On the mass and mixings of the ZE

The experimental data on the neutral current couplings are used to derive lower bounds on the mass of Z_E, the extra neutral gauge boson appearing in the minimal ‘beyond the standard model’ scenario favoured in superstring compactifications. This is based on the gauge group SU(3)_c×SU(2)_L×U(1)_Y×U(1)_E. Taking sin²θ_w=0.229, m_W=80.76 GeV and m_Z=91.59 GeV it is found that the mixing angle θ between Z and Z_E must satisfy −0.136<sin θ<−0.007 corresponding to m_ZE>152 GeV or, assuming E₆ unification m_ZE>155 GeV.     

Left-right symmetry breaking scale and supersymmetry in unified theories

We propose a class of supersymmetric grand unified models where parity and SU(2)_R breaking scales are widely separated and compatible with a low-lying mass for the right-handed gauge boson W_R. The intermediate symmetry SU(4)_c×SU(2)_L×SU(2)_R and Higgs content are uniquely fixed if m_WR < 10⁹ GeV. The unification scale lies within an order of magnitude below the Planck mass.     

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.     

Early unification and the Weinberg angle in the SU(4)4 grand unified model

In the framework of the grand unified gauge group SU(4)⁴ we discuss possibilities to reconcile the low unification scale (10⁵?10⁷ GeV) with the acceptable value of sin²θ_w. We consider various specific models which differ by the values of the intermediate mass scale, the choice of the fermion multiplets and by the embedding of the electroweak group SU(2) into SU(4)⁴. The class of theories with early unification and correct sin²θ_w is constructed. They all predict new non-sequential fermions which are SU(2)_L,R singlets and have unconventional electric charges. Cosmological implications of such theories are discussed and it is argued that new particles may well account for the positive results of searches for fractional charge in terrestrial matter.     

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：     

Light singlet particles and their cosmological consequences in witten-type supersymmetric models

In a class of supersymmetric gauge models which generate a large mass scale from a supersymmetry breaking mass scale M through loop corrections, there exists generally a very light scalar particle which transforms like a singlet under SU(3)_c × SU(2)_L with no U(1) charge. Cosmological constraints on such a particle are so severe that an upper bound is set on possible values of supersymmetry breaking scale in this class of models as M ? 500 TeV provided that the large mass scale is 10¹⁵ GeV and the mass of the light scalar particle is generated in one-loop order. This bound holds even if the goldstino is not absorbed into the gravitino.     

On superstring-inspired SU(3) × SU(2) × (U(1))2 models with SO(10) unification

Alternative compactification of the heterotic superstring can give rise to a residual four-dimensional SO(10) gauge symmetry for the observable sector. We consider a model with gauge group SU(3) × SU(2) × (U(1))², resulting from the Hosotani breaking of SO(10), study its further gauge symmetry breaking and calculate the particle spectrum. We find that all breakings can occur close to the weak scale; the top mass lies preferentially between 40 and 60 GeV, the second Z boson mass is O(200–400) GeV. The sparticle spectrum is quite heavy, apart possibly from a light chargino, whose mass can be as light as O(30) GeV.     

Gauge hierarchies of SU(N) grand unification

The structure of spontaneous breaking of SU(N) gauge symmetry for grand unification is investigated. The results obtained are applied to the analysis of SU(8) symmetry for which possible ways of breaking and intermediate symmetries are considered. It is assumed that the SU(8) group unifies the subgroups of colour, standard electroweak and horizontal symmetries. We find conditions which it is necessary to impose on the vacuum expectation values of Higgs multiplets to provide an arbitrary breaking pattern of SU(N) symmetry and conserve any intermediate symmetry. If in the SU(8) models considered fermions and mirror fermions do not violate the (V-A) and (V+A) structure of weak interactions, then their masses should not be greater than ～10² GeV. It is also shown that the contributions of fermion and Higgs multiplets to the renormalization group equation for the coupling constant of any subgroup of SU(N) are identical. Renormalization group identities for the case of arbitrary SU(N) breaking are given where the contribution of Higgs multiplets have been taken into account (but they cancel each other). Using these identities one can calculate the mass values for the breaking of the intermediate symmetries in the SU(8) models, and also exclude part of the possible breaking patterns.     

Gauge hierarchies in the E8 × E′8 superstring theory

We present a systematic approach to the problem of gauge hierarchy structure in E₈ × E′₈ superstring theory. It is shown that only very limited E₆ breaking schemes are allowed from the group-theoretical and phenomenological point of view. The ordinary GUTs are not permitted and moreover the unification of SU(3), and SU(2)_w cannot occur at the energy scale below M_PI. We give four promising models and add some comments on each of them.     

Dynamically broken supergravity and the hierarchy problem

We propose a scenario for grand unified models based on local supersymmetry. We give arguments that condensates of strongly interacting gauge theories might break local supersymmetry. The gravitino mass induces mass splittings in the low energy theory and allows us to understand a hierarchy of M_p = 10¹⁹ GeV to M_w = 10² GeV naturally.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

Supersymmetric flipped SU(5) revitalized

We describe a simple N = 1 supersymmetric GUT based on the group SU(5)×U(1) which has the following virtues: the gauge group is broken down to the SU(3)_C×SU(2)_L×U(1)_Y of the standard model using just 10, $\text{10}$ Higgs representations, and doublet-triplet mass splitting problem is solved naturally by a very simple missing-partner mechanism. The successful supersymmetric GUT prediction for sin²θ_w can be maintained, whilst there are no fermion mass relations. The gauge group and representation structure of the model may be obtainable from the superstring.     

Aspects of left-right symmetric models in superstring phenomenology

The general features of low-energy, rank-six left-right symmetric models as inspired by the superstring are examined. Particular attention is paid to the mass-mixing matrix of the exotic and downtype quarks. It is found that the class of models based on the groupSU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R is plagued with the problem of unnatural fine tuning. Models based on the other left-right group, namelySU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R , work rather well from the points of view investigated. In this case a parameter fitting is presented which is compatible with the lowering of the group rank by two units via radiative breaking, without conflicting either with weak universality or with lepton conservation. The unification scale comes in the 10¹⁷ GeV mass range, the intermediate (righthanded) scale is quite low, not exceeding the 10⁴ GeV range, and the Weinberg angle is correct. Good prospects are also obtained for proton decay and neutrino masses.     

Renormalization group analysis and the top quark mass in the SU(4) × O(4) string model

We perform a two-loop renormalization group analysis for the gauge couplings in the SU(4) × O(4) model. We use the string theory prediction for the unification scale and the experimentally acceptable low energy values for ₃ and sin² θ_w, to determine the magnitudes of the various symmetry breaking scales as well as the value of the common gauge coupling at the unification scale. We solve the coupled differential system for the gauge and top and bottom Yukawa couplings, and determine the top mass as a function of two parameters which could be chosen to be the ratio of the Higgs VEV's that give masses to the up and down quarks and the value of the top coupling at the unification scale. We find a relatively heavy top quark mass which lies in the range 130m_t180 GeV.     

Fractional charges and the renormalization group in theSU(4)×O(4) string model

We study the renormalization group equations of the gauge couplings in theSU(4)×O(4)～SU(4)×SU(2) _L ×SU(2_ _R string model, derived in the context of the free fermionic formulation of the four dimensional superstring. We calculate the effective string unification scale taking into account string threshold corrections and we consider the consequences of then _L andn _R fractionally charged states, sitting in the (1, 2, 1) and (1, 1, 2) representations correspondingly, of the gauge symmetry of the model. Some of these states become massive at a very high scale, when a number of singlet fields acquire vev's. However, many of them (the precise number depends on the specific choice of the flat direction) remain in the massless spectrum. We consider various cases and find that, for specific choices of flat directions, the physical parameters of the model, like the grand unification scale and the low energy parameters sin²θ _W and α₃, depend only on the differencen _?=n_L-n_R. We study more general cases where remnants of the exotic doublets remain below theSU(4) breaking scale. We also solve the coupled differential system of the renormalization group equations for the gauge and the Yukawa couplings and estimate the range of the top quark mass which is found to lie in the range 140 GeV<m _t<190GeV.     

Mass scales for grand unified theories: Are there testable alternatives to SU(5)?

We consider the effects of the existence of new interactions consistent with the Weinberg angle, quark masses, and grand unification of all interactions except gravity. With one very specific exception, we find that the mass scales for such new interactions are greater than 10⁷ GeV. We conclude that if proton decay is not found at the SU(5) rate, then experiments at extremely high energies or sensitive to microweak or smaller effects will be necessary to decide among the alternatives. The exceptional case is viable only if new weak interactions exist with a mass scale below 10⁵ GeV.     

Low-scale axion from large extra dimensions

The mass of the axion and its decay rate are known to depend only on the scale of Peccei–Quinn symmetry breaking, which is constrained by astrophysics and cosmology to be between 10⁹ and 10¹² GeV. We propose a new mechanism such that this effective scale is preserved and yet the fundamental breaking scale of U(1)_PQ is very small (a kind of inverse seesaw) in the context of large extra dimensions with an anomalous U(1) gauge symmetry in our brane. The production and decay of the associated Z_A gauge boson, which ends up as two gluons and two axions, is a distinct collider signature of this scenario.     

A supersymmetricSU(5)×U(1) model with natural gauge hierarchy

We present a supersymmetricSU(5)×U(1) model. This model has the following features. The gauge hierarchy is naturally generated by the quadratically divergent nature of the Fayet-IliopoulosD term. TheSU(5)×U(1) gauge symmetry breaks uniquely intoSU(3) _W ×SU(2) _c ×U(1) _y at an energy scale of 10^17–18GeV. The non-vanishing vacuum expectation value of an auxiliary field component ofU(1) gauge vector multiplet induces the breaking ofSU(2) _W ×U(1) _y . It gives a mass of 10^2–3GeV to scalar quarks and scalar leptons at the tree level. The renormalization group analysis shows that the color fine structure constant α _C (M _W ) becomes somewhat small and the Weinberg angle sin²θ _W (M _W ) somewhat too large in a simple version of the model.     

Fermion mass hierarchy based onN=8 supergravity

A possible mechanism is proposed to realize fermion mass hierarchy based on the superunification model of Ellis et al. In addition to the usual fermion (F)—Higgs (B) coupling, “non-renormalizable” interactions such as(1/(M _p ) ⁿ )(F) ² (B) ⁿ⁺¹ are introduced. It is assumed that three kinds of Higgs scalars respectively develop v.e.v. of orderM _P ,M _X andM _W , corresponding to the symmetry breaking pattern ofSU(8)→SU(5)→SU(3)×SU(3)×U(1)→SU(3)×U(1). As a result, fermions acquire their masses of orderM _w ,M _W (M _X /M _P) andM _W (M _X /M _P )². An example of the model is presented which shows nice feature of hierarchical mass patterns.     

Possibility of a doubly-charged structure at theS-meson mass

The various symmetry breaking patterns that are possible with a 24-plet and a 5-plet of Higgs fields in SU(5) are classified. Spontaneous breakdown of SU(5) to SU(3)_colour×U(1) _em can be achieved (excluding the gauge hierarchy problem) without imposing unnatural constraints on the parameters of the Higgs potential.