Aspects of left-right symmetric models in superstring phenomenology

The general features of low-energy, rank-six left-right symmetric models as inspired by the superstring are examined. Particular attention is paid to the mass-mixing matrix of the exotic and downtype quarks. It is found that the class of models based on the groupSU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R is plagued with the problem of unnatural fine tuning. Models based on the other left-right group, namelySU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R , work rather well from the points of view investigated. In this case a parameter fitting is presented which is compatible with the lowering of the group rank by two units via radiative breaking, without conflicting either with weak universality or with lepton conservation. The unification scale comes in the 10¹⁷ GeV mass range, the intermediate (righthanded) scale is quite low, not exceeding the 10⁴ GeV range, and the Weinberg angle is correct. Good prospects are also obtained for proton decay and neutrino masses.     

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.     

Fractional charges and the renormalization group in theSU(4)×O(4) string model

We study the renormalization group equations of the gauge couplings in theSU(4)×O(4)～SU(4)×SU(2) _L ×SU(2_ _R string model, derived in the context of the free fermionic formulation of the four dimensional superstring. We calculate the effective string unification scale taking into account string threshold corrections and we consider the consequences of then _L andn _R fractionally charged states, sitting in the (1, 2, 1) and (1, 1, 2) representations correspondingly, of the gauge symmetry of the model. Some of these states become massive at a very high scale, when a number of singlet fields acquire vev's. However, many of them (the precise number depends on the specific choice of the flat direction) remain in the massless spectrum. We consider various cases and find that, for specific choices of flat directions, the physical parameters of the model, like the grand unification scale and the low energy parameters sin²θ _W and α₃, depend only on the differencen _?=n_L-n_R. We study more general cases where remnants of the exotic doublets remain below theSU(4) breaking scale. We also solve the coupled differential system of the renormalization group equations for the gauge and the Yukawa couplings and estimate the range of the top quark mass which is found to lie in the range 140 GeV<m _t<190GeV.     

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.     

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.     

Proton decay in theSU(4) c ×SU(2) L ×SU(2) R model

Possible proton decays in theSU(4) _C ×SU(2) _L ×SU(2) _R unification model are discussed. There are some characteristics in the decay products, which are different from those in the standardSU(5) orSO (10) model, in certain cases.     

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).     

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).     

A q-deformed Lorentz algebra

We derive a q-deformed version of the Lorentz algebra by deforming the algebraSL(2,C). The method is based on linear representations of the algebra on the complex quantum spinor space. We find that the generators usually identified withSL _q(2,C) generateSU _q (2) only. Four additional generators are added which generate Lorentz boosts. The full algebra of all seven generators and their coproduct is presented. We show that in the limitq→1 the generators are those of the classical Lorentz algebra plus an additionalU(1). Thus we have a deformation ofSL(2,C)×U(1).     

Low mass-scale parity restoration in expanded gauge theories

It is shown that schemes of grand unification withSU(2n)⁴ gauge symmetry permit the embedding of the left-right symmetricSU(2) _L ×SU(2) _R ×U(1)×SU(3) ^c intermediate symmetry at relativelylow energies [between 250 GeV and a few TeV] as well as allows light unification mass-scales (≦10⁵ TeV) ifn≧3 for values of the weak angle Sin² θ _W and the strong coupling α _S in the ranges 0.20≦Sin² θ _W ≦0.25, 0.10≦α _S ≦0.15.     

A see-saw model of sterile neutrino

If the smallness of the mass of the sterile neutrino is to be explained by the see-saw mechanism, the off-diagonal entries of the mass matrix needs to be protected by some symmetry not far above the electroweak scale. We implement see-saw mechanism in a gauge model based on SU(2)^q_L×SU(2)^l_L×U(1)^q_Y×U(1)^l_Y un-unified gauge group which breaks to SU(2)_L×U(1)_Y at the TeV region via a two-step symmetry breaking chain. The right handed diagonal block is tied to the highest scale up to which the un-unification symmetry holds. The sterile neutrino emerges from a quark-lepton mixed representation of the un-unified group.     

Spontaneous SU(2) symmetry violation in the SU(2) L × SU(2) R × SU(4) electroweak model

A new approach to electroweak (EW) composite scalars is developed starting from the fundamental gauge interaction on high scale. The latter is assumed to have the group structure SU(2) _L × SU(2) _R × SU(4), where SU(4) is the Pati-Salam color-lepton group. The topological EW vacuum filled by instantons is explicitly constructed and the resulting equations for fermion masses exhibit spontaneous SU(2) flavor symmetry violation with possibility of very large mass ratios.     

Construction of grand unified models under maximal subalgebras

A construction of grand unified models of the strong, weak and electromagnetic interactions is described based on the transformation properties of the group generators under a maximal subgroup decomposition without recourse to large representation matrices or to the specific algebraic structures of some classical Lie-groups, such as the Clifford algebra associated with the orthogonal groups or the octonionic structure of the exceptional groups. To illustrate the procedure an explicit construction is given of the SU(5) model useful in the discussion of higher rank groups, of SO(10) under the maximal subalgebras SU(2)_L × SU(2)_R × SU(4)_c and SU(5) × U(1)_r and of the exceptional group E₆ under SU(3)_L × SU(3)_R × SU(3)_c and SO(10) × U(1)_t. The construction procedure can be used as well with any classical Lie-group.     

Intensities and half-widths at different temperatures for the 201III←000 band of CO2 at 4854 cm−1

Measurements made at temperatures of 197, 233, and 294°K of the absolute intensities and self-broadening coefficients for the vibration-rotation lines of the 201_III←000 band of the ¹²C¹⁶O₂ molecule, are reported. From these measurements, values have been derived for the vibration-rotation interaction factor (F_VR), the purely vibrational transition moment (|R(O)|), and the intensity (S_Band). The results are: E_VR(m) = 1+(2.2±0.7)×10^?3m+(5.6±1.6)×10^×5m², |R(0)| = (2.064±0.017)×10^?3 debye, S_Band = 21,329±69 cm^?1km^?1atm^?1_STP. The results for the self-broadening coefficients are presented in the text.     

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.     

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.     

Flavour non-conservation induced by Higgs particle exchange inSU(2)L×SU(2)R×U(1) model

The VEV of the Higgs field inSU(2)_L×SU(2)_R×U(1) model is discussed in the context of the flavour changing neutral currents. The lower bound of Higgs particle mass is found (m _H ?3 TeV).     

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.     

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.