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.     

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).     

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.     

The weak mixing angle and unification mass in supersymmetric SU(5)

We consider the predictions for the weak mixing angle θ_W and the scale M of unification in a supersymmetric extension of SU(5), with particular emphasis on the sensitivity to the number of Higgs multiplets. In the one-loop approximation, we also calculate the ratio m_b/m_τ. We discuss generally the effects of an intermediate threshold between the weak interaction scale and M and estimate the sensitivity of θ_W and M to the scale of supersymmetry breaking.The evolution of the coupling constants of the supersymmetric SU(3) ? SU(2) ? U(1) effective gauge theory is described and the two-loop corrections to θ_{W and M} are calculated.     

Phases of resonant amplitudes: πN → ϱN

Using SU(6)_W symmetry in its l-broken form we find that the newly reported relative signs of πN → ?N resonant amplitudes seem to indicate a universal “SU (6)_W-like” preference for all observed multiplets. Since the corresponding πN → πΔ phases favour an “anti-SU(6)_W” solution for the 70, L^P = 1^? multiplet the l-broken SU (6)_W model now faces a serious contradiction.     

Unification constraints in composite models

We consider unification constraints on composite models with special emphasis on two-loop effects due to relatively large metacolor coupling. Two classes of models are discussed. The first consists of those which do not have gaugedSU(2) _W and the second of those which include technicolor and gaugedSU(2) _W . The outcome is that in each specific composite model the two-loop contributions can affect noticeably several important quantities, such as the grand unified mass or the weak mixing angle. We find also that it may not be possible to have a unified composite model based on the symmetryG _MC ×SU(3) _c × U(1) _em with low (<10⁶ GeV) metacolor mass scale.     

Non-abelian traveling wave solutions for massless QCD2

The field equations for quantum chromodynamics in 1 + 1 dimensions (QCD₂) with massless fermions are shown to admit classical non-abelian traveling wave solutions. In this case, the field equations reduce to the linear Frenet-Serret equations for a curve in the three-space corresponding to an SU(2) subalgebra of the SU(N) gauge group.     

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.     

Polarization amplitudes fore + e − →W + W − ande + e − →ZZ

The main purpose of this work is to study the three weak boson vertex. We give explicit formulae for all polarization amplitudes of the processese ⁺ e ^? →W ⁺ W ^? ande ⁺ e ^? →ZZ, with arbitrary couplings between the various intermediate vector bosons. Using these expressions we discuss possible signatures ofC, P andT violation in the three vector boson coupling, as well as the effects of anomalous magnetic dipole and electric quadrupole moments ofW ^±. The amplitudes for the above processes in any SU(2) × U(1) and SU(2)_L × SU(2)_R × U(1) gauge theory are also given, while the special case of the Weinberg-Salam model is studied in detail.     

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.     

On W±, Z0, γ self-interactions: High energy behaviour and tree unitarity bounds

We analyze the high-energy behaviour of vector boson scattering amplitudes within the framework of a recently suggested lagrangian model based on global weak isospin symmetry broken by electromagnetism. Requiring vanishing of the most strongly (as s²) rising contribution to vector boson scattering amplitudes leads to vector boson self-interactions dependent on a single parameter, for which the anomalous W^± magnetic moment, κ, can be chosen. Tree unitarity is violated at about 2 TeV for arbitrary κ as in the SU(2)_L × U(1)_Y theory for m_H → ∞. The model is well suited for significant tests of the vector boson sector of the SU(2)_L × U(1)_Y electroweak theory in processes such as e⁺e⁻ → W⁺W⁻.     

Vortex free energy and string tension at strong and intermediate coupling

We present results of high temperature expansions up to order g^?24 for the vortex free energy respectively string tension in pure lattice gauge theories with gauge groups SU(2) and Z₂ in 3 and 4 dimensions. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement. An intermediate coupling region is seen, where the string tension smoothly interpolates between strong coupling and weak coupling behaviour.     

γ-W0 mixing as an alternative to unified weak-electromagnetic gauge theories

A very simple model based on γ-W⁰ mixing (but not on spontaneously broken gauge symmetry) is shown to reproduce all the quantitative predictions of the standard (Weinberg-Salam) model as far as low-energy phenomenology is concerned. The model predicts intermediate-boson mass relations weaker than Weinberg's. Weinberg's mass formulae, however, can be accommodated in our model provided the γ-W⁰ mixing parameter and the coupling constants (e and g) satisfy a special relation. This relation also guarantees asymptotic SU(2) × U(1), decent high-energy behavior in processes like $\text{v +}\text{v}\text{→}\text{W}{}^{\mathrm{+}}\text{+}\text{W}{}^{\mathrm{?}}$ and the SU(2) × U(1) value for the W^± boson gyromagnetic ratio. Speculative attempts are made to understand the sign and magnitude of “sin² θ_W”.     

SU(6)W and πN→ϱN revisited

We point out that the intersection of the Berkeley-SLAC and Saclay signs of πN→?N resonant amplitudes are consistent with ?-broken SU(6)_W if both the 70, L^P = 1^?and 56, L^P = 2⁺ multiplets choose anti-SU(6)_W solutions. The symmetry scheme still fails in that the πN→πΔ relative signs require an SU(6)_W-like solution for the 56, L^P = 2⁺. This failure however now rests on a single incorrect sign prediction among all N? and Δπ amplitudes.     

SU(6)W and decays of baryon resonances

The decay rates of baryon resonances assigned to the {70, 1^?} and {56, 2⁺} presentations of SU(6)_W ? O(3) are subjected to a detailed comparison with an SU(6)_W model motivated by the recent work of Melosh. We conclude that SU(6)_W is remarkably successful as an approximate symmetry for decay vertices.     

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).     

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.     

Hydrogen atom on null-plane and Melosh transformation

The null-plane dynamics of hydrogen-like atoms is studied in approximations depending on c, the velocity of light, being large. Neglecting terms in the Hamiltonian of order c^?3 (relative to electron rest energy) a symmetry SU (2)_W appears which is analogous to the SU (6)_W of hadron classification. This symmetry, if accurate, would dictate zero ground state magnetic moment. The symmetry is broken by terms of third order, which can, however, be transformed a way by the appropriate approximation to the Melosh transformation. There then emerges a better symmetry, SU (2)_M, broken only at fourth order. The ground state magnetic moment acquires its usual non-relativistic value. The symmetry SU (2)_M corresponds to a subgroup of a symmetry [U (2) × U (2)]_FW which appears in the old Foldy-Wouthuysen approach when spin-orbit coupling is neglected. As well as “current” and “constituent” pictures, “classification” pictures are distinguished; it is to one of the latter that the Melosh transformation transforms.     

Cabibbo angle,CP violation and quark masses

By adding suitable discrete flavor symmetries to SU(2)_L ? SU(2)_R ? U(1) left-right symmetric gauge models of weak and electromagnetic interactions, we are able to express all the mixing angles between the quark flavors (u, d, s,c) in terms of the quark masses. This enables us to compute the Cabibbo angle and the CP violating phases using plausible values for the quark masses. The CP violating K ar 2π decay amplitude η_+? (and η₀₀ in the model is then given purely in terms of the parity violating parameter of the model (m_WL⁺/m_WR⁺)².     

Low-energy parity restoration and unification mass scale within maximal symmetries

We investigate the hierarchy of gauge boson masses in the maximal grand unified theory by studying the renormalization group equations for the running coupling constants associated with the symmetry breaking of SU(16)viaSU(12) _q×SU(4) _l×U(1) _|B|?|L| chain. Particular attention is given to the contribution of Higgs scalars to these equations. It is found that the intermediate mass scale M_L, associated with right-handed gauge bosons could be as low as 10 ³ GeV only for sin ²θ _w(M _L) as high as 0.265 with α _s(M _L)=0.13. In this chain of symmetry breaking, we have also examined the lowest unification mass that is allowed by the low-energy data for sin ²θ _w(M _L) and the assumed gauge hierarchy. This has been done in two cases; first for the case where SU(3) ^c is vectorial, second, for the case where SU(3) ^c is axial. In both cases the lowest unification mass scales were found to be 10 ¹³, 10 ¹¹, 10 ⁸ and 10 ⁷ GeV for sin ²θ _w(M _L) = 0.22, 0.24, 0.26,and0.265 respectively with α _s(M _L) = 0.13. The implication of these low unification masses on baryon non-conserving processes is also discussed.