Threshold and compactification effects in GUTS

We review general results on threshold effects and their implications on GUTs in the context of LEP data. Among the blooming grand-desert models, threshold effects are computed in the presence of a single real scalar ζ (3, 0, 8) with M_ζ?10¹⁰ GeV leading to experimentally testable predictions on the proton lifetimeτ _p in SU (5) and, in addition, small neutrino masses in SO (10) needed for the solar neutrino flux and the dark matter of the universe. The fine structure constant matching at M_Z is ensured by including threshold effects on the unification coupling. In the minimal SUSY SU (5) such effects at the GUT scale modify the prediction of the supersymmetric mass threshold near the TeV scale and the precision measurments of the Standard Model couplings at M_Z probe into the superheavy mass spectrum. Consequences of theorems proved very useful for threshold, compactification and multiloop effects are discussed. It is noted that in a class of GUTs the highest intermediate scale M_I above which G_224P becomes a good symmetry is not affected by the GUT threshold or compactification effects or multiloop contributions in the range M_I-M_U. But spontaneous compatification effects can decrease the intermediate scale drastically in models where parity and SU(2)_R breakings are decoupled. Low mass W_R-bsosns are permitted in models with decoupled parity and SU (2)_R breakings.     

Gauge coupling unification,the GUT scale,and magic fields

We consider field sets that do not form complete SU(5) multiplets, but exactly preserve the one-loop MSSM prediction for α₃(MZ)${\alpha }_3(M_Z)$ independently of the value of their mass. Such fields can raise the unification scale in different ways, through a delayed convergence of the gauge couplings, a fake unified running below the GUT scale, or a postponed unification after a hoax crossing at a lower scale. The α₃(MZ)${\alpha }_3(M_Z)$ prediction is independent of the mass of the new fields, while the GUT scale often is not, which allows to vary the GUT scale. Such “magic” fields represent a useful tool in GUT model building. For example, they can be used to fix gauge coupling unification in certain two step breakings of the unified group, to suppress large KK thresholds in models with extra dimensions, or they can be interpreted as messengers of supersymmetry breaking in GMSB models.     

Constrained supersymmetric flipped SU(5) GUT phenomenology

We explore the phenomenology of the minimal supersymmetric flipped SU(5) GUT model (CFSU(5)), whose soft supersymmetry-breaking (SSB) mass parameters are constrained to be universal at some input scale, M _in , above the GUT scale, M _GUT. We analyze the parameter space of CFSU(5) assuming that the lightest supersymmetric particle (LSP) provides the cosmological cold dark matter, paying careful attention to the matching of parameters at the GUT scale. We first display some specific examples of the evolutions of the SSB parameters that exhibit some generic features. Specifically, we note that the relationship between the masses of the lightest neutralino χ and the lighter stau [(t)\tilde]₁{\tilde{\tau}_{1}} is sensitive to M _in , as is the relationship between m _χ and the masses of the heavier Higgs bosons A,H. For these reasons, prominent features in generic (m _1/2,m ₀) planes such as coannihilation strips and rapid-annihilation funnels are also sensitive to M _in , as we illustrate for several cases with tan β=10 and 55. However, these features do not necessarily disappear at large M _in , unlike the case in the minimal conventional SU(5) GUT. Our results are relatively insensitive to neutrino masses.     

Effect on Jarlskog Determinant Above the GUT Scale Within Four Flavor Neutrino Framework

We study the Planck scale effects on Jarlskog determiant in the four flavor framework. On electroweak symmetry breaking, quantum gravitational effects lead to an effective SU(2) × U(1) invariant dimension-5 Lagrangian including neutrino and Higgs forces, which perturbed the neutrino mass term and produce an extra terms in the neutrino mass matrix. We consider that gravitational interaction is independent from flavor and compute the Jarlskog determiant due to Planck scale effects. In the case of leptonic sector, the strentgh of CP violation is measured by Jarlskog determiant. We applied our approach to study Jarlskog determinant in the four flavor neutrino mixing above the GUT scale.

     

Effects of superstrings in collisions

Superstring theory in d = 10 dimensions after Calabi—Yau compactification yields a minimum low-energy gauge group SU(3)_C × SU(2)_L × U(1)_Y × U(1)_E. The low-energy theory includes particles with the quantum numbers of 27 representations of E₆, each of which contains an extra neutrino ν^c conventionally called a “right-handed neutrino”. The contributions of ν and ν^c to through Z⁰ and Z_E mixing is calculated. Small contributions are found of the new right-handed neutrino and of the superstring boson Z_E to σ(e⁺e⁻ → γ + nothing).     

Small Dirac neutrino mass and left-right symmetry

We analyze the possibility of generating light Dirac neutrinos at the tree level in a left-right symmetric scenario. We present a minimal extension of the standard SU(2) _L × SU(2) _R × U(1) _Y′ model where the above result is achieved through a “see-saw” like mechanism induced by the minimization of the Higgs potential. The Dirac neutrinos thus obtained are naturally light; indeed we show that the scheme is stable under radiative corrections. The neutrino mass is inversely related to the scale of parity breaking, which may naturally be in the TeV range, leading to new phenomenology in an interesting energy domain.     

Does CP Phase Exist Above the GUT Scale

We consider non-reormalizable interaction term as a perturbation of the conventional neutrino mass matrix. Quantum gravitational (Planck scale )effects lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. In particular, for the $\theta_{13}'$ range 0.00005–0.28, indicates the existence of CP violating phase above the GUT scale. We assume that the gravitational interaction is flavor blind. In this paper, we further investigate the possibility of CP phase exist from Quantum gravity.     

Neutrino mixing and masses in a left–right model with mirror fermions

In the framework of a left–right model containing mirror fermions with gauge group SU(3) _C ⊗SU(2) _L ⊗SU(2) _R ⊗U(1) _Y′, we estimate the neutrino masses, which are found to be consistent with their experimental bounds and hierarchy. We evaluate the decay rates of the Lepton Flavor Violation (LFV) processes μ→eγ, τ→μγ and τ→eγ. We obtain upper limits for the flavor-changing branching ratios in agreement with their present experimental bounds. We also estimate the decay rates of heavy Majorana neutrinos in the channels N→W ^± l ^∓, N→Zν _l and N→Hν _l , which are roughly equal for large values of the heavy neutrino mass. Starting from the most general Majorana neutrino mass matrix, the smallness of active neutrino masses turns out from the interplay of the hierarchy of the involved scales and the double application of seesaw mechanism. An appropriate parameterization on the structure of the neutrino mass matrix imposing a symmetric mixing of electron neutrino with muon and tau neutrinos leads to tri-bimaximal mixing matrix for light neutrinos.     

<Emphasis Type="Italic">SU</Emphasis><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>(4)×<Emphasis Type="Italic">U</Emphasis>(1) model for electroweak unification and sterile neutrinos

Some of the basic problems in neutrino physics, such as new energy scales, the enormous gap between the neutrino masses and the lightest charged fermion mass, and the possible existence of sterile neutrinos in the eV mass range are studied in the local gauge group SU _L (4)×U(1) for electroweak unification, which does not contain fermions with exotic electric charges. It is shown that the neutrino mass spectrum can be decoupled from that of the other fermions. The further normal seesaw mechanism for neutrinos, with right-handed neutrino Majorana masses of order M≫M _weak as well a new eV-scale can be accommodated. The eV-scale seesaw may manifest itself in experiments like the Liquid Scintillation Neutrino Detector (LSND) and MiniBooNE (MB) experimental results and future neutrino experiments.     

Three Flavor Neutrino Mixing and Dark Energy Above GUT Scale

Neutrino mixing lead to a non zero contribution to the dark energy of the universe. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. The mechanism of neutrino mixing is a possible candidate to contribute the cosmological dark energy. Quantum gravitational (Planck scale) effects lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that the gravitational interaction is flavor. In this paper, we discuss the three flavor neutrino mixing and cosmological dark energy contributes due to Planck scale effects.     

Towards low energy physics from the heterotic string

We investigate orbifold compactifications of the heterotic string, addressing in detail their construction, classification and phenomenological potential. We present a strategy to search for models resembling the minimal supersymmetric extension of the standard model (MSSM) in ℤ₆‐II orbifold compactifications. We find several MSSM candidates with the gauge group and the exact spectrum of the MSSM, and supersymmetric vacua below the compactification scale. They also exhibit the following realistic features: R‐parity, seesaw suppressed neutrino masses, and intermediate scale of supersymmetry breakdown. In addition, we find that similar models also exist in other ℤ_N orbifolds and in the SO(32) heterotic theory.     

New minimal <Emphasis Type="Italic">SO</Emphasis>(10) GUT: A theory for all epochs

The supersymmetric SO(10) theory (NMSO(10)GUT) based on the \({{\mathbf {210}+\mathbf {126} +\overline {\mathbf {126}}}}\) Higgs system proposed in 1982 has evolved into a realistic theory capable of fitting the known low energy particle physics data besides providing a dark matter candidate and embedding inflationary cosmology. It dynamically resolves longstanding issues such as fast dimension five-operator mediated proton decay in SUSY GUTs by allowing explicit and complete calculation of crucial threshold effects at M_SUSY and M_GUT in terms of fundamental parameters. This shows that SO(10) Yukawas responsible for observed fermion masses as well as operator dimension-five-mediated proton decay can be highly suppressed on a ‘Higgs dissolution edge’ in the parameter space of GUTs with rich superheavy spectra. This novel and generically relevant result highlights the need for every realistic UV completion model with a large /infinite number of heavy fields coupled to the light Higgs doublets to explicitly account for the large wave function renormalization effects on emergent light Higgs fields. The NMSGUT predicts large-soft SUSY breaking trilinear couplings and distinctive sparticle spectra. Measurable or near measurable level of tensor perturbations – and thus large inflaton mass scale – may be accommodated within the NMSGUT by supersymmetric see-saw inflation based on an LHN flat direction inflaton if the Higgs component contains contributions from heavy Higgs components. Successful NMSGUT fits suggest a renormalizable Yukawon ultraminimal gauged theory of flavour based upon the NMSGUT Higgs structure.     

A possible minimal gauge–Higgs unification

A possible minimal model of the gauge–Higgs unification based on the higher dimensional spacetime M ⁴⊗(S ¹/Z ₂) and the bulk gauge symmetry SU(3) _C ⊗SU(3) _W ⊗U(1) _X is constructed in some detail. We argue that the Weinberg angle and the electromagnetic current can be correctly identified if one introduces the extra U(1) _X above and a bulk scalar triplet. The VEV of this scalar as well as the orbifold boundary conditions will break the bulk gauge symmetry down to that of the standard model. A new neutral zero-mode gauge boson Z′ exists that gains mass via this VEV. We propose a simple fermion content that is free from all the anomalies when the extra brane-localized chiral fermions are taken into account as well. The issues on recovering a standard model chiral-fermion spectrum with the masses and flavor mixing are also discussed, where we need to introduce the two other brane scalars which also contribute to the Z′ mass in the similar way as the scalar triplet. The neutrinos can get small masses via a type I seesaw mechanism. In this model, the mass of the Z′ boson and the compactification scale are very constrained being, respectively, given in the ranges: 2.7 TeV<m _Z′<13.6 TeV and 40 TeV<1/R<200 TeV.     

Supersymmetric unification in the light of neutrino mass

We argue that with the discovery of neutrino mass effects at super-Kamiokande there is a clear logical chain leading from the standard model through the MSSM and the recently developed minimal left right supersymmetric models with a renormalizable see-saw mechanism for neutrino mass to left right symmetric SUSY GUTS: in particular, SO(10) and SU(2) _L × SU(2) _R × SU(4) _c . The progress in constructing such GUTS explicitly is reviewed and their testability/falsifiability by proton decay measurements emphasized.     

SupersymmetricSU (11), the invisible axion,and proton decay

We supersymmetrize the very attractive flavour unification modelSU (11). As with other supersymmetric GUTs the gauge hierarchy problem is simplified, but we may also have observable (τ _p ≈10³³ yrs) proton decay. The required split multiplets are obtained by making the adjoint take a particular direction. Supersymmetry is broken softly at the TeV scale. There is a uniqueU(1) _A symmetry, and hence there are no true Nambu-Goldstone bosons. TheU(1) _A is broken at the GUT scale and there result an invisible axion and neutrino masses.     

Sterile neutrino in a minimal three-generation see-saw model

We investigate symmetries in Dirac and Majorana mass matrices of neutrinos in a three-generation scenario. We show that if we invokeL _e +L _μ-L _τ x S _2R symmetry, one combination of right-handed neutrino states remains massless which can be interpreted as a sterile neutrino. Next we consider a SU2_L x U(1)_y x U(l)_R gauge model and show how higher-dimensional operators can induce mixing between left- and right-handed states which explains solar, atmospheric and LSND experimental results.     

Neutrino Mixing Matrix and Leptogenesis from Quantum Gravity

We consider non renormalization 1/M _x interaction term as a perturbation of the neutrino mass matrix. We find that for the degenerate neutrino mass spectrum. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. We also assume, above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bimaximal. The perturbation generates a non zero value of θ ₁₃, which is within reach of the high performance neutrino factory. In this paper, we find that the non zero value of θ ₁₃ due to Planck scale effects indicates the possibility of CP violation.     

Parity violations in electron-nucleon scattering and the SU(2)L ×SU(2)R ×U(1)L+R electroweak symmetry

The SU(2)_L ×SU(2)_R ×U(1)_L+R model of elecroweak interactions is described with the most general gauge couplings g_L, g_Randg_L+R. The case in which neutrino neutral current interactions are identical to the standard SU(2)_L ×U(1)_L+R model is discussed in detail. It is shown that with the weak angle lying in the experimental range sin²θ_w = 0.23 ± 0.015 and 1 < g_L²/g_R² < 3 it is possible to explain the amount of parity violation observed at SLAC and at the same time predict values of the “weak charge” in bismuth to lie in the range admitted by the controversal data from different experiments.     

Cancellation of energy divergences in Coulomb gauge QCD

Electroweak unification is obtained in anSU(7) model at a mass scale 3×10¹⁰≦M≦3×10¹⁶ GeV's, with left-right symmetric subgroups and sin² θ _w (M)=3/8. BelowM, the model reduces toSU(3) _L ×SU(3) _R , the flavor sector of the “trinification theory” of Glashow et al., or of theE ₆ grand unified theory. This model predicts a natural massless neutrino, and fractionally charged leptons with masses in theM regime.     

Higgs charged bosons and the problem of solar neutrinos

For a model with the SU(2)L×SU(2)_R×U(1)_{B−L} gauge group, the passage of neutrino flux through a substance is studied. It is shown that Higgs charged physical bosons can considerably change the potential of neutrino interaction with the solar substance. An analytical expression for the survival probability of left-handed electron neutrinos is derived in the two-flavor approximation. Yanka Kupala Grodno State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 32–37, January, 2000.