The effect of Higgses and “technions” on the calculation of sin2θw and Mx

The effect of the scalar sector on the calculation of sin²θ_w and M_x in grand unified theories is studied. We consider first elementary Higgs scalars and assume the “big desert” hypothesis. It is argued that Higgses other than the usual doublet can also be light (～ M_w). One can obtain bigger values for sin²θ_w by having light (～ M_w) scalar colour sextets which can give rise to interesting phenomenology. As an example, one can build an SU(5) model giving sin²θ_w ? 0.23 at the one-loop level. We also calculate the uncertainty in sin²θ_w and M_x due to the lack of knowledge of the specific masses of superheavy Higgses. We find that this uncertainty is small for reasonable SU(5) models but large in all the SO(10) versions except the minimal. Finally (and alternatively) we consider the effect of a technicolour interaction. The pseudo-Goldstone bosons (technions) increase the calculated sin²θ_w by as much as ～0.01 but M_x remains nearly unchanged. Second-order contributions due to the technifermions tend to cancel the increase on sin²θ_w and in turn increase M_x.     

How to compare the SU(5) value of sin2θw with experiments?

We establish the relation between κsin²θ_w to be found from neutral-current experiments and sin²θ_w(Q) for Q=M_W predicted by grand unified theories. We then calculate sin²θ_W(M_W) in the minimal SU(5) model taking the M_W as well as M_x threshold effects into account. We find that these two threshold effects on sin²θ_W(M_W) cancel with each other and sin²θ_W(M_W)=0.211± 0.005.     

Gravitational corrections to the unification scale in SO(10) with a low right-handed mass scale

In a recent paper, Hill examined the influence of a higher dimensional operator induced in the SU(5) lagrangian by gravity. It was found that this operator could produce a significant increase in the unification scale and in a drastic lowering of the value of sin²Θ_W in disagreement with phenomenology. In the low-energy parity restoration scenario within SO(10) we arrive at values of sin²θ_W which are too large. We examine the possible influence of the corresponding operator in SO(10) to see if it can lower sin²θ_W sufficiently to agree with data. We find agreement with data is possible with several possible choices of the Higgs sector.     

Heavy particle effects in grand unified theories with fine-structure constant matching

We note the presence of very significant mismatchings in α(M_w) in some GUT predictions where superheavy particle effects have been included, and adopt a new method to correct them leading to new solutions for the GUT coupling, τ_p or sin²θ_w. An SO(10) model with a grand desert is also noted to yield τ_p ≅ 10³²−10³³ yr and sin²θ_w = 0.225−0.235.     

Weak-electromagnetic unification and broken S4 symmetry

A left-right symmetrical model on weak-electromagnetic unification with four neutral gauge particles obeying S₄ symmetry in their mass generation mechanism is proposed. The Weinberg-Salam results are obtained with sin²θ_w fixed naturally to be 0.25, and further results about superweak interactions are also given.     

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.     

Sensitivity of low energy neutral current parameters to new mass scales withinSU(2)×SU(2)×U(1) andSO(10) unification

Sensitivity of low energy weak parameters to possible new mass scales is discussed withinSU(2) ×SU(2)×U(1) models andSO(10) unification. Accuracy better than 0.5% is needed for meaningful tests of the standard model in region up to 1 TeV and of theSU(5) prediction for sin²θ.     

On the phenomenological group in the unified SO(10) model

We analyze possible low energy effects of the additional U(1) contained in the symmetry breaking chain: SO(10)→SU(5) ? U(1) →…, stressing the importance of considering extensions of SU(2) ? U(1) as subgroups of grand unified models, in order to use the relations between the coupling constants provided by the renormalization group. We also investigate the possibility of employing this extra U(1) for an explanation of the possible discrepancy between the experimental value of sin²θ_w and its renormalized value in the SU(5) model.     

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).     

One-loop threshold effects in string unification

Like grand unification of old, string unification predicts simple tree-level relations between the couplings of all unbroken gauge groups such as SU(3)_C or SU(2)_W. I show here how to compute one-loop corrections to these relations for any four-dimensional model based on a classical vacuum of the heterotic string. The result can be used to calculate both sin²θ_Wand Λ_QCD in terms of α_QCD and M_Planck.     

Higgs bosons and matter-antimatter oscillations in GUTS

The presence of Higgs bosons of diquark and dilepton types at intermediate mass scales in GUTs is analysed in connection with the possible generation of neutron-antineutron and hydrogen-antihydrogen oscillations. Their renormalization effects on the calculation of the parameters sin²θ_w and m_b/m_τ are investigated in SU(5) and in an SO(10) version with a left-right symmetric breaking chain. In correspondence with suitable combination of higgses, we find solutions in SU(5) for n_G=3 and reasonable values of sin²θ_w, m_b/m_τ and proton lifetime τ_p, which allow detectable $\text{n}\text{-}\text{n}$, but undetectable $\text{H}\text{-}\text{H}$ transitions. Solutions of this type, but with higher τ_p, are also found in a particular scheme of SO(10), where the intermediate mass is at the scale M_R at which the left-right symmetry is broken and is of order 10²×m_w. This modifies then conclusions of analyses of SO(10) models, where either no diquarks and dileptons or only a specific set of them are taken into account.An extension of our analysis to supersymmetric versions of SU(5) and SO(10) does not produce acceptable solutions.     

Anti-Su(5)

We discuss ordinary as well as supersymmetric SU(5) ×?(1) models in the hope of accomodating acceptable τ_p and sin²θ_W. The ordinary SU(5) ×?(1) model does not have the monopole. The supersymmetric SU(5) ×?(1) model can be unified in SO(10).     

Threshold effects in SUSY and non-SUSY GUTs

We discuss recent contributions on threshold effects in grand unfiied theories including minimal SUSY SU (5), non-SUSY modifications of the grand desert in SU(5) and SO(10), and SO(10) with single intermediate symmetires. Consequences of theorems on vanishing GUT-scale corrections to sin² θ_w in SO(10) with SU(2) _L XSU(2) _R XSU(4) _c (g_2l =g_2R ) intermediate symmetry are discussed and vanishing corrections on the inter-mediate scale are explicitly demonstrated where predictions are more precise. Threshold and higher dimensional operator effects in SUSY SU(5) recently derived by a number of authors are presented.     

Phenomenological consequences of N = 1 supergravity theories with non-minimal kinetic energy terms for vector superfields

It is shown that N=1 supergravity theories can have a GUT scale as large as the Planck scale if the kinetic energy terms for vector superfields are non-minimal. The canonical values for sin²θ_W (M_W), α₃ (M_W) and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}\text{(M}{}_{\mathrm{<mtext>W</mtext>}}\text{)}$ are respected. In those theories masses of SU(3), SU(2) and U(1) gauginos may be different at the unification scale. Consequences for the low-energy particle spectrum are discussed in the extreme case where one of the gaugino masses is large while the other two vanish.     

Horizontal interactions and their symmetries in GUTs

Using very general assumptions we find and discuss a large class of unified models with horizontal symmetries. We classify them and show on the basis of renormalisation group equations that the typical horizontal mass scale must be at least 10⁹–10¹³ GeV, depending on the model. A class of nonsupersymmetric theories with horizontal symmetries is discovered which predicts a proton lifetimeτ _p ≧10³³ and sin² θ _w ?0.23. It is also argued that supersymmetric unified models involving horizontal symmetries are unlikely to meet present experimental and theoretical requirements—contrary to ordinary supersymmetric theories without horizontal sector.     

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.     

A measurement of the neutral current electroweak parameters using the fermilab narrow band neutrino beam

We report a measurement of the electroweak parameters sin₂θ ^w and ? based on the ratios of neutral current to charged current events measured in the Fermilab narrow-band neutrino beam at energies of 30–240 GeV. The data are fully corrected for radiative effects, heavy-quark production, and other effects. The best value for sin₂θ ^w obtained, sin₂θ ^w =0.239±0.011, is consistent with the most recent values fromW andZ production, as well as from other neutrino experiments.     

Uncertainties in the proton lifetime

We discuss the masses of the leptoquark bosons m_x and the proton lifetime in grand unified theories based principally on SU(5). It is emphasized that estimates of m_x based on the QCD coupling and the fine structure constant are probably more reliable than those using the experimental value of sin²θ_w. Uncertainties in the QCD Λ parameter and the correct value of α are discussed. We estimate higher-order effects on the evolution of coupling constants in a momentum-space renormalization scheme. It is shown that increasing the number of generations of fermions beyond the minimal three increases m_x by almost a factor of 2 per generation. Additional uncertainties exist for each generation of technifermions that may exist. We discuss and discount the possibility that proton decay could be “Cabibbo rotated” away, and a speculation that Lorentz invariance may be violated in proton decay at a detectable level. We estimate that in the absence of any substantial new physics beyond that in the minimal SU(5) model the proton lifetime is 8 × 10^30±2 years.     

Electromagnetic corrections to neutrino processes in the leading logarithmic approximation,the value of sin θ and the W and Z masses

The parameters of the Weinberg-Salam model can be defined by amplitudes at a momentum scale M = O(M_W, M_Z). We derive the leading logarithmic e.m. correction to the relations giving the neutrino amplitudes at a momentum scale μ ? M in terms of sin²θ(M), α(M), M_W and M_Z. For leptonic processes, the Fermi constant is not corrected, but a running, universal, sin²θ(μ) > sin²θ(M) should be used. The Fermi constant for semileptonic processes is renormalized by a factor $\text{?(μ) > 1}$, for charged currents, and is not renormalized, for neutral current processes. The latter are described by the same sin²θ(μ) as the leptonic ones. We estimate that sin²θ(M) is about 0.013 smaller than the value of sin²θ obtained from semileptonic data with no correction, thereby improving the agreement with grand unified theories. The prediction for W (Z) masses and widths in terms of the low energy parameters are discussed. Using previous calculations at order α, we obtain predictions for the masses which are accurate up to and including terms of order (αlnM²)².     

An SO(10) model with 54 + 126 + 10 higgs

We find an absolute minimum of an SO(10) symmetric potential with SU(3) × U(1) invariance. By fixing the higher scales M_R(〈126〉) ? M_x(〈54〉), the model is consistent with the experimental knowledge about matter stability and the value of sin²θ_w. We determine the spectrum of scalar particles and show that their tree-diagram contributions to nucleon decay amplitudes are proportional to 1/M_x².