Top quark mass from gut mass relations

Using one-loop renormalization group equations of SU(3)×SU(2)×U(1) and mass relations of minimal SU(5) we obtain m₁=203±30 GeV and m_s=0.20±0.03 GeV for the top and strange quark masses. For general GUT with m_b=m_τ at E=M_x<M_P1 we get m_t > 165 GeV. These values appear to be consistent with recent experimental data.     

A light neutral intermediate vector boson without large e+e−→ μ+μ− asymmetries

An effective SU(2)×U(1)×U(1)' electroweak theory is shown to permit the occurence of a pair of neutral intermediate vector bosons with masses 40 GeV?m_light?70 GeV, m^W.S._Z⁰<m_heavy?100 GeV. Neutrino neutral current interactions are shown to be the same as in the standard electroweak model, and e⁺e^?→μ⁺μ^? forward-backward asymmetries are within experimental bounds for m_light?40 GeV.     

Cosmological constant in a model with superstring-inspired E 6 unification and shadow θ-particles

We have developed the concept of parallel existence of the ordinary (O-) and mirror (M-), or shadow (Sh-) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking E ₆→SU(3)³ in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. E ₆ unification, inspired by superstring theory, restores the broken mirror parity at the scale ～10¹⁸ GeV. With the aim to explain the tiny cosmological constant, in the second part we consider the breakings: E ₆→SO(10)×U(1) _Z in the O-world, and E′₆→SU(6)′×SU(2)′ _θ in the Sh-world. We assume the existence of shadow θ-particles and the low-energy symmetry group SU(3)′ _C ×SU(2)′ _L ×SU(2)′ _θ ×U(1)′ _Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)′ _θ group with massless gauge fields, “thetons”, has a macroscopic confinement radius 1/Λ′ _θ . The assumption that Λ′ _θ ≈2.3?10^?3 eV explains the tiny cosmological constant given by recent astrophysical measurements. In this way the present work opens the possibility to specify a grand unification group, such as E ₆, from cosmology.     

Quark masses and cabibbo angles

A simple symmetric pattern of Higgs fields in an SU (2)_L × SU (2)_R × U (1) gauge model with six quarks yields: tan²θ_c = m_d/m_s and θ_c = 15° in good agreement with experiment. A eight-quark extension of the model leads to successful determination of the three Cabibbo-like angles connecting the first six quarks and to the prediction m_t ～ 9.3 m_c ～ 14 GeV.     

Can the superstring inspire the standard model?

We discuss general features of models in which the E₈ × E′₈ heterotic superstring is compactified on a specific Calabi-Yau manifold. The gauge group of rank-6 in four dimensions is supposed to be broken down at an intermediate scale m_I to the standard model group SU(3)_C × SU(2)_L × U(1)_Y, as a result of two neutral scalar fields acquiring large vacuum expectations (vev's) in one of many flat directions of the effective potential. We find that it is difficult to generate such an intermediate scale by radiative symmetry breaking, whilst such models have prima facie problems with baryon decay mediated by massive particles and with non-perturbative behaviour of the gauge couplings, unless m_I ≳ 10¹⁶ GeV. Rapid baryon decay mediated by light particles, large neutrino masses, other Δ L ≠ 0 processes and flavour-changing neutral currents are generic features of these models. We illustrate these observations with explicit calculations in a number of different models given by vev's in different flat directions.     

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.     

On the structure of the low energy superpotential in superstring theory

We show that after the gauge symmetry breaking of the E₆ grand unified group to the H=SU(3)^c×SU(2)_L×U(1)_Y× U(1)_E subgroup by the Hosotany mechanism a number of additional Yukawa terms not present in a decomposition of 27×27×27 may appear in the low energy superpotential. Some of these terms cause a rapid proton decay.     

Perturbation constraint on the Higgs boson mass

It is shown that a systematic perturbation expansion of spontaneously broken gauge theory imposes a constraint on the upper as well as the lower limit of the Higgs boson mass. In the standard SU(2) × U(1) model, the Higgs boson mass is calculated to be between 13 GeV and 500 GeV for the weak mixing angle, θ ≈ 35°.     

On the sign of the n-p mass difference in gauge models

We examine the sign of the n-p mass difference in some gauge models based on the SU(2) × U(1) × U(1) or SU(2)_L × SU(2)_R × U(1) group, and show that a few specific elements of the neutral-vector-meson mass matrix can determine the sign of Δm|_n?p. We also present an SU(2) × U(1) × U(1) model which can give the correct Δm|_n?p.     

Parity violations in hydrogen and the fundamental structure of the weak current

Experiments in progress with hydrogen and deuterium may in practice determine the fundamental parameters and constituents of the weak interaction within the framework of unified gauge theories. In particular, for SU (2) × U (1) theories, from the results of these experiments one can infer the masses of the charged and neutral weak vector bosons (and thus sin²θ_W), and the isospin classification of the right-handed portions of the electron and the u- and d-quarks. Non-singlet assignments for e_R, u_R and d_R would imply the existence of additional leptons and/or quarks. Hydrogen/deuterium data also may be used to discriminate between SU (2) × U (1) models and various models based on larger gauge groups.     

Low-energy predictions from grand unified theories

A theoretical framework to compute low-energy processes in a spontaneously broken gauge theory is devised. It applies in any gauge and uses conventional renormalisation schemes. Application of the method to SU(5) gives a range for M_X of 4.10¹³ GeV < M_X < 1.3 · 10¹⁵ GeV with a best value of 6.6 · 10¹⁴ GeV.     

Fermion spectra from superstrings

Some compactifications of the ten-dimensional anomaly-free E₈ × E₈ and SO(32) theories that correspond to superstrings are studied. Compactification is achieved by setting the classical gauge field equal to the spin connection. The resulting chiral fermion spectra are obtained for any six-dimensional manifold, under the condition Tr F² = 30 Tr R², plus a quantization condition for U(1) charges. For E₈ × E₈ these conditions lead to potentially realistic models for any irreducible six-dimensional manifold and any embedding of the holonomy group. Apart from a few more exotic examples, the four-dimensional models we obtain are more or less standard SU(5), SO(10), SU(4) × SU(2) × SU(2) or E₆ models.     

Generalization of the radiative corrections to β and μ decays in the SU(2)L × U(1) gauge model

Previous results for the radiative corrections to the ratio of decay probabilities of β and μ decays are generalized to the case of arbitrary symmetry breaking in the framework of the SU(2)_L × U(1) gauge model. In this more general case, the results remain very simple: the corrections are given by the corresponding expressions of the local V-A theory with m_W substituted for the cutoff Λ plus a positive definite contribution which depends on θ_W and R = m_W²/m_Z².Thus, the corrections in the general case are still constrained to have large values as required by Cabibbo universality and the present experimental values on β and μ decays. For reasonable values of m_Z and m_W the results in the general case are numerically close to those previously obtained in the simplest version of the theory. To illustrate this point the corrections are compared for two different choices of the parameters of the theory. In an appendix we discuss, rather briefly, the theoretical arguments that allow us to generalize pprevious discussions the case of fractionally charged quarks.     

Grand unification of effective gauge theories

An effective non-renormalizable SU(3)×SU(2)×U(1) invariant gauge theory results at ordinary energies when superheavy fields are integrated out from a grand unified theory based on a simple gauge group G. The solutions of the second-order renormalization-group equations for the gauge coupling constants of the effective theory are examined. General formulae for the superheavy vector boson mass and for sin²θ near M_W are given in this approach to grand unification. The superheavy vector boson mass is plotted against the QCD scale parameter Λ for a certain set of grand unified models. Corrections to the prediction when the set of models is enlarged are discussed, and illustrated with examples from G≡SU(5) and O(10).     

Pattern of E6 symmetry breaking in the superstring theory

A mechanism of symmetry breaking by the Wilson loop is discussed. In particular, we take the Wilson loop to break the E₆ symmetry of superstring theory down to SU(6)×U(1)_T3R and then to SU(3)_L×U(1)_Y in succession. By the fine tuning parameters we obtain sin²θ_W=0.215, the proton life time τ_p≈10³⁴yr and the two intermediate mass scales M_I≈10¹⁶⁻¹⁷ GeV and M_II≈10⁵⁻¹⁰ GeV.     

Radiative corrections to νμ + N → μ− + X and their effect on the determination of ϱ2 and sin2θW

We study the O(α) corrections to σ_T(ν_μ + N → μ^? + X). The coefficient of the leading O(αln m_Z) contribution is given by a general theorem as in the case of β decay, while the energy scale accompanying m_Z in the argument of the logarithm as well as mass singularities and non-logarithmic terms are obtained by a detailed quark-parton model calculation. The effect of muon mass singularities, when there is an experimental vut in the low range of the y distribution, is also investigated. Combining these new results with our previous analysis of σ_T(ν_μ + N → ν_μ + X), we calculate theSU(2)_L × U(1) parameter ?_(νμ;h)² and evaluate the effect of the O(α) corrections on the determination of sin²θ_W^exp from deep inelastic ν_μ scattering. Applying these corrections to existing data, we obtain the weigthed average sin²θ_W^exp = 0.216 ± 0.010 ± 0.004. This value when used in conjuction with our previous analysis of the W^± and Z⁰ masses provides the predictions m_W = 83.0_?2.8^+3.0 GeV and m_Z = 93.8_?2.4^+2.5 GeV. For the weak interaction angle defined by modified minimal subtraction we find sin²θ_W(m_W) = 0.215 ± 0.010 ± 0.004, which is in very good agreement with the SU(5) prediction we have recently given.     

Neutral currents within beyond the standard model

We present new, model-independent analyses of the observables in low-energy neutral-current experiments in the neutrino-hadron, neutrino-electron, electron/muon-hadron and electron- muon/tau sectors. We combine them with the latest experimental measurements of the W and Z masses to make global fits in the context of the standard model and of superstring-inspired models. We find in the standard model that sin ²θ _w = 0.228 ± 0.004 if ϱ is fixed to be 1, whilst a two parameter fit yields sin ²θ _w = 0.229 ± 0.006 and ϱ = 1.001 ± 0.007. This new value of sin ²θ _w for ϱ = 1 lies uncomfortably outside the predicted region of the minimal SU(5) model, but is consistent with supersymmetric SU(5) models. In the minimal standard model with ϱ = 1 and equal Higgs and Z masses we find that m_t<168 GeV at the 90% confidence level. We establish lower bounds on the masses of additional neutral gauge bosons Z′ in three superstring-inspired models and upper limits on their mixing with the standard model Z ⁰. In particular, we find that m_Z′129 GeV at the 90% confidence level in a minimal rank-5 superstring-inspired model with canonical Higgs structure.     

Virtual effects of Higgs particles

The possibility of observing Higgs particles through virtual effects is considered in detail for a general gauge theory. The effect of charged Higgs particles on low-energy weak interaction processes, like muon decay, tau decay, nuclear beta decay, pion decay, and some higher-order processes is analyzed. The effect of flavor-changing neutral Higgs particles on rare decay modes of the muon and kaon, μe conversion, K^o-$\text{K}$^o and D^o-$\text{D}$^o mixing is also studied. We discuss constraints on possible extensions of the Weinberg-Salam model and experiments sensitive to their Higgs particles. In particular, we analyze the neutral Higgs which couple to fermions in the minimal SU(2)_L×SU(2)_R×U(1) model and find that they probably have mass greater than 100 GeV.     

Monte Carlo variational study of glueball masses in SU (2) lattice gauge theory for coupling less than one

A Monte Carlo variational calculation of glueball masses is performed in SU (2) lattice gauge theory for coupling less than 1. The preliminary upper bounds are obtained, on a 4³×8 lattice, M(0⁺)=1.38±0.26 GeV, M(2⁺)=1.39±0.41 GeV. Evidence of the existence of differences from the results for g²> 1 is observed.     

大统一对禁闭弱作用规范模型的限制

本文基于两个条件:10¹⁴GeV≤M_u≤10¹⁹GeV,300GeV≤Λ_hc≤1TeV,得到在禁闭弱作用规范模型中SU(N)超色规范群满足N≤3;大统一规范群的可能候选者为:SU(N)N≥7,SU(N)×SU(N)N≥4,SO(14)和SO(18)。 关键词：