Unification Scale Research Articles

GUT phase transition and hybrid inflation

The supersymmetric model of hybrid inflation is interesting not only because of its naturalness but also because of another reason. Its energy scale determined by the COBE normalization is 1015–1016 GeV. It happens to be the energy scale of interest in particle physics, namely, the mass scale of right-handed neutrinos or the energy scale of the gauge-coupling unification. It is true that topological defects are produced after the hybrid inflation if it is related to a U(1)B−L or a GUT-symmetry breaking, and hence one cannot naively identify models of particle physics with that of inflation. But those defects are not necessarily found in modified models. We show in this Letter that quite a simple extension of the minimal supersymmetric hybrid inflation model is free from monopoles or cosmic strings. Moreover, it happens to be exactly the same as a well-motivated extension of SU(5)-unified theories. The vacuum energy is dominated by F-term. The η-problem is not necessarily serious when the model is realized by D-branes. Although it has been considered that a coupling constant has to be very small when the vacuum energy is dominated by F-term, this constraint is not applied either to the D-brane model. They are due to a particular form of the Kähler potential and interaction of the model. Reheating process is also discussed.

Late time phase transition as dark energy

We show that the dark energy field can naturally be described by the scalar condensates of a non-abelian gauge group. This gauge group is unified with the standard model gauge groups and it has a late time phase transition. The small phase transition explains why the positive acceleration of the universe is occurring only recently. The model hasno free parameters but for the matter content of the group. The initial energy density at the unification scale and at the condensation scale are fixed by the number of degrees of freedom of the gauge group.

GUT precursors and fixed points in higher-dimensional theories

Within the context of traditional logarithmic grand unification atM GUT ≈ 1016 GeV, we show that it is nevertheless possible to observe certain GUT states such asX andY gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as ‘GUT precursors’. Such states offer an interesting alternative possibility for new physics at the TeV scale, even when the scale of gauge coupling unification remains high, and suggest that it may be possible to probe GUT physics directly even within the context of high-scale gauge coupling unification. More generally, our results also suggest that it is possible to construct self-consistent ‘hybrid’ models containing widely separated energy scales, and give rise to a Kaluza-Klein realization of non-trivial fixed points in higher-dimensional gauge theories.

Quantum gravity, Clifford algebras, fuzzy set theory and the fundamental constants of nature

In a recent paper entitled “Quantum gravity from descriptive set theory”, published in Chaos, Solitons & Fractals, we considered following the P-adic quantum theory, the possibility of abandoning the Archimedean axiom and introducing a fundamental physical limitation on the smallest length in quantum spacetime. Proceeding that way we arrived at the conclusion that maximising the Hawking–Bekenstein informational content of spacetime makes the existence of a transfinite geometry for physical “spacetime” plausible or even inevitable. Subsequently we introduced a mathematical description of a transfinite, non-Archimedean geometry using descriptive set theory where a similar conclusion regarding the transfiniteness of quantum spacetime may be drawn from the existence of the Unruh temperature. In particular we introduced a straight forward logarithmic gauge transformation linking, as far as we are aware for the first time, classical gravity with the electroweak via a version of informational entropy. That way we found using ε (∞) and complexity theory that α ̄ G =(2) α ̄ ew −1 =1.7×10 38 where α ̄ G is the dimensionless Newton gravity constant and α ̄ ew =128 is the fine structure constant at the electroweak unification scale. The present work is concerned with more or less the same category of fundamental questions pertinent to quantum gravity. However we switch our mathematical apparatus to a combination of Clifford algebras and set theory. In doing that, the central and vital role of the work of D. Finkelstein becomes much more tangible and clearer than in most of our previous works.

Neutrino masses in 5D orbifold SU(5) unification models without right-handed singlets

We explore a mechanism for radiatively generating neutrino Majorana masses in a 5 dimensional orbifold SU(5) unification model without introducing right-handed singlets. The model is non-supersymmetric and the extra dimension is compactified via a $s_1/(Z_2\times Z'_2)$ orbifold geometry. The necessary lepton number violating interaction arises from the Yukawa interactions either between a 10-plet or a 15-plet bulk scalar field and the fermion quintuplets which are residents on the SU(5) symmetrical brane located at one of the orbifold fixed points. The model is engineered to give realistic charged fermion masses and mixing and in the same time avoiding the rapid proton and neutron decays by geometric construction. The gauge unification can be maintained by adding extra fermion or scalar fields. The unification scale is found to be larger then $10^{15}$ GeV by adding a bulk vector decuplet pair whose zero mode has masses around $10\sim 100$ TeV range. We found that neutrino mass matrix of the normal hierarchy type is favored by using 15-plet scalar. We give a solution of this type which has detectable $\mu\ra 3e$ transition. On the other hand, by introducing 10-plet scalar, the leading neutrino mass matrix can only be inverted hierarchical and gives at most bi-maximal mixing.

Probing quintessence with time variation of couplings

Many models of quintessence predict a time variation of the fundamentalconstants as well as a composition-dependent gravity-likelong-range force mediated by the cosmon. We present bounds forthe cosmon coupling to matter and radiation within a grand unified framework.The unification scale, the unified gauge coupling and the Fermi scale are allowed tovary independently. We find that the variation of the weak scale compared to the nucleonmass isseverely restricted. The violation of the equivalence principle turns out to be substantiallylarger than in models where only the electromagnetic fine structure constant varies withtime. We also show that in contrast to gravity the local cosmon field in acondensed object does not decouple from the cosmological evolution. In consequence, thecosmon interaction constitutes a possible quantitativelink between cosmological observations and several areas ofhigh precision experiments concerning the local time or space variation of couplings andtests of the equivalence principle.

A THEORETICAL CASE FOR NEGATIVE MASS-SQUARE FOR SUB-eV PARTICLES

Electroweak gauge bosons have masses of the order of 102 GeV [/c2], while masses of additional bosons involved in gravito-electroweak unification are expected to be still higher. These are at least eleven orders of magnitude higher than sub-eV range indications for neutrino masses. Under these circumstances we suspect that the sub-eV particles are created in a spacetime where gravitational effects of massive gauge bosons may become important. The question that we thus ask is: What is the spacetime group around a gravito-electroweak vertex? Modeling it as de-Sitter we find that sub-eV particles may carry a negative mass square of the order of [Formula: see text]. Neutrino oscillation data then hints at 30–75 TeV scale for M unif. , where M unif. characterizes gravito-electroweak unification scale.

Standard-Model Coupling Constants from Compositeness

A coupling-constant definition is given based on the compositeness property of some particle states with respect to the elementary states of other particles. It is applied in the context of the vector-spin-1/2-particle interaction vertices of a field theory, and the standard model. The definition reproduces Weinberg's angle in a grand-unified theory. One obtains coupling values close to the experimental ones for appropriate configurations of the standard-model vector particles, at the unification scale within grand-unified models, and at the electroweak breaking scale.

Lower bound on the neutralino mass from new data on CMB and implications for relic neutralinos

In the framework of an effective minimal supersymmetric extension of the standard model without gaugino-mass unification at a grand unification scale, we set a lower bound on the neutralino mass based on the new WMAP data on ${\ensuremath{\Omega}}_{\mathrm{CDM}}$ $(R$-parity conservation is assumed). Our lower bound ${m}_{\ensuremath{\chi}}\ensuremath{\gtrsim}6\mathrm{GeV}$ leaves much room for relic neutralinos significantly lighter than those commonly considered ${(m}_{\ensuremath{\chi}}\ensuremath{\gtrsim}50\mathrm{GeV}).$ We prove that these light neutralinos may produce measurable effects in weakly interacting massive particle direct detection experiments of low energy threshold and large exposure.

Robustness and predictivity of 4 TeV unification

The stability of the predictions of two of the standard model parameters, α3(MZ) and sin2θ(MZ), in a MU∼4 TeV unification model is examined. It is concluded that varying the unification scale between MU≃2.5 TeV and MU≃5 TeV leaves robust all predictions within reasonable bounds. Choosing MU=3.8±0.4 TeV gives, at lowest order, accurate predictions at MZ. The impact of threshold effects on unification depends on the spectrum of states beyond the standard model.

Grand unified theory precursors and nontrivial fixed points in higher-dimensional gauge theories.

Within the context of traditional logarithmic grand unification at M(GUT) approximately equal to 10(16) GeV, we show that it is nevertheless possible to observe certain GUT states such as X and Y gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as "GUT precursors." These states offer an interesting alternative possibility for new physics at the TeV scale, and could be used to directly probe GUT physics even though the scale of gauge coupling unification remains high. Our results also give rise to a Kaluza-Klein realization of nontrivial fixed points in higher-dimensional gauge theories.

Gauge quintessence

We discuss a new model of quintessence in which the quintessence field is identified with the extra component of a gauge field in a compactified five-dimensional theory. We show that the extremely tiny energy scale $\ensuremath{\sim}(3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\mathrm{eV}{)}^{4}$ needed to account for the present acceleration of the Universe can be naturally explained in terms of high energy scales such as the scale of grand unification.

Optical Unification

We discuss string scale unification facilitated by exotic matter with masses at intermediate scales, between the observable sector supersymmetry breaking scale and the string scale. We point out a mechanism by which string scale unification may occur while producing a (lower) virtual unification scale independent of the location of the intermediate scale and the value of the string coupling. The apparent unification obtained by extrapolating low energy gauge couplings is not accidental when this mechanism is invoked; virtual unification is robust.

Gauge unification in supersymmetric intersecting brane worlds

We show that contrary to first expectations realistic three generation supersymmetric intersecting brane world models give rise to phenomenologically interesting predictions about gauge coupling unification. Assuming the most economical way of realizing the matter content of the MSSM via intersecting branes we obtain a model independent relation among the three gauge coupling constants at the string scale. In order to correctly reproduce the experimentally known values of sin^2[theta_W(M_z)] and alpha_s(M_z) this relation leads to natural gauge coupling unification at a string scale close to the standard GUT scale 2 x 10^16 GeV. Additional vector-like matter can push the unification scale up to the Planck scale.

Mass predictions based on a supersymmetric SU(5) fixed point

I examine the possibility that the third generation fermion masses are determined by an exact fixed point of the minimal supersymmetric SU(5) model. When one-loop supersymmetric thresholds are included, this unified fixed point successfully predicts the top quark mass, $175\ifmmode\pm\else\textpm\fi{}2\mathrm{GeV},$ as well as the weak mixing angle. The bottom quark mass prediction is sensitive to the supersymmetric thresholds; it approaches the measured value for $\ensuremath{\mu}<0$ and very large unified gaugino mass. The experimental measurement of the tau lepton mass determines $\mathrm{tan}\ensuremath{\beta},$ and the strong gauge coupling and fine structure constant fix the unification scale and the unified gauge coupling.

Neutralino relic density in supersymmetric GUTs with no-scale boundary conditions above the unification scale

We investigate SU(5) and SO(10) GUTs with vanishing scalar masses and trilinear scalar couplings at a scale higher than the unification scale. The parameter space of the models, further constrained by b-\tau Yukawa coupling unification, consists of a common gaugino mass and of \tan\beta. We analyze the low energy phenomenology, finding that A-pole annihilations of neutralinos and/or coannihilations with the lightest stau drive the relic density within the cosmologically preferred range in a significant region of the allowed parameter space. Implications for neutralino direct detection and for CERN LHC experiments are also discussed.

Symmetry breaking and time variation of the QCD coupling

Astrophysical indications that the fine structure constant has undergone a small time variation during the cosmological evolution are discussed within the framework of the standard model of the electroweak and strong interactions and of grand unification. A variation of the electromagnetic coupling constant could either be generated by a corresponding time variation of the unified coupling constant or by a time variation of the unification scale, of by both. The various possibilities, differing substantially in their implications for the variation of low energy physics parameters like the nuclear mass scale, are discussed. The case in which the variation is caused by a time variation of the unification scale is of special interest. It is supported in addition by recent hints towards a time change of the proton-electron mass ratio.

Seesaw induced Higgs mechanism

We discuss a two scalar doublets model which induces the Higgs mechanism by means of a seesaw mechanism. This model naturally predicts a light Higgs scalar whose mass is suppressed by the grand unification scale. The model predicts an intermediate scale between the electroweak symmetry breaking scale and the grand unification scale at $10^9$ GeV. Below this intermediate energy scale the usual standard model appears as an effective theory. A seesaw mechanism in the scalar sector of the model not only induces the standard Higgs mechanism, but also solves the hierarchy problem. An implementation of this mechanism in models where the Planck scale is in the TeV region is discussed.

Unification of gauge, Higgs and matter in extra dimensions

We consider the unification of gauge, Higgs as well as the matter fields in a 6D N=2 supersymmetric SU(8) gauge theory. The gauge symmetry SU(8) is broken down to SU(4)×SU(2)L×SU(2)R×U(1)2 in 4D through T2/Z6 orbifold compactification, and the theory is reduced to 4D N=1 supersymmetric Pati–Salam model. The electroweak Higgs fields as well as the third family of fermions are unified in the 6D N=2 gauge multiplet. The 6D bulk gauge interaction provides both gauge and Yukawa interactions for the third family predicting α1=α2=α3=αt=αb=ατ at the unification scale, in good agreement with experiment. Incorporation of the first and second family as well as other orbifolds are also briefly discussed.

Grand unification in higher dimensions

We have recently proposed an alternative picture for the physics at the scale of gauge coupling unification, where the unified symmetry is realized in higher dimensions but is broken locally by a symmetry breaking defect. Gauge coupling unification, the quantum numbers of quarks and leptons and the longevity of the proton arise as phenomena of the symmetrical bulk, while the lightness of the Higgs doublets and the masses of the light quarks and leptons probe the symmetry breaking defect. Moreover, the framework is extremely predictive if the effective higher dimensional theory is valid over a large energy interval up to the scale of strong coupling. Precise agreement with experiments is obtained in the simplest theory— SU(5) in five dimensions with two Higgs multiplets propagating in the bulk. The weak mixing angle is predicted to be sin 2 θ w =0.2313±0.0004, which fits the data with extraordinary accuracy. The compactification scale and the strong coupling scale are determined to be M c≃5×10 14 GeV and M s≃1×10 17 GeV , respectively. Proton decay with a lifetime of order 10 34 years is expected with a variety of final states such as e + π 0, and several aspects of flavor, including large neutrino mixing angles, are understood by the geometrical locations of the matter fields. When combined with a particular supersymmetry breaking mechanism, the theory predicts large lepton flavor violating μ→ e and τ→ μ transitions, with all superpartner masses determined by only two free parameters. The predicted value of the bottom quark mass from Yukawa unification agrees well with the data. This paper is mainly a review of the work presented in hep-ph/0103125, hep-ph/0111068, and hep-ph/0205067 [1–3].