E6 Grand Unified Theory Research Articles

Trinification from E6 symmetry breaking

In the context of E6 Grand Unified Theories (GUTs), an intriguing possibility for symmetry breaking to the Standard Model (SM) group involves an intermediate stage characterized by either SU(3) × SU(3) × SU(3) (trinification) or SU(6) × SU(2). The more common choices of SU(5) and SO(10) GUT symmetry groups do not offer such breaking chains. We argue that the presence of a real (rank 2 tensor) representation 650 of E6 in the scalar sector is the minimal and likely only reasonable possibility to obtain one of the novel intermediate stages. We analyze the renormalizable scalar potential of a single copy of the 650 and find vacuum solutions that support regularly embedded subgroups SU(3) × SU(3) × SU(3), SU(6) × SU(2), and SO(10) × U(1), as well as specially embedded subgroups F4 and SU(3) × G2 that do not contain the SM gauge symmetry. We show that for a suitable choice of parameters, each of the regular cases can be obtained as the lowest among the analyzed minima in the potential.

E6 GUT and Baryon Asymmetry Generation in the E6CHM

Grand unified theories (GUTs) may result in the E6-inspired composite Higgs model (E6CHM) at low energies, almost stabilizing the electroweak scale. We consider an orbifold GUT in 6 dimensions in which the E6-gauge group is broken to the gauge symmetry of the standard model (SM) while different multiplets of the SM fermions come from different 27-plets. The strongly coupled sector of the E6CHM is confined on the brane where E6 is broken down to its SU(6) subgroup. Near the scale of f≳5TeV, this approximate SU(6) symmetry is expected to be further broken down to its SU(5) subgroup, which contains the SM-gauge group. Such a breakdown leads to a set of pseudo-Nambu–Goldstone bosons (pNGBs) that includes an SM-like Higgs doublet. The approximate gauge coupling unification in the E6CHM takes place at high energies when the right-handed top quark is a composite fermion. To ensure anomaly cancellation, the weakly coupled sector of this model contains extra exotic matter beyond the SM. We discuss the mechanism of the generation of matter–antimatter asymmetry within the variant of the E6CHM in which the baryon number and CP invariance are violated.

Threshold effects on prediction for proton decay in non-supersymmetric E6 GUT with intermediate trinification symmetry

We consider a non-supersymmetric E6 Grand Unified Theory (GUT) with intermediate trinification symmetry SU(3)C×SU(3)L×SU(3)R×D (D denoted as D-parity for discrete left-right symmetry) and study the effect of one-loop threshold corrections arising due to every class of superheavy particles (scalars, fermions and vectors). It is observed that, the intermediate mass scale MI and sin2⁡θW remain unaffected by GUT threshold contributions. The threshold modified unification mass scale MU is in excellent agreement with the present experimental proton decay constraint. The novel feature of the model is that GUT threshold uncertainty of MU is found to be controlled by superheavy scalars only, leading to a very predictive scenario for proton decay, which can be verifiable within the foreseeable experiments.

Monopoles, strings, and necklaces in SO(10) and E6

We employ a variety of symmetry breaking patterns in SO(10) and E6 Grand Unified Theories to demonstrate the appearance of topological defects including magnetic monopoles, strings, and necklaces. We show that independent of the symmetry breaking pattern, a topologically stable superheavy monopole carrying a single unit of Dirac charge as well as color magnetic charge is always present. Lighter intermediate mass topologically stable monopoles carrying two or three quanta of Dirac charge can appear in SO(10) and E6 models respectively. These lighter monopoles as well as topologically stable intermediate scale strings can survive an inflationary epoch. We also show the ap­ pearance of a novel necklace configuration in SO(10) broken to the Standard Model via SU(4)c × SU(2)L × SU(2)R. It consists of SU(4)c and SU(2)R monopoles connected by flux tubes. Necklaces consisting of monopoles and antimonopoles joined together by flux tubes are also identified. Even in the absence of topologically stable strings, a monopole-string system can temporarily appear. This system decays by emitting gravity waves and we provide an example in which the spectrum of these waves is strongly peaked around 10−4 Hz with Ωqwh2 ≃10−12. This spectrum should be within the detection capability of LISA.

General structure of democratic mass matrix of lepton sector in E6 model

An extension of the Standard Model (SM) fermion sector, which is inspired by the E6 grand unified theory model, may be a good candidate to explain a number of unanswered questions in SM. Existence of the E6 leptons may explain great mass difference of charged and neutral leptons. Also, democracy on mass matrix elements is a natural approach in SM. In this study, we have given general structure of democratic mass matrix of lepton sector in E6 model.

Flavor changing nucleon decay

Recent discovery of neutrino large mixings implies the large mixings in the diagonalizing matrices of 5¯ fields in SU(5) grand unified theory (GUT), while the diagonalizing matrices of 10 fields of SU(5) are expected to have small mixings like Cabibbo–Kobayashi–Maskawa matrix. We calculate the predictions of flavor changing nucleon decays (FCND) in SU(5), SO(10), and E6 GUT models which have the above features for mixings. We found that FCND can be the main decay mode and play an important role to test GUT models.

Effects of dimension-5 operators in E6 grand unified theories

The effective dimension-5 operators can be induced by quantum gravity or inspired by string and M theories. They have important impacts on grand unified theories. We investigate their effects for the well known E(6) model. Considering the breaking chains E6↦H = SO (10)×UV′(1)↦ SU (5)× U V(1)× U V′(1)↦ SU (3)× SU (2)× U Z(1)× U V(1)× U V′(1) and E6↦H = SO (10)× U V′(1)↦ SU (4)× SU L(2)× SU R(2)× U V′(1)↦ SU (3)× SU L(2)× SU R(2)× U S(1)× U V′(1), we derive and give all of the Clebsch–Gordan coefficients [Formula: see text] associated with E6 breaking to the Standard Model (SM). Physical effects of nonzero vacuum expectations of SM singlets Higgs in E6 grand unified theories are discussed.

CLASSIFICATION OF STANDARD MODEL PARTICLES IN E6ORBIFOLD GRAND UNIFIED THEORIES

We classify the standard model fermions, which originate from bulk fields of the 27 or [Formula: see text] representation after orbifold breaking, in E6grand unified theories on five- or six-dimensional space–time, under the condition that q, ecand ucsurvive as zero modes for each 27 or [Formula: see text]. We study features of supersymmetric SU(5) ×U(1)1×U(1)2model.

Flavor Structure of E6 GUT Models

It has been pointed out that in E6 grand unified theory with SU(2) family symmetry, the spontaneous CP violation can solve the supersymmetric CP problem. The scenario predicts V_{ub} \sim O(\lambda^4) rather than O(\lambda^3) which is naively expected value, because of a cancellation at the leading order. Since the experimental value of V_{ub} is O(\lambda^4), it must be important to consider the reason and the conditions for the cancellation. In this paper, we give a simple reason for the cancellation and show that in some E6 models such a cancellation requires that the vacuum expectation value (VEV) of the adjoint Higgs does not break U(1)_{B-L}. Note that this direction of the VEV plays an important role in solving the doublet-triplet splitting problem by Dimopoulos-Wilczek mechanism. In this E6 models, the experiments may measure the direction of the adjoint Higgs VEV by measuring the size of V_{ub} \sim O(\lambda^4).

E6 Unification, Large Neutrino Mixings and SUSY Flavor Problem

This study indicates that in E6 grand unified theories (GUTs), once a hierarchical structure of up-quark-type Yukawa couplings is given as a basic structure of flavor, larger lepton mixings than the quark mixings and milder down-quark-type (and charged-lepton-type) mass hierarchies than up-quark-type mass hierarchy can generically be obtained under a few natural assumptions. The basic flavor structure is compatible with non-Abelian horizontal symmetry, which can solve the SUSY flavor problem. It is shown that in solving the SUSY flavor problem, the E6 structure, which realizes bi-large neutrino mixings, also solves a problem that results from the large neutrino mixing angles.

Non-Abelian horizontal symmetry and anomalous U(1) symmetry for the supersymmetric flavor problem

It is shown that using non-Abelian horizontal gauge symmetry and anomalous U(1)A symmetry in grand unified theories (GUTs), realistic quark and lepton mass matrices including large neutrino mixings can be obtained, while the differences among the scalar fermion masses are sufficiently small for suppression of various flavor changing neutral current (FCNC) processes, especially in E6 GUT. Combining the Higgs sector, in which doublet–triplet splitting is realized, a complete E6×SU(3)H GUT, in which three generations are unified into a single multiplet, Ψ(27,3), is obtained.

Exotic fermion production in a new left-right model at ep colliders

We consider the production at ep colliders of exotic fermions expected in E6 grand unified theories within the context of a new, superstring-inspired, left-right symmetric model. The process e−p→nh+X (with n and h being exotic fermions) proceeds via t-channel WR exchange and can lead to significant production cross sections at HERA energies (√s = 314 GeV) as well as at higher energy ep colliders.

Solar-neutrino oscillations from a supersymmetric E6 grand unified theory.

The solar-neutrino puzzle is solved in the supersymmetric ${\mathrm{E}}_{6}$ grand unified theory by including the contributions of the 5-dimensional terms. The model is shown to lead naturally to large vacuum oscillations of the doublet neutrino into a sterile fermion leading to the possibility of substantial depletion of the solar-electron-neutrino flux.

Naturally light Higgs doublet in supersymmetric E6 grand unified theory.

We show how some supersymmetric E6 grand unified theories, which may arise as the low-energy limit of superstring theory, provide a natural solution of the fine-tuning problem.Received 20 March 1985DOI:https://doi.org/10.1103/PhysRevLett.55.33©1985 American Physical Society