Phenomenology of non-Abelian flat directions in a minimal superstring standard model

Recently, we presented the first non-Abelian flat directions that produce from a heterotic string model solely the three-generation MSSM states as the massless spectrum in the observable sector of the low energy effective field theory. In this paper we continue to develop the systematic techniques for the analysis of non-renormalizable superpotential terms and non-Abelian flat direction in realistic string models. Some of our non-Abelian directions were F-flat to all finite orders in the superpotential. We study for the same string model the varying phenomenologies resulting from a large set of such all-order flat directions. We focus on the quark, charged lepton, and Higgs doublet mass matrices resulting for our phenomenologically superior non-Abelian flat direction. We review and apply a string-related method for generating large mass hierarchies between MSSM generations, first discussed in string-derived flipped SU(5) models, when all generational mass terms are of renormalizable or very low non-renormalizable order.     

Investigation of quasi-realistic heterotic string models with reduced Higgs spectrum

Quasi-realistic heterotic-string models in the free fermionic formulation typically contain an anomalous U(1) that leads to supersymmetry breaking. Supersymmetry is restored by imposing F- and D-flatness on the vacuum. A three generation free fermionic standard-like model which did not admit stringent F- and D-flat directions has been presented (Cleaver et al. in Phys. Rev. D 78, 046009, 2008) and it was argued that all the moduli in that model were fixed. The particular property of that model was the reduction of the untwisted Higgs spectrum by a combination of symmetric and asymmetric internal dimension boundary conditions with respect to the internal fermions associated with the compactified dimensions. This reduction occurred without the need or presence of flat directions. In this paper we extend the analysis of free fermionic models with reduced Higgs spectrum to models with the same internal space but with modified gauge groups: SO(10) or flipped SU(5) subgroup. We show that all the models studied in this paper do admit stringent flat directions. Currently, the only examples of models that do not admit stringent flat directions are the standard-like models of Cleaver et al. (Phys. Rev. D 78, 046009, 2008). We comment on the relationship between flat directions and reduced Higgs in free fermionic models as well as the possible connection between moduli stabilization and model phenomenology.     

Constraints from charge and colour breaking minima in the (M+1)SSM

We study the constraints on the parameter space of the supersymmetric standard model extended by a gauge singlet, which arise from the absence of global minima of the effective potential with slepton or squark vevs. Particular attention is paid to the so-called “UFB” directions in field space, which are F-flat in the MSSM. Although these directions are no longer F-flat in the (M+1)SSM, we show that the corresponding MSSM-like constraints on m₀/M_1/2 apply also to the (M+1)SSM. The net effect of all constraints on the parameter space are more dramatic than in the MSSM. We discuss the phenomenological implications of these constraints.     

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.     

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.     

A modification of Einstein–Schrödinger theory that contains Einstein–Maxwell–Yang–Mills theory

The Lambda-renormalized Einstein–Schrödinger theory is a modification of the original Einstein–Schrödinger theory in which a cosmological constant term is added to the Lagrangian, and it has been shown to closely approximate Einstein– Maxwell theory. Here we generalize this theory to non-Abelian fields by letting the fields be composed of d × d Hermitian matrices. The resulting theory incorporates the U(1) and SU(d) gauge terms of Einstein–Maxwell–Yang–Mills theory, and is invariant under U(1) and SU(d) gauge transformations. The special case where symmetric fields are multiples of the identity matrix closely approximates Einstein–Maxwell–Yang–Mills theory in that the extra terms in the field equations are < 10^?13 of the usual terms for worst-case fields accessible to measurement. The theory contains a symmetric metric and Hermitian vector potential, and is easily coupled to the additional fields of Weinberg–Salam theory or flipped SU(5) GUT theory. We also consider the case where symmetric fields have small traceless parts, and show how this suggests a possible dark matter candidate.     

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.     

Gauge coupling unification in realistic free-fermionic string models

We discuss the unification of gauge couplings within the framework of a wide class of realistic free-fermionic string models which have appeared in the literature, including the flipped SU(5), SO(6) × SO(4), and various SU(3) × SU(2) × U(1) models. If the matter spectrum below the string scale is that of the Minimal Supersymmetric Standard Model (MSSM), then string unification is in disagreement with experiment. We therefore examine several effects that may modify the minimal string predictions. First, we develop a systematic procedure for evaluating the one-loop heavy string threshold corrections in free-fermionic string models, and we explicitly evaluate these corrections for each of the realistic models. We find that these string threshold corrections are small, and we provide general arguments explaining why such threshold corrections are suppressed in string theory. Thus heavy thresholds cannot resolve the disagreement with experiment. We also study the effect of non-standard hypercharge normalizations, light SUSY thresholds, and intermediate-scale gauge structure, and similarly conclude that these effects cannot resolve the disagreement with low-energy data. Finally, we examine the effects of additional color triplets and electroweak doublets beyond the MSSM. Although not required in ordinary grand unification scenarios, such states generically appear within the context of certain realistic free-fermionic string models. We show that if these states exist at the appropriate thresholds, then the gauge couplings will indeed unify at the string scale. Thus, within these string models, string unification can be in agreement with low-energy data.     

Two dimensional gases of weight charges and SU(N) fermino theories

We analyze two dimensional gases composed of particles interacting via a Coulomb or Yakawa potential through their “non-Abelian” charges. These charges are taken to be elementary weight or root vectors of SU(N). The grand partition function of these gases is shown to be equivalent to the generating functional of sine-Gordon models with weight vectors and hence to that of SU(N) fermion models. The fermion field creates or annihilates topological solitons which have elementary weight vectors as topological quantum numbers. Then, we discuss the confinement of fermions in the SU(N) Higgs models, where instantons (Z_N vortices) constitute a Yukawa gas of weight charges. We prove that fermions are confirmed by the effects of instantons in the SU(N) Higgs models in contrast with the Abelian Higgs model.     

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.     

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.     

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.     

Spectral function sum rules for gluonic currents

We determine the masses and the decay amplitudes of the 2⁺⁺, 0^?+ and 0⁺⁺ gluonia in anSU(3) _c Yang-Mills theory. We estimate the so-called topological susceptibility of theU(1) sector. We discuss theSU(3) _F breaking effects to the η′(896) massrelation from current algebra and predict the η′ parameter values.     

Physical mechanisms responsible for the relaxation time distribution in disordered dielectrics

The relaxation time distribution function F(τ) is calculated in the framework of the random-field theory. The function F(τ) is expressed through the distribution function f(E) of a random electric field E with due regard for the derived dependence of the relaxation time τ on the electric field. The distribution function F(τ) is calculated in terms of the statistical theory within the random-field approximation. The nonlinear random-field contributions and spatial effects of correlations between randomly distributed electric dipoles are taken into account. The calculations are performed for a mixed ferroelectric glassy phase in which the short-range and long-range polar orders coexist. It is demonstrated that the inclusion of nonlinear contributions of the random field leads to an asymmetric relaxation time distribution function F(τ), whereas allowance made only for the linear random-field contributions results in a symmetric function F(τ). A comparison of the calculated functions F(τ) with empirical functions derived from the Cole-Cole (CC), Davidson-Cole (DC), Kohlrausch-Williams-Watts (KWW), and Havriliak-Negami (HN) laws for the dielectric response shows that these laws correspond to disordered systems in which the long-range and short-range orders coexist. Different forms of the function F(τ) are determined by either linear (the CC law) or nonlinear (the DC, KWW, and HN laws) contributions of the random field.     

Comparison of lattice gauge theories with gauge groups Z2 and SU(2)

We study a model of a pure Yang Mills theory with gauge group SU(2) on a lattice in Euclidean space. We compare it with the model obtained by restricting variables to $\text{Z}$₂. An inequality relating expectation values of the Wilson loop integral in the two theories is established. It shows that confinement of static quarks is true in our SU(2) model whenever it holds for the corresponding $\text{Z}$₂-model. The SU(2) model is shown to have high and low temperature phases that are distinguished by a qualitatively different behavior of the 't Hooft disorder parameter.     

The second EMC effect,semileptonic baryon decays and the chiral bag

TheU(1) anomaly gives a massiveη ₀ in the chiralSU(3) limit. We show in this limit how a chiral bag model givesboth theF andD amplitudes consistent with all baryon semileptonic decays,and the integral over the spin structure function measured by the EMC collaboration.     

Natural fermion mass hierarchy and mixings in family unification

We present an SU(9)$\mathit{SU}(9)$ model of family unification with three light chiral families, and a natural hierarchy of charged fermion masses and mixings. The existence of singlet right handed neutrinos with masses about two orders of magnitude smaller than the GUT scale, as needed to understand the light neutrinos masses via the see-saw mechanism, is compelling in our 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).     

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.     

Renormalization group naturalness of GUT Higgs potentials

We analyze the symmetry-breaking patterns of grand unified theories from the point of view of a recently proposed criterion of renormalization-group naturalness. We perform the analysis on simple non-SUSY SU(5) and SO(10) and SUSY SU(5) GUTs. We find that the naturalness criterion can favor spontaneous symmetry breaking in the direction of the smallest of the maximal little groups. Some differences between theories with and without supersymmetry are also emphasized.