Grand Unified Gauge Group Research Articles

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.

Evaluating the price of tiny kinetic mixing

We consider both "bottom-up" and "top-down" approaches to the origin of gauge kinetic mixing. We focus on the possibilities for obtaining kinetic mixings $\epsilon$ which are consistent with experimental constraints and are much smaller than the naive estimates ($\epsilon \sim 10^{-2} - 10^{-1}$) at the one-loop level. In the bottom-up approach, we consider the possible suppression from multi-loop processes. Indeed we argue that kinetic mixing through gravity alone, requires at least six loops and could be as large as $\sim 10^{-13}$. In the top-down approach we consider embedding the Standard Model and a $U(1)_X$ in a single grand-unified gauge group as well as the mixing between Abelian and non-Abelian gauge sectors.

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.

Improving naturalness in gauge mediation with nonunified messenger sectors

We study models of gauge-mediated supersymmetry breaking with messengers that do not belong to complete representations of grand-unified gauge groups. We show that certain setups characterized by heavy Wino can greatly improve the fine tuning with respect to models with unified messengers, such as minimal gauge mediation. The typical models with low tuning feature multi-TeV superparticles, with the exception of the Higgsinos and possibly Bino and right-handed sleptons. As a consequence, the absence of signals for supersymmetry at the LHC is trivially accommodated in our framework. On the other hand, testing these models will be challenging at the LHC. We finally show that the gravitino can be a consistent candidate for cold dark matter, provided a rather low reheating temperature, if a standard thermal history of the universe is assumed.

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.

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.

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.

Dimension-five operators in grand unified theories

Extensions of the standard model with low-energy supersymmetry generically allow baryon- and lepton-number violating operators of dimension four and five, yielding rapid proton decay. The dimension-four operators are usually forbidden by matter parity. We investigate to what extent the appearance of dimension-five operators at the Planck scale may be constrained by the different grand-unified gauge groups. Dimension-five operators are suppressed in models based on E{sub 6} and SU(3){sub C}xSU(3){sub L}xSU(3){sub R}, where four matter fields do not form a gauge singlet. An intermediate scale offers the possibility to sufficiently suppress these dimension-five operators.

Theory and phenomenology of an exceptional supersymmetric standard model

We make a comprehensive study of the theory and phenomenology of a low-energy supersymmetric standard model originating from a string-inspired ${E}_{6}$ grand unified gauge group. The exceptional supersymmetric standard model (ESSM) considered here is based on the low-energy standard model gauge group together with an extra ${Z}^{\ensuremath{'}}$ corresponding to an extra $U(1{)}_{N}$ gauge symmetry under which right-handed neutrinos have zero charge. The low-energy matter content of the ESSM corresponds to three 27 representations of the ${E}_{6}$ symmetry group, to ensure anomaly cancellation, plus an additional pair of Higgs-like doublets as required for high-energy gauge coupling unification. The ESSM is therefore a low-energy alternative to the minimal supersymmetric standard model (MSSM) or next-to-minimal supersymmetric standard model (NMSSM). The ESSM involves extra matter beyond the MSSM contained in three $5+{5}^{*}$ representations of $SU(5)$, plus three $SU(5)$ singlets which carry $U(1{)}_{N}$ charges, one of which develops a vacuum expectation value, providing the effective $\ensuremath{\mu}$ term for the Higgs doublets, as well as the necessary exotic fermion masses. We explore the renormalization group flow of the ESSM and examine theoretical restrictions on the values of new Yukawa couplings caused by the validity of perturbation theory up to the grand unification scale. We then discuss electroweak symmetry breaking and Higgs phenomenology and establish an upper limit on the mass of the lightest Higgs particle which can be significantly heavier than in the MSSM and NMSSM, in leading two-loop approximation. We also discuss the phenomenology of the ${Z}^{\ensuremath{'}}$ and the extra matter, whose discovery will provide a smoking gun signal of the model.

Triplicated trinification

Gauge-coupling unification is just as successful in the standard model with six Higgs doublets as it is in the minimal supersymmetric standard model. However, the gauge couplings unify at 1014 GeV, which yields rapid proton decay in the SU(5) model. I propose that the grand-unified gauge group is instead SU(3)c×SU(3)L×SU(3)R, in which baryon number is conserved by the gauge interactions.

SYMMETRY RESTORATION IN THE SUPERSTRING THEORY

The grand unified gauge group G 6≡ SU (3) C × SU (3) L × SU (3) R , which results from compactification of the heterotic superstring onto a three-generation Calabi–Yau space as a maximal subgroup of E 6, contains two superfields, whose scalar components are the conjugates neutrino [Formula: see text] and the neutral Higgs N, which are singlets of the standard-model gauge group G 4≡ SU (3) C × SU (2) L × U (1) Y , and which therefore break G 6to G 4 when they acquire non-vanishing vacuum expectative values. Here, we show how this process can be implemented in two steps when the scalar potential V(ϕi) is chosen along a non-D-flat direction, using the "superconducting" model due to Mohapatra and Senjanović, in which one of two scalar fields remains in the asymmetric state up to a temperature T0~ 1017 GeV , above which the kinetic energy exceeds the potential drop, forcing restoration of the symmetry below the compactification scale T c ≈ 1017 GeV . This implies that [Formula: see text] initially, but at low temperatures T ≪ M w , we find that [Formula: see text], thus avoiding the problems associated with large intermediate scales M I ≳ 109 GeV while keeping the Higgs mixing term ~ NH1H2 at the right level. A discrete gauge symmetry can prevent the proton from decaying too rapidly.

Chiral four-dimensional N=1 supersymmetric type IIA orientifolds from intersecting D6-branes

We construct N=1 supersymmetric four-dimensional orientifolds of type IIA on T 6 /( Z 2× Z 2) with D6-branes intersecting at angles. The use of D6-branes not fully aligned with the O6-planes in the model allows for a construction of many supersymmetric models with chiral matter, including those with the Standard Model and grand unified gauge groups. We perform a search for realistic gauge sectors, and construct the first example of a supersymmetric type II orientifold with SU(3) C × SU(2) L × U(1) Y gauge group and three quark–lepton families. In addition to the supersymmetric Standard Model content, the model contains right-handed neutrinos, a (chiral but anomaly-free) set of exotic multiplets, and diverse vector-like multiplets. The general class of these constructions are related to familiar type II orientifolds by small instanton transitions, which in some cases change the number of generations, as discussed in specific models. These constructions are supersymmetric only for special choices of untwisted moduli. We briefly discuss the supersymmetry breaking effects away from that point. The M-theory lift of this general class of supersymmetric orientifold models should correspond to purely geometrical backgrounds admitting a singular G 2 holonomy metric and leading to four-dimensional M-theory vacua with chiral fermions.

Dynamical doublet-triplet Higgs boson mass splitting

We propose a new mechanism towards the solution to the doublet-triplet Higgs mass splitting problem in the supersymmetric grand unified theory. Our model is based on the gauge group $SU(5)_H \times SU(5)_{GUT}$, where $SU(5)_H$ and $SU(5)_{GUT}$ are a new strong gauge interaction and the ordinary grand unified gauge group, respectively. The doublet-triplet Higgs mass splitting is realized through the quantum deformation of moduli space caused by the strong $SU(5)_H$ gauge dynamics. The low energy description of our model is given by the minimal supersymmetric standard model.

Anomaly-free flavor symmetry and neutrino anarchy

We show that one can describe the quark and lepton masses with a single anomaly-free $U(1)$ flavor symmetry provided a single order one parameter is enhanced by roughly 4--5. The flavor symmetry can be seen to arise from inside the ${E}_{6}$ symmetry group in such a way that it commutes with the $\mathrm{SU}(5)$ grand unified gauge group. The scenario does not distinguish between the left-handed lepton doublets and hence is a model of neutrino anarchy. It can therefore account for the large mixing observed in atmospheric neutrino experiments and predicts that the solar neutrino oscillation data are consistent with the large mixing angle solution of matter-enhanced oscillations.

Monopoles, axions and intermediate mass dark matter

We present a solution to the cosmological problem encountered in (supersymmetric) grand unified theories due to copious monopole production at the end of hybrid inflation. By employing thermal inflation `driven' by the U(1) axion symmetry, the superheavy monopole flux can be naturally suppressed to values that should be accessible to dedicated large scale experiments. The U(1) axion symmetry also helps generate the right magnitude for the μ term of the minimal supersymmetric standard model. An important by-product is the predicted existence of stable or very long-living fermions possessing intermediate scale masses of order 10 12 GeV . Their presence is required for implementing thermal inflation, and their stability is due to a Z 2 symmetry. They may constitute a sizable fraction of cold dark matter, and possibly help explain the ultra-high energy cosmic ray events. The rest of cold dark matter may consist of axions. Although our discussion is carried out within the framework of supersymmetric SU(4) c × SU(2) L × SU(2) R , it can be extended to other grand unified gauge groups such as SU(3) c × SU(3) L × SU(3) R or SO(10).

Moduli spaces of fivebranes on elliptic Calabi-Yau threefolds

We present a general method for calculating the moduli spaces of fivebranes wrapped on holomorphic curves in elliptically fibered Calabi-Yau threefolds, in particular, in the context of heterotic M theory. The cases of fivebranes wrapped purely on a fiber curve, purely on a curve in the base and, generically, on a curve with components both in the fiber and the base are each discussed in detail. The number of irreducible components of the fivebrane and their properties, such as their intersections and phase transitions in moduli space, follow from the analysis. Even though generic curves have a large number of moduli, we show that there are isolated curves that have no moduli associated with the Calabi-Yau threefold. We present several explicit examples, including cases which correspond to potentially realistic three family models with grand unified gauge group SU(5).

Non-perturbative vacua and particle physics in M-theory

In this letter, we introduce a general theory for the construction of particle physics theories, with three families and realistic gauge groups, within the context of heterotic M-theory. This is achieved using semi-stable holomorphic gauge bundles over elliptically fibered Calabi-Yau three-folds. Construction of realistic theories is facilitated by the appearance of non-perturbative five-branes in the vacuum. The complete moduli space of these five-branes is computed and their worldvolume gauge theory discussed. It is shown, within the context of holomorphic gauge bundles, how grand unified gauge groups can be spontaneously broken to the gauge group of the standard model. These ideas are illustrated in an explicit SU(5) three-family example.

Phenomenology of 3-family grand unified string models

In the 3-family grand unified string models constructed so far, there is only one adjoint (and no higher dimensional representation) Higgs field in the grand unified gauge group. In this preliminary analysis, we address the proton-decay problem in the 3-family E_6 and related SO(10) string models. In particular, we analyze the doublet-triplet splitting (within certain assumptions about non-perturbative dynamics). It appears that generically some fine-tuning is necessary to arrange for a pair of Higgs doublets to be light, while having color Higgs triplets superheavy. We also discuss charge-2/3 quark mass matrix that generically also seems to require some fine-tuning to have rank 1.

Classification of three-family grand unification in string theory. I. The SO(10) andE6models

We give a classification of three-family SO(10) and E${}_{6}$ grand unification in string theory within the framework of conformal (free) field theory and asymmetric orbifolds. We argue that the construction of such models in heterotic string theory requires certain ${\mathbf{Z}}_{6}$ asymmetric orbifolds that include a ${\mathbf{Z}}_{3}$ outerautomorphism, the latter yielding a level-three current algebra for the grand unification gauge group SO(10) or E${}_{6}$. We then classify all such ${\mathbf{Z}}_{6}$ asymmetric orbifolds that result in models with a non-Abelian hidden sector. All models classified in this paper have only one adjoint (but no other higher representation) Higgs field in the grand unified gauge group. In addition, all of them are completely anomaly-free. There are two types of such three-family models. The first type consists of the unique SO(10) model with SU(2) $\ensuremath{\bigotimes}$ SU(2) $\ensuremath{\bigotimes}$ SU(2) as its hidden sector (which is not asymptotically free at the string scale). This SO(10) model has four left-handed and one right-handed $16$'s. The second type is described by a moduli space containing 17 models (distinguished by their massless spectra). All these models have an SU(2) hidden sector, and five left-handed and two right-handed families in the grand unified gauge group. One of these models is the unique E${}_{6}$ model with an asymptotically free SU(2) hidden sector. The others are SO(10) models, eight of them with an asymptotically free hidden sector at the string scale.