Grand Unified Models Research Articles

An SO(10) GUT model with lopsided mass matrix and neutrino mixing angle [formula omitted

An alternative supersymmetric SO(10) grand unification model with lopsided fermion mass matrices is introduced. It generates a large solar-neutrino mixing angle through the neutrinos' Dirac mass matrix constrained by the SO(10) group structure, avoiding the fine-tuning required in the Majorana mass matrix of right-handed neutrinos. The model fits well the known data on masses and mixings of quarks and leptons, and predicts a sizable lepton mixing sin22θ13≃0.074, which is significantly larger than that of the original lopsided model.

Unification via intermediate symmetry breaking scales with the quartification gauge group

The idea of quark-lepton universality at high energies has been introduced as a natural extension to the standard model. This is achieved by endowing leptons with new degrees of freedom---leptonic color, an analogue of the familiar quark color. Grand and partially unified models which utilize this new gauge symmetry $SU(3{)}_{\ensuremath{\ell}}$ have been proposed in the context of the quartification gauge group $SU(3{)}^{4}$. Phenomenologically successful gauge coupling constant unification without supersymmetry has been demonstrated for cases where the symmetry breaking leaves a residual $SU(2{)}_{\ensuremath{\ell}}$ unbroken. Though attractive, these schemes either incorporate ad hoc discrete symmetries and nonrenormalizable mass terms, or achieve only partial unification. We show that grand unified models can be constructed where the quartification group can be broken fully [i.e. no residual $SU(2{)}_{\ensuremath{\ell}}$] to the standard model gauge group without requiring additional discrete symmetries or higher dimension operators. These models also automatically have suppressed nonzero neutrino masses. We perform a systematic analysis of the renormalization-group equations for all possible symmetry breaking routes from $SU(3{)}^{4}\ensuremath{\rightarrow}SU(3{)}_{q}\ensuremath{\bigotimes}SU(2{)}_{L}\ensuremath{\bigotimes}U(1{)}_{Y}$. This analysis indicates that gauge coupling unification can be achieved for several different symmetry breaking patterns and we outline the requirements that each gives on the unification scale. We also show that the unification scenarios of those models which leave a residual $SU(2{)}_{\ensuremath{\ell}}$ symmetry are not unique. In both symmetry breaking cases, some of the scenarios require new physics at the TeV scale, while others do not allow for new TeV phenomenology in the fermionic sector.

Search for nucleon decay via modes favored by supersymmetric grand unification models in Super-Kamiokande-I

We report the results for nucleon decay searches via modes favored by supersymmetric grand unified models in Super-Kamiokande. Using 1489 days of full Super-Kamiokande-I data, we searched for p{yields}{nu}K{sup +}, n{yields}{nu}K{sup 0}, p{yields}{mu}{sup +}K{sup 0}, and p{yields}e{sup +}K{sup 0} modes. We found no evidence for nucleon decay in any of these modes. We set lower limits of partial nucleon lifetime 2.3x10{sup 33}, 1.3x10{sup 32}, 1.3x10{sup 33}, and 1.0x10{sup 33} years at 90% confidence level for p{yields}{nu}K{sup +}, n{yields}{nu}K{sup 0}, p{yields}{mu}{sup +}K{sup 0}, and p{yields}e{sup +}K{sup 0} modes, respectively. These results give a strong constraint on supersymmetric grand unification models.

How long could we live?

We investigate model independent upper bounds on total proton lifetime in the context of grand unified theories with the Standard Model matter content. We find them to be τ p ⩽ 1.5 −0.3 +0.5 × 10 39 ( M X / 10 16 GeV ) 4 α GUT 2 ( 0.003 GeV 3 / α ) 2 years and τ p ⩽ 7.1 −0.0 +0.0 × 10 36 ( M X / 10 16 GeV ) 4 α GUT 2 ( 0.003 GeV 3 / α ) 2 years in the Majorana and Dirac neutrino case, respectively. These bounds, in conjunction with experimental limits, put lower limit on the mass M X of gauge bosons responsible for the proton and bound-neutron decay processes. For central values of relevant input parameters we obtain M X ⩾ 4.3 × 10 14 α GUT GeV . Our result implies that a large class of non-supersymmetric grand unified models, with typical values α GUT ∼ 1 / 39 , still satisfies experimental constraints on proton lifetime. Our result is independent on any CP violating phase and the only significant source of uncertainty is associated with imprecise knowledge of α—the nucleon decay matrix element.

How a non-hierarchical neutrino mass matrix can arise

One puzzle of neutrino masses and mixings is that they do not exhibit the kind of strong “hierarchy” that is found for the quarks and charged leptons. Neutrino mass ratios and mixing angles are not small. A possible reason for this is proposed here. It is based on the fact that typical realistic grand unified models contain particles with unification-scale masses which, when integrated out, can yield a neutrino mass matrix that is not of the standard see-saw form.

Density perturbations from both the inflaton and the curvaton

We consider a supersymmetric grand unified model which leads to hybrid inflation and solves the strong CP and mu problems via a Peccei-Quinn symmetry, with the Peccei-Quinn field acting as a curvaton generating together with the inflaton the curvature perturbation. The model yields an isocurvature perturbation too of mixed correlation with the adiabatic one. Two choices of parameters are confronted with the Wilkinson microwave anisotropy probe and other cosmic microwave background radiation data. For the choice giving the best fitting, the curvaton contribution to the amplitude of the adiabatic perturbation must be smaller than 67% at 95% confidence level and the best-fit power spectra are dominated by the adiabatic inflaton contribution. This case is disfavored relative to the pure inflaton scale-invariant case with odds of 50 to 1. For the second choice, the adiabatic mode is dominated by the curvaton, but this case is strongly disfavored relative to the pure inflaton case (with odds of 10^7 to 1). Thus, in this model, the perturbations must be dominated by the adiabatic component from the inflaton.

PerturbativeSO(10)grand unification

We consider a phenomenologically viable $SO(10)$ grand unification model of the unification scale ${M}_{G}$ around ${10}^{16}\text{ }\text{ }\mathrm{GeV}$ which reproduces the minimal supersymmetric standard model at low energy and allows perturbative calculations up to the Planck scale ${M}_{P}$ or the string scale ${M}_{st}$. Both requirements strongly restrict a choice of Higgs representations in a model. We propose a simple $SO(10)$ model with a set of Higgs representations ${2\ifmmode\times\else\texttimes\fi{}\mathbf{10}+\overline{\mathbf{16}}+\mathbf{16}+\mathbf{45}}$ and show its phenomenological viability. This model can indeed reproduce the low-energy experimental data relating the charged fermion masses and mixings. Neutrino oscillation data can be consistently incorporated in the model, leading to the right-handed neutrino mass scale ${M}_{R}\ensuremath{\simeq}{M}_{G}^{2}/{M}_{P}$. Furthermore, there exists a parameter region which results the proton lifetime consistent with the experimental results.

Proton Lifetime from SU(5) Unification in Extra Dimensions

We provide detailed estimates of the proton lifetime in the context of simple supersymmetric SU(5) grand unified models with an extra compact spatial dimension, described by the orbifold S/(Z_2 x Z_2') and by a large compactification scale Mc. We focus on a class of models where the grand unified symmetry is broken by the compactification mechanism and where baryon violation proceeds mainly through gauge vector boson exchange so that the proton lifetime scales as the fourth power of Mc. We carefully compute Mc from a next-to-leading analysis of gauge coupling unification and we find that Mc can only be predicted up to an overall factor one hundred. The simplest model, where the dominant decay mode is (pi^0 e+) and has no flavour suppression, is strongly constrained by existing data, but not totally ruled out. We also analyze models where some of the matter fields are localized in the extra space and proton decay is flavour suppressed. In models associated to anarchy in the neutrino sector the preferred decay channel is (K+ {\bar \nu}) and the lifetime can be within the reach of the next generation of experiments.

Tripletless unification in the conformal window

A product SU(5)xSp(4) grand unified model is proposed with no fundamental Higgs fields transforming under SU(5). Higgs doublets are instead embedded into a four dimensional representation of the Sp(4) gauge group, and hence there is no doublet-triplet splitting problem because there are no triplets. The Sp(4) group contains enough matter to lie in the conformal window, causing its gauge coupling to flow to a strongly-coupled infrared fixed-point at low energy, naturally preserving gauge coupling unification to percent level accuracy. Yukawa couplings, including the top, arise through dimension five operators that are enhanced by the large anomalous dimension of the Higgs fields. Proton decay mediated by dimension five operators is absent at the perturbative level. It reappears, however, non-perturbatively due to Sp(4) instantons but the rate is suppressed by a high power of the ratio of the dynamical scale to the unification scale. With gravity- or gaugino-mediated supersymmetry breaking, non-universal gaugino masses are predicted, satisfying specific one-loop renormalization group invariant relations. These predictions should be easily testable with the LHC and a linear collider.

Constraints on a mixed inflaton and curvaton scenario for the generation of the curvature perturbation

We consider a supersymmetric grand unified model which naturally solves the strong CP and mu problems via a Peccei-Quinn symmetry and leads to the standard realization of hybrid inflation. We show that the Peccei-Quinn field of this model can act as curvaton. In contrast to the standard curvaton hypothesis, both the inflaton and the curvaton contribute to the total curvature perturbation. The model predicts an isocurvature perturbation too which has mixed correlation with the adiabatic one. The cold dark matter of the universe is mostly constituted by axions plus a small amount of lightest sparticles. The predictions of the model are confronted with the Wilkinson microwave anisotropy probe and other cosmic microwave background radiation data. We analyze two representative choices of parameters and derive bounds on the curvaton contribution to the adiabatic perturbation. We find that, for the choice which provides the best fitting of the data, the curvaton contribution to the adiabatic amplitude must be smaller than about 67% (at 95% confidence level). The best-fit power spectra are dominated by the adiabatic part of the inflaton contribution. We use Bayesian model comparison to show that this choice of parameters is disfavored with respect to the pure inflaton scale-invariant case with odds of 50 to 1. For the second choice of parameters, the adiabatic mode is dominated by the curvaton, but this choice is strongly disfavored relative to the pure inflaton scale-invariant case (with odds of 10^7 to 1). We conclude that in the present framework the perturbations must be dominated by the adiabatic component from the inflaton.

Empirical formulas for the fermion spectra and Yukawa matrices

We present empirical relations that connect the dimensionless ratios of fermion masses for the charged lepton, up-type quark and down-type quark sectors. Explaining these relations from first principles imposes strong constraints on the search for the theory of flavor. We present a simple set of normalized Yukawa matrices, with only two real parameters and one complex phase, which accounts with precision for these mass relations and for the CKM matrix elements and also suggests a simpler parametrization of the CKM matrix. The proposed Yukawa matrices accommodate the measured CP-violation, giving a particular relation between standard model CP-violating phases, beta=Arg(2 - exp^{-i*gamma}). According to this relation, the measured value of beta is close to the maximum value that can be reached. Finally, the particular mass relations with the charged lepton sector find their simplest explanation in the context of grand unified models through the use of the Georgi-Jarlskog factor.

Heterotic brane world

Orbifold compactification of heterotic E{sub 8}xE{sub 8}{sup '} string theory is a source for promising grand unified model building. It can accommodate the successful aspects of grand unification while avoiding problems like doublet-triplet splitting in the Higgs sector. Many of the phenomenological properties of the four-dimensional effective theory find an explanation through the geometry of compact space and the location of matter and Higgs fields. These geometrical properties can be used as a guideline for realistic model building.

Reconciling Neutralino relic Density with Yukawa Unified Supersymmetric Models

Supersymmetric grand unified models based on the gauge group SO(10) are especially attractive in light of recent data on neutrino masses. The simplest SO(10) SUSY GUT models predict unification of third generation Yukawa couplings in addition to the usual gauge coupling unification. Recent surveys of Yukawa unified SUSY GUT models predict an inverted scalar mass hierarchy in the spectrum of sparticle masses if the superpotential mu term is positive. In general, such models tend to predict an overabundance of dark matter in the universe. We survey several solutions to the dark matter problem in Yukawa unified supersymmetric models. One solution-- lowering the GUT scale mass value of first and second generation scalars-- leads to u_R and c_R squark masses in the 90-120 GeV regime, which should be accessible to Fermilab Tevatron experiments. We also examine relaxing gaugino mass universality which may solve the relic density problem by having neutralino annihilations via the Z or h resonances, or by having a wino-like LSP.

General analysis of corrections to the standard seesaw formula in grand unified models

In realistic grand unified models there are typically extra vectorlike matter multiplets at the GUT-scale that are needed to explain the family hierarchy. These contain neutrinos that, when integrated out, can modify the usual neutrino seesaw formula. A general analysis is given. It is noted that such modifications can explain why the neutrinos do not exhibit a strong family hierarchy like the other types of fermions.

Simple description of neutrinos in [formula omitted

We show that experimental results for the masses and mixing of the neutrinos can be understood naturally by a simple grand unification model of SU ( 5 ) coupled to N = 1 supergravity. No right-handed neutrinos are included. The left-handed neutrinos receive Majorana masses through the couplings with a Higgs boson of symmetric 15 representation. Introducing 45 ¯ representation is optional for describing the masses of down-type quarks and charged leptons.

Normal vs. inverted hierarchy in type I seesaw models

We demonstrate that, for every grand unified model based on a conventional type I seesaw mechanism leading to a normal light neutrino mass hierarchy, one can easily generate a corresponding model with an inverted hierarchy which yields the same neutrino oscillation parameters. However, the latter type model has several unattractive instabilities which will disfavor any grand unified type I seesaw model, if an inverted neutrino mass hierarchy is observed experimentally. This should be contrasted with the softly-broken Le–Lμ–Lτ flavor symmetry models which are eliminated, if the data favors a normal mass hierarchy.

Resonant leptogenesis in a predictiveSO(10)grand unified model

An SO(10) grand unified model considered previously by the authors featuring lopsided down quark and charged lepton mass matrices is successfully predictive and requires that the lightest two right-handed Majorana neutrinons be nearly degenerate in order to obtain the LMA solar neutrino solution. Here we use this model to test its predictions for baryogenesis through resonant-enhanced leptogenesis. With the conventional type I seesaw mechanism, the best predictions for baryogenesis appear to fall a factor of three short of the observed value. However, with a proposed type III seesaw mechanism leading to three pairs of massive pseudo-Dirac neutrinos, resonant leptogenesis is decoupled from the neutrino mass and mixing issues with successful baryogenesis easily obtained.

Fermion masses and coupling unification inE6:Life in the desert

We present an ${E}_{6}$ grand unified model with a realistic pattern of fermion masses. All standard model fermions are unified in three fundamental 27-plets (i.e., supersymmetry is not invoked), which involve in addition right-handed neutrinos and three families of vectorlike heavy quarks and leptons. The lightest of those can lie in the low-TeV range, being accessible to future collider experiments. As a result of the high symmetry, the masses and mixings of all fermions are closely related. The new heavy fermions play a crucial role for the quark and lepton mass matrices and the bilarge neutrino oscillations. In all channels generation mixing and $\mathcal{C}P$ violation arise from a single antisymmetric matrix. The ${E}_{6}$ breaking proceeds via an intermediate-energy region with ${\mathrm{SU}(3)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(3)}_{R}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(3)}_{C}$ gauge symmetry and a discrete left-right symmetry. This breaking pattern leads in a straightforward way to the unification of the three gauge coupling constants at high scales, providing for a long proton lifetime. The model also provides for the unification of the top, bottom, and tau Yukawa couplings and for new interesting relations in flavor and generation space.

Minimal grand unification model in an anthropic landscape

It has been recently pointed out by Arkani-Hamed and Dimopoulos that if the universe is a landscape of vacua, and if therefore fine-tuning is not a valid guidance principle for searching for physics beyond the standard model, supersymmetric unification only requires the fermionic superpartners. We argue that in that landscape scenario, the fermionic superpartners are not needed for unification, which can be achieved in SO(10) either via a direct breaking to the standard model at the grand unification scale or through an intermediate gauge symmetry. In most minimal SO(10) models, the proton lifetime is long enough to avoid the experimental bounds. These models are the truly minimal fine-tuned extensions of the standard model in the sense proposed by Davoudiasl et al..

Grand unified inflation confronts WMAP

In a class of realistic four and five dimensional supersymmetric grand unified models, the scalar spectral index is found to be $n_s=0.98 (\pm 0.01)$, in excellent agreement with the values determined by several previous experiments and most recently by the Wilkinson Microwave Anisotropy Probe (WMAP). The models predict $dn_s/d{\rm ln}k\sim 10^{-3}$ and a negligible tensor-to-scalar ratio $r\sim 10^{-8}$. A new five dimensional supersymmetric SO(10) model along these is presented in which inflation is associated with the breaking of SO(10) to SU(5) at scale $M$, with $\delta T/T\propto (M/M_{\rm Planck})^2$, so that $M\simeq 10^{16}$ GeV. The inflaton decay leads to the observed baryon asymmetry via leptogenesis. We also discuss how the monopole problem is solved without the use of non-renormalizable terms.