange of the heavyW-boson and through gluino exchange in the supersymmetric version of the model. The calculated mixing is much smaller in both cases than the observed effect and the model is, therefore, ruled out.     

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.     

The anomalous 3-boson couplings as an implication of the Higgs sector

We discuss the possible new electroweak interactions which may be generated by the Higgs sector at the scale of theZ mass. For this purpose, we give a set ofSU(2)×U(1) gauge invariant operators constructed in terms ofW, Z, γ and Higgs fields which in the unitary gauge describe all possible γWW andZWW anomalous couplings. The dimension of these operators varies from 6 to 12. This fact allows us to consider various scenaria for the manifestations of the New Physics. We conclude that the underlying dynamics induced by the Higgs sector can be tested through a model-independent amplitude analysis of gauge boson pair production at LEP2 and future colliders.     

Gauge symmetries of electroweak interactions

By considering the symmetries associated with baryon number and lepton number conservation as gauge symmetries, the underlying gauge symmetry of weak electromagnetic interactions is shown to beSU(2) _L ×U(1)×U(1)Baryon×U(1)_Lepton. If right-handed currents exist on a par with the observed left-handed ones, then the full symmetry of electroweak interactions that emerges isSU(2)_L×SU(2)_R×U(1)_Baryon×U(1)_Lepton. These symmetries offer a rich spectrum of massive neutral gauge bosons, one of which is the massive neutral boson of the standardSU(2) _L ×U(1) _Y model.     

Algebraic constraints for higgs multiplets

The phenomenon of spontaneous breaking of a gauge symmetry group, provides a number of algebraic constraints which Scalar Higgs mesons have to satisfy. We discuss these constraints and give details for the cases ofSU(2),SU(2) ×U(1) andSU(3).