Simple Grand Unified Theory Research Articles

Proton decay matrix elements on the lattice at physical pion mass

Proton decay is a major prediction of grand-unified theories (GUT) and its observation would indicate baryon number violation that is required for baryogenesis. Many decades of searching for proton decay have constrained its rate and ruled out some of the simplest GUT models. Apart from the baryon number-violating interactions, this rate also depends on transition amplitudes between the protons and mesons or leptons produced in the decay, which are matrix elements of three-quark operators. We report the nonperturbative calculation of these matrix elements for the most studied two-body decay channels into a meson and antilepton done on a lattice with physical light and strange quark masses and lattice spacings $a\ensuremath{\approx}0.14\text{ }\text{ }\mathrm{fm}$ and 0.20 fm. We perform nonperturbative renormalization and excited state analysis to control associated systematic effects. Our results largely agree with previous lattice calculations done with heavier quark masses and thus remove ambiguity in ruling out some simple GUT theories due to quark mass dependence of hadron structure.

Spontaneous SUSY breaking in natural SO(10) grand unified theory

We propose a simple grand unified theory (GUT) scenario in which supersymmetry (SUSY) is spontaneously broken in visible sector. Our model is based on the GUT model that has been proposed to solve almost all problems in conventional GUT scenarios. In the previous work, the problems can be solved by a natural assumption in a supersymmetric vacuum. In this paper, we consider an extension of the model (i.e. omitting one singlet field) and break SUSY spontaneously without new sector. Our model does not have hidden sector and predicts high-scale SUSY where sfermion masses are of order 100-1000 TeV and flavor violating processes are suppressed. In this scenario, we can see an explicit signature of GUT in sfermion mass spectrum since the sfermion mass spectrum respects SU(5) matter unification. In addition, we find a superheavy long lived charged lepton as a proof of our scenario, and it may be seen in the LHC.

Inflation, proton decay, and Higgs-portal dark matter in SO(10) times U(1)_psi

We propose a simple non-supersymmetric grand unified theory (GUT) based on the gauge group SO(10) times U(1)_psi . The model includes 3 generations of fermions in mathbf{16} (+1), mathbf{10} (-2) and mathbf{1} (+4) representations. The mathbf{16}-plets contain Standard Model (SM) fermions plus right-handed neutrinos, and the mathbf{10}-plet and the singlet fermions are introduced to make the model anomaly-free. Gauge coupling unification at M_{GUT} simeq 5 times 10^{15}{-}10^{16} GeV is achieved by including an intermediate Pati–Salam breaking at M_{I} simeq 10^{12}{-}10^{11} GeV, which is a natural scale for the seesaw mechanism. For M_{I} simeq 10^{12}{-}10^{11}, proton decay will be tested by the Hyper-Kamiokande experiment. The extra fermions acquire their masses from U(1)_psi symmetry breaking, and a U(1)_psi Higgs field drives a successful inflection-point inflation with a low Hubble parameter during inflation, H_{inf} ll M_{I}. Hence, cosmologically dangerous monopoles produced from SO(10) and PS breakings are diluted away. This is the first SO(10) model we are aware of in which relatively light intermediate mass (sim 10^{10}{-}10^{12} GeV) primordial monopoles can be adequately suppressed. The reheating temperature after inflation can be high enough for successful leptogenesis. With the Higgs field contents of our model, a mathbf{Z}_2 symmetry remains unbroken after GUT symmetry breaking, and the lightest mass eigenstate among linear combinations of the mathbf{10}-plet and the singlet fermions serves as a Higgs-portal dark matter (DM). We identify the parameter regions to reproduce the observed DM relic density while satisfying the current constraint from the direct DM detection experiments. The present allowed region will be fully covered by the future direct detection experiments such as LUX-ZEPLIN DM experiment. In the presence of the extra fermions, the SM Higgs potential is stabilized up to M_{I}.

The QCD axion and unification

The QCD axion is one of the most appealing candidates for the dark matter in the Universe. In this article, we discuss the possibility to predict the axion mass in the context of a simple renormalizable grand unified theory where the Peccei-Quinn scale is determined by the unification scale. In this framework, the axion mass is predicted to be in the range ma ≃ (3–13) × 10−9 eV. We study the axion phenomenology and find that the ABRACADABRA and CASPEr-Electric experiments will be able to fully probe this mass window.

Neutrino mass and grand unification

Simple grand unified theories (GUT) of matter and forces provide a natural home for the seesaw paradigm for understanding small neutrino masses within a framework that also connects quark flavor to that of leptons. This provides a promising possibility for a unified approach to the flavor puzzle. To see what recent indications of a "large" value for the neutrino mixing parameter θ13 mean for this approach, I report on investigations based on supersymmetric SO(10) GUTs with type II seesaw for neutrino masses and find that it seem to support this point of view, with other predictions testable in near future.

Origin of quark-lepton flavor in SO(10) with type II seesaw mechanism

Diverse mass and mixing patterns between the quarks and leptons makes it challenging to construct a simple grand unified theory of flavor. We show that SO(10) SUSY GUTs with type II seesaw mechanism giving neutrino masses provide a natural framework for addressing this issue. A simple ansatz that the dominant Yukawa matrix (the 10-Higgs coupling to matter) has rank one, appears to simultaneously explain both the large lepton mixings as well as the observed quark flavor hierarchy in these models. A testable prediction of this ansatz is the neutrino mixing, U_{e3}, which should be observable in planned long baseline experiments.

Neutron–anti-neutron oscillation: theory and phenomenology

The discovery of neutrino masses has provided strong hints in favor of the possibility that B–L symmetry is an intimate feature of physics beyond the standard model. I discuss how important information about this symmetry as well as other scenarios for TeV scale new physics can be obtained from the baryon number violating process, n– oscillation. This paper presents an overview of different aspects of neutron–anti-neutron oscillation and is divided into the following parts: (i) the phenomenon, (ii) the physics, (iii) plausible models and (iv) applications to cosmology. In particular, it is argued how the discovery of n– oscillation can significantly affect our thinking about simple grand unified theory paradigms for physics beyond the standard model, elucidate the nature of forces behind neutrino mass and provide a new microphysical view of the origin of matter in the universe.

ON THE ROLE OF LOW-ENERGY CP VIOLATION IN LEPTOGENESIS

The link between low-energy CP violation and leptogenesis became more accessible with the understanding of flavor effects. However, a definite well-motivated model where such a link occurs was still lacking. Adjoint SU(5) is a simple grand unified theory where neutrino masses are generated through the Type I and Type III seesaw mechanisms, and the lepton asymmetry is generated by the fermionic triplet responsible for the Type III seesaw. We focus exclusively on the case of inverted hierarchy for neutrinos, and we show that successful flavored leptogenesis in this theory strongly points towards low-energy CP violation. Moreover, since the range of allowed masses for the triplet is very restricted, we find that the discovery at the LHC of new states present in the theory, together with proton decay and unification of gauge couplings, can conspire to provide a hint in favor of leptogenesis.

Leptoquarks and neutrino masses at the LHC

The properties of light leptoquarks predicted in the context of a simple grand unified theory and their observability at the LHC are investigated. The SU ( 5 ) symmetry of the theory implies that the leptoquark couplings to matter are related to the neutrino mass matrix. We study the resulting connection between neutrino masses and mixing parameters and the leptoquark decays, and show that different light neutrino hierarchies imply distinctive leptoquark decay signatures. We also discuss low-energy constraints implied by searches for charged lepton flavour violation, studies of meson decays, and electroweak precision data. We perform a detailed parton-level study of the leptoquark signals and the Standard Model backgrounds at the LHC. With the clean final states containing a di-lepton plus two jets, the QCD production of the leptoquark pair can be observed for a leptoquark mass of one TeV and beyond. By examining the lepton flavor structure of the observed events, one could further test the model predictions related to the neutrino mass spectrum. In particular, b-flavor tagging will be useful in distinguishing the neutrino mass pattern and possibly probing an unknown Majorana phase in the Inverted Hierarchy or the Quasi-Degenerate scenario. Electroweak associated production of the leptoquark doublet can also be useful in identifying the quantum numbers of the leptoquarks and distinguishing between the neutrino mass spectra, even though the corresponding event rates are smaller than for QCD production. We find that with only the clean channel of μ + E̸ T + jets , one could expect an observable signal for a leptoquark masses of about 600 GeV or higher.

Fermion Mass Hierarchy in the Grand Unified Theory on an S1/(Z2 xZ2') Orbifold

We suggest a simple grand unified theory where the fifth dimensional coordinate is compactified on an $S_1/(Z_2 \times Z_2')$ orbifold. This model is based on the supersymmetric flipped $SU(5) \times U(1)$ grand unified theory, which can realize not only the triplet-doublet splitting but also the natural fermion mass hierarchies. The triplet-doublet splitting is realized by $S_1/(Z_2 \times Z_2')$ orbifolding, which also reduces the gauge group as $SU(5) \times U(1) \to SU(3)_c \times SU(2)_L \times U(1)_Z \times U(1)_X$. The suitable fermion mass hierarchies are generated by integrating out extra three sets of vector-like heavy fields which can propagate in five dimensions. The radiative corrections to the large Yukawa coupling of right-handed neutrinos can reduce the gauge group to $SU(3)_c \times SU(2)_L \times U(1)_Y$.

Model with Gauge Coupling Unification on an S1 /(Z2 x Z2') Orbifold

We suggest a simple grand unified theory where the fifth dimensional coordinate is compactified on an $S^1/(Z_2 \times Z_2')$ orbifold. This model contains additional ${\bf 10 + \overline{10}}$, (${\bf 15 + \overline{15}}$) and two ${\bf 24}$ Higgs multiplets in the non-supersymmetric SU(5) grand unified theory. Although this model is non-supersymmetric theory, the gauge coupling unification is realized due to the mass splittings of Higgs multiplets by $S^1/(Z_2 \times Z_2')$ orbifolding. The constraints from the $b \to s \gamma$, $\mu \to e \gamma$, and electron and muon anomalous magnetic moments are also discussed.

Focus point supersymmetry: Proton decay, flavor andCPviolation, and the Higgs boson mass

In focus point supersymmetry, all squarks and sleptons, including those of the third generation, have multi-TeV masses without sacrificing naturalness. We examine the implications of this framework for low energy constraints and the light Higgs boson mass. Undesirable contributions to proton decay and electric dipole moments, generic in many supersymmetric models, are strongly suppressed. As a result, the prediction for {alpha}{sub s} in simple grand unified theories is 3{sigma}--5{sigma} closer to the experimental value, and the allowed CP-violating phases are larger by one to two orders of magnitude. In addition, the very heavy top and bottom squarks of focus point supersymmetry naturally produce a Higgs boson mass at or above 115 GeV without requiring heavy gauginos. We conclude with an extended discussion of issues related to the definition of naturalness and comment on several other prescriptions given in the literature.

Light-fermion mass hierarchies in supersymmetric models.

Radiative fermion mass hierarchies in grand unified supersymmetric models are discussed. There are arguments in the literature that these cannot arise. It is shown that these arguments only apply to a certain type of radiative hierarchy. Another type of radiative hierarchy can arise in simple supersymmetric grand unified theories. Examples are discussed.

Precocious unification in simple grand unified theories.

We investigate how simple grand unified theories with a precocious-unification mass can be constructed. The maximal local symmetry of 2mn left-handed fermions and their left-handed antiparticles is shown to be a viable candidate, where m and n are the number of families and colors, respectively. The predictions of such a model are studied.

Flipping away proton decay

General conditions for the suppression of proton decay mediated by gauge boson exchange are considered. One appealing way to satisfy these conditions is to delay the unification of left-handed with right-handed quarks. The simplest grand unified theories which have a two-stage breaking of the gauge group to SU(3) × SU(2) × U(1) are discussed. A general analysis of gauge mediated ΔB ≠ 0 interactions is given for the various ways of embedding SU(6) × SU(2) × U(1) in the maximal subgroup of E 6. A model based on the SU(6) × SU(2) R subgroup of E 6 is considered in detail, and is shown to give a proton lifetime up to a few thousand times longer than in the minimal SU(5) theory.

The end may be hastened by magnetic monopoles

In an open Universe, or even in just a long-lived Universe (as predicted in inflationary Universe models1–3), the ultimate demise of matter is a certainty. Stars, of course, have only a fleeting existence as they must eventually exhaust their nuclear fuels (in ∼1010 yr for a 1 M⊙ star). In 1014 yr or so new star formation will have ceased, and only neutron stars, white dwarfs, planetary-sized objects (such as Jupiter and Earth) and black holes will remain4. In the simplest grand unified theories (GUTs) the proton lifetime is but 0(1030 yr), so that after this time neutron stars, white dwarfs, and planets will cease to exist. (Due to gravitational effects alone the proton lifetime is expected to be 0(1046 yr) or less.) Although they could outlive the other three, black holes will also eventually disappear, evaporating through the Hawking process5 in a time ≃1064(M/M⊙)3 yr. I point out here that the existence of just a tiny flux of superheavy magnetic monopoles, say F≃F−21 × 10−21 cm−2 sr−1 s−1, will, due to monopole-catalysed nucleon decay6,7, hasten the demise of matter. Due to the monopoles that collect inside them, the lifetime of a neutron star will be ≃1011F−½−21 yr, of a white dwarf ≃1014F−½−21 yr, and of an Earth-like planet ≃1018F−½−21 yr.

From the standard model to grand unification

This paper reviews the limitations o f the standard SU (3) x SU (2) x U (l) model and develops the philosophy of grand unification. Some simple grand unified theories are presented, and calculations made of the order of magnitude of the fine-structure constant a, as well as of sin 2 0 W and some quark masses. Predictions for nucleon decay and neutrino masses are then discussed; they may be observable in the near future. It is suggested that grand unified theories complex enough for the understanding of the baryon asymmetry of the Universe may also predict a neutron electric dipole moment large enough to be measured. Finally, some inadequacies of GUTs are mentioned.

Cosmic strings in unified gauge theories

Some spontaneously broken gauge theories can give rise to stringlike vacuum structures (vortices). It has been pointed out by Vilenkin that in grand unified theories these can be sufficiently massive to have cosmological implications, e.g., in explaining the formation of galaxies. The circumstances in which such structures occur are examined. They do not occur in the simplest grand unified theories, but can occur in some more elaborate models which have been proposed. The cross section for the scattering of elementary particles by strings is estimated. This is used to evaluate the effect of collisions on the dynamics of a collapsing circular string, with particular attention to the question of whether energy dissipation by collision can reduce the rate of formation of black holes by collapsed strings, which may be unacceptably large in models where strings occur. It is found that the effect of collisions is not important in the case of grand unified strings, although it can be important for lighter strings.

Grand unification and parity restoration at low energies. Phenomenology

Recently, we have shown that simple grand unified theories, such as SO(10), allow the possibility of low-energy parity restoration. In this paper a detailed phenomenological analysis of the left-right-symmetric model is presented. It turns out that the theory passes all the charged- and neutral-current tests for M/sub W/R as low as 100 --300 GeV, if simultaneously sin/sup 2/theta/sub W/approx. =0.25-- 0.31. We also estimate masses, widths, and branching ratios for the gauge bosons, as well as their production rates in pp and p-barp reactions.

Can There Be Low Intermediate Mass Scales in Grand Unified Theories?

It is well known that the simple grand-unified theories, such as O(10), allow the mass scale at which the parity is presumably restored to be as low as 100 --200 GeV.