Unified Gauge Group Research Articles

Models of accidental dark matter with a fundamental scalar

We consider models of accidental dark matter, namely models in which the dark matter is a composite state that is stable thanks to an accidental symmetry of the theory. The fundamental constituents are vectorlike fermions, taken to be fragments of representations of the grand unifying gauge group SU(5), as well as a scalar singlet. All the new fields are charged under a new confining gauge group, which we take to be SU(N), leading to models with complex dark matter. We analyse the models in the context of SU(5) grand unification with a non-standard approach recently proposed in the literature. The advantage of including the scalar mainly resides in the fact that it allows several undesired accidental symmetries to be broken, leading to a larger set of viable models with respect to previous literature, in which only fermions (or only scalars) were considered. Moreover these models present distinct novelties, namely dark states with non-zero baryon and lepton number and the existence of composite hybrid states of fermions and scalars. We identify phenomena that are specific to the inclusion of the scalar and discuss possibilities to test this setup.

Attempt at constructing a model of grand gauge-Higgs unification with family unification

We discuss a possibility whether a model of grand gauge-Higgs unification incorporating family unification in higher dimensions can be constructed. We first extend a five-dimensional SU(6) grand gauge-Higgs unification model to a five-dimensional SU(7) grand gauge-Higgs unification model compactified on an orbifold S1/Z2 to obtain three generations of quarks and leptons after symmetry breaking of the larger family unified gauge group. A prescription of constructing a six-dimensional SU(N) grand gauge-Higgs unification model including a five-dimensional SU(7) grand gauge-Higgs unification after compactifying the sixth dimension on an orbifold S1/Z2 is given. We find a six-dimensional SU(14) grand gauge-Higgs unification model with a set of representations containing three generations of quarks and leptons. Published by the American Physical Society 2024

GUTs, hybrid topological defects, and gravitational waves

The symmetry breaking of grand unified gauge groups in the early Universe often leaves behind relic topological defects such as cosmic strings, domain walls, or monopoles. For some symmetry breaking chains, hybrid defects can form where cosmic strings attach to domain walls or monopoles attach to strings. In general, such hybrid defects are unstable, with one defect ``eating'' the other via the conversion of its rest mass into the other's kinetic energy and, subsequently, decaying via gravitational waves. In this work, we determine the gravitational wave spectrum from 1) the destruction of a cosmic string network by the nucleation of monopoles which cut up and ``eat'' the strings, 2) the collapse and decay of a monopole-string network by strings that eat the monopoles, 3) the destruction of a domain wall network by the nucleation of string-bounded holes on the wall that expand and eat the wall, and 4) the collapse and decay of a string-bounded wall network by walls that eat the strings. We call the gravitational wave signals produced from the eating of one topological defect by another ``gravitational wave gastronomy.'' We find that the four gravitational wave gastronomy signals considered yield unique spectra that can be used to narrow down the $SO(10)$ symmetry breaking chain to the Standard Model and the scales of symmetry breaking associated with the consumed topological defects. Moreover, the systems we consider are unlikely to have a residual monopole or domain wall problem.

Unification of Strong-Weak Interactions and Possible Unified Scheme of Four-Interactions

First, various known unified theories of interactions in particle physics are reviewed. Next, strong and weak interactions are all short-range, which should more be unified. Except different action ranges their main character is: strong interactions are attraction each other, and weak interactions are mutual repulsion and derive decay. We propose a possible method on their unification, whose coupling constants are negative and positive, respectively. Further, we propose a figure on the unification of the four basic interactions in three-dimensional space, and search some possible tests and predictions, for example, strong-weak interactions transform each other, some waves may be produced. Finally, based on the simplest unified gauge group GL(6,C) of four-interactions, a possible form of Lagrangian is researched. Some relations and equations of different interactions are discussed.

Bosonic higher spin gravity in any dimension with dynamical two-form

We alter Vasiliev’s original bosonic higher spin gravity in any dimension beyond the linearized level by factoring out a modified sp(2) gauge algebra. The new model can be embedded together with a dynamical two-form and an extra dynamical one-form into a flat Quillen superconnection. Further duality and sp(2) ghost extensions lead to a FrobeniusChern-Simons action in which the sp(2) and higher spin gauge symmetries are subsumed into a unified Cartan gauge group at the fully non-linear level.

A review of neutrino properties Neutrino oscillations - a historical overview and its projection

In a first part neutrino properties are presented from the beginnings through the letter of Wolfgang Pauli on 4. December 1930 suggesting a new neutral fermion to the “Radioactive Ladies and Gentlemen” at a Conference in Tübingen, contributing to the first oscillation cycle, based on my review at the meeting “Neutrino Telescopes in Venice” in 2005. cited in [1]. In the remaining part I shall present a selection of neutrino properties featuring the structure of mass and mixing of the light and heavy neutrino flavors, a symmetric, complex 6 by 6 matrix within the unifying SO10 gauge group, and present prospects for the detection of the leptonflavor violating processes Bs → μe; B → K μ e, also such involving b-flavored baryons .

GUT and Flavor Models for Neutrino Masses and Mixing

In the recent years experiments have established the existence of neutrino oscillations and most of the oscillation parameters have been measured with a good accuracy. However, in spite of many interesting ideas, no real illumination was sparked on the problem of flavor in the lepton sector. In this review, we discuss the state of the art of models for neutrino masses and mixings formulated in the context of flavor symmetries, with particular emphasis on the role played by grand unified gauge groups.

Analysis of the right-handed Majorana neutrino mass in an SU(4)×SU(2)L×SU(2)R Pati-Salam model with democratic texture

In this paper, we attempt to build an unified model with democratic texture, that have some unification between $Y_{\nu}$ and $Y_{u}$. Since the $S_{3L} \times S_{3R}$ flavor symmetry is chiral, the unified gauge group is assumed to be Pati-Salam type $SU(4)_{c} \times SU(2)_{L} \times SU(2)_{R}$. The flavor symmetry breaking scheme is considered to be $S_{3L} \times S_{3R} \to S_{2L} \times S_{2R} \to 0$. In this picture, the four-zero texture is desirable for realistic mass and mixings. This texture is realized by a specific representation for the second breaking of the $S_{3L} \times S_{3R}$ flavor symmetry. Assuming only renormalizable Yukawa interactions, type-I seesaw mechanism, and neglecting $CP$ phases for simplicity, the right-handed neutrino mass matrix $M_{R}$ can be reconstructed from low energy input values. Numerical analysis shows that the texture of $M_{R}$ basically behaves like the "waterfall texture". Since $M_{R}$ tends to be the "cascade texture" in the democratic texture approach, a model with type-I seesaw and up-type Yukawa unification $Y_{\nu} \simeq Y_{u}$ basically requires fine-tunings between parameters. Therefore, it seems to be more realistic to consider universal waterfall textures for both $Y_{f}$ and $M_{R}$, e.g., by the radiative mass generation or the Froggatt--Nielsen mechanism. Moreover, analysis of eigenvalues shows that the lightest mass eigenvalue $M_{R1}$ is too light to achieve successful thermal leptogenesis. Although the resonant leptogenesis might be possible, it also requires fine-tunings of parameters.

Threshold corrections to baryon number violating operators in supersymmetric [formula omitted] GUTs

The nucleon decay is a significant phenomenon to verify grand unified theories (GUTs). For the precise prediction of the nucleon lifetime induced by the gauge bosons associated with the unified gauge group, it is important to include the renormalization effects on the Wilson coefficients of the dimension-six baryon number violating operators. In this study, we have derived the threshold corrections to these coefficients at the one-loop level in the minimal supersymmetric SU(5) GUT and the extended one with additional SU(5) vector-like pairs. As a result, it is found that the nucleon decay rate is suppressed about 5% in the minimal setup, and then the suppression could be O(10)% in the vector-like matter extensions.

Neutrino masses and SO10 unification

We present the embedding of the SM gauge group in SO10, a simple, compact unifying gauge group, with each of the three basic spin 1/2 families forming a unitary, irreducible 16-dimensional representation of spin10, which is complex, i.e. chiral. Subtle differences to the mixed representations of SU5, contained in the SO10 scheme, are pointed out. These have consequences for neutrino flavors, which become paired in a light [Formula: see text]-active doublet mode and a heavy SM singlet mode, one [Formula: see text], [Formula: see text]-pair per family.

Naturalness and dimensional transmutation in classically scale-invariant gravity

We discuss the nature of quantum field theories involving gravity that are classically scale-invariant. We show that gravitational radiative corrections are crucial in the determination of the nature of the vacuum state in such theories, which are renormalisable, technically natural, and can be asymptotically free in all dimensionless couplings. In the pure gravity case, we discuss the role of the Gauss-Bonnet term, and we find that Dimensional Transmutation (DT) \`a la Coleman-Weinberg leads to extrema of the effective action corresponding to nonzero values of the curvature, but such that these extrema are local maxima. In even the simplest extension of the theory to include scalar fields, we show that the same phenomenon can lead to extrema that are local minima of the effective action, with both non-zero curvature and non-zero scalar vacuum expectation values, leading to spontaneous generation of the Planck mass. Although we find an asymptotically free (AF) fixed point exists, unfortunately, no running of the couplings connect the region of DT to the basin of attraction of the AF fixed point. We also find there remains a flat direction for one of the conformal modes. We suggest that in more realistic models AF and DT could be compatible, and that the same scalar vacuum expectation values could be responsible both for DT and for spontaneous breaking of a Grand Unified gauge group.

Unified Theories of Gravitational and Electromagnetic Fields in Riemannian Geometry and Higher Dimension

Some unified theories on the gravitational and electromagnetic fields are researched. We investigate mainly two new geometric unified theories. A method is that the gravitational field and the source-free electromagnetic field can be unified by the equations Rklmi = κTklmi* in the Riemannian geometry, both are contractions of im and ik, respectively. If Rklmi = κTklmi* =constant, it will be equivalent to the Yang’s gravitational equations Rkm;l –Rkl;m = 0, which include Rlm= 0. From Rlm= 0 we can obtain the Lorentz equations of motion, the first system and second source-free system of Maxwell’s field equations. This unification can be included in the gauge theory, and the unified gauge group is SL(2,C) × U(1)=GL(2,C), which is just the same as the gauge group of the Riemannian manifold. Another unified method on the general nonsymmetric metric field with high-dimensional space-time and its matrix representations are analyzed mathematically. Further, the general unified theory of five-dimensional space-time combined quantum theory and four interactions is researched. Some possible unification ways on the gravitational and electromagnetic fields are discussed. The general matrix and various corresponding theories may decompose to a sum of symmetry and antisymmetry. Moreover, we proposed an imaginative representation on the ten dimensional space-time.

Proton stability in low-scale extra-dimensional grand unified theories

We propose an extra-dimensional mechanism that adequately suppresses the rate of proton decay mediated by the $X$ bosons in grand unified theories. The $X$ bosons and their Kaluza-Klein modes are localized in the extra spatial dimensions due to the kink configuration of the adjoint Higgs multiplet that is responsible for the spontaneous breaking of the unified gauge group while the standard model gauge bosons freely propagate in the bulk. By localizing fermion multiplets apart from the $X$ bosons in the extra dimensions, the resulting four-dimensional couplings that give rise to proton decay are exponentially suppressed, leading to the longevity of the proton even when the mass scale of the $X$ bosons is much lower than the usual unification scale.

Beam polarization effects in the radiative production of lightest neutralinos ine+e−collisions in supersymmetric grand unified models

We study the production of the lightest neutralinos in the process $e^+ e^- \rightarrow \chi_1^0 \chi_1^0 \gamma$ in supersymmetric grand unified models for the International Linear Collider Energies with longitudinally polarized beams. We consider cases where the standard model gauge group is unified into the grand unified gauge groups SU(5), or SO(10). We have carried out a comprehensive study of this process in the SU(5) and SO(10) grand unified theories which includes the QED radiative corrections. We compare and contrast the dependence of the signal cross section on the grand unified gauge group, and on the different representations of the grand unified gauge group, when the the electron and positron beams are longitudinally polarized. To assess the feasibility of experimentally observing the radiative production process, we have also considered in detail the background to this process coming from the radiative neutrino production process $e^+ e^- \rightarrow \nu \bar\nu \gamma$ with longitudinally polarized electron and positron beams. In addition we have also considered the supersymmetric background coming from the radiative production of scalar neutrinos in the process $e^+ e^- \rightarrow \tilde \nu \tilde\nu^* \gamma$ with longitudinally polarized beams. The process can be a major background to the radiative production of neutralinos when the scalar neutrinos decay invisibly.

RADIATIVE PRODUCTION OF LIGHTEST NEUTRALINOS IN e+e-COLLISIONS IN SUPERSYMMETRIC GRAND UNIFIED MODELS

We study the production of the lightest neutralinos in the radiative process [Formula: see text] in supersymmetric models with grand unification. We consider models wherein the standard model (SM) gauge group SU(3)c×SU(2)L×U(1)Yis unified into the grand unified gauge groups SU(5) or SO(10). We study this process at energies that may be accessible at a future International Linear Collider (ILC). We compare and contrast the dependence of the signal cross-section on the grand unified gauge group, and different representations of the grand unified gauge group, into which the SM gauge group is unified. We carry out a comprehensive study of the radiative production process which includes higher-order QED corrections in our calculations. In addition we carry out a detailed study of the background to the signal process coming from the SM radiative neutrino production [Formula: see text], as well as from the radiative production of the scalar partners of the neutrinos (sneutrinos) [Formula: see text]. The latter can be a major supersymmetric background to the radiative production of neutralinos when the sneutrinos decay invisibly. It is likely that the radiative production of the lightest neutralinos may be a viable channel to study supersymmetric partners of the SM particles at the first stage of an ILC, where heavier sparticles may be too heavy to be produced in pairs.

Enhancement of proton decay rates in supersymmetric SU(5) grand unified models

In the supersymmetric grand unified theories (SUSY GUTs), gauge bosons associated with the unified gauge group induce proton decay. We investigate the proton decay rate via the gauge bosons in the SUSY GUTs under the two situations; one is with extra vector-like multiplets, and the other is with heavy sfermions. It is found that the proton lifetime is significantly reduced in the former case, while in the latter case it is slightly prolonged. Determination of the particle contents and their mass spectrum below the GUT scale is important to predict the proton lifetime. The proton decay searches have started to access to the 1016GeV scale.

Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo–Kobayashi–Maskawa (CKM) unitarity triangle, α ≈ 90 ° . The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU ( 5 ) , a discrete family symmetry such as A 4 or S 4 , a shaping symmetry including products of Z 2 and Z 4 groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of α ≈ 90 ° by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1–3 texture zeros that satisfy the “phase sum rule” and lepton mass matrices that satisfy the “lepton mixing sum rule” together with a new prediction that the leptonic CP violating oscillation phase is close to either 0°, 90°, 180°, or 270° depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors.

Right-handed neutrinos in F-theory compactifications

F-theory is one of the frameworks where up-type Yukawa couplings of SU(5) unified theories are naturally generated. As charged matter fields have localized zero modes in F-theory, a study of flavor structure could be easier in F-theory than in Heterotic string theory. In a study of flavor structure in the lepton sector, however, an important role is played by right-handed neutrinos, which are not charged under the SU(5) unified gauge group. It is therefore solicited to find out what right-handed neutrinos are in F-theory compactifications and how their Majorana mass terms are generated together with developing a theoretical framework where effective Yukawa couplings involving both SU(5)-neutral and charged fields can be calculated. We find that the complex structure moduli chiral multiplets of F-theory compactifications are good candidates to be right-handed neutrinos, and that their Majorana masses are automatically generated in flux compactifications. The mass scale is predicted to be somewhat below the GUT scale, which is in nice agreement with the Δ m 2 of the atmospheric neutrino oscillation through the see-saw mechanism. We also discuss various scenarios of solving the dimension-4 proton decay problem in supersymmetric F-theory compactifications, along with considering the consequences of those scenarios in the nature of right-handed neutrinos.

Cosmotopological relation for a unified field theory

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){yields}SU(3)xSU(2)xU(1) is preferred over the pattern SU(5){yields}SU(4)xU(1). On the basis of the argument one expects an asymmetry in the early universe microwave data, which might have been detected already.

SPARTICLE MASS SPECTRUM IN GRAND UNIFIED THEORIES

We carry out a detailed analysis of sparticle mass spectrum in supersymmetric grand unified theories. We consider the spectroscopy of the squarks and sleptons in SU (5) and SO (10) grand unified theories, and show how the underlying supersymmetry breaking parameters of these theories can be determined from a measurement of different sparticle masses. This analysis is done analytically by integrating the one-loop renormalization group equations with appropriate boundary conditions implied by the underlying grand unified gauge group. We also consider the impact of nonuniversal gaugino masses on the sparticle spectrum, especially the neutralino and chargino masses which arise in supersymmetric grand unified theories with nonminimal gauge kinetic function. In particular, we study the interrelationships between the squark and slepton masses which arise in grand unified theories at the one-loop level, which can be used to distinguish between the different underlying gauge groups and their breaking pattern to the Standard Model gauge group. We also comment on the corrections that can affect these one-loop results.