Possible structures of the neutral current within a gauge theory framework

We examine a class of gauge theories based on U(1)×SU(2)×G allowing for an arbitrary number of gauge bosons, while retaining the lowq ² four fermion interaction of the standard model. Measurable consequences fore ⁺ e ^?→μ ⁺ μ ^? ande ⁺ e ^?→e ⁺ e ^? at presently available as well as LEP energies are presented. Implications of the recently determined QED cut-offΛ _? ? 100 GeV on gauge boson properties and the anomalous magnetic moment of the muon are pointed out.     

Operator quantization of non-abelian gauge theories in a completely fixed axial gauge

A consistent quantization of chromodynamics in a completely fixed axial gauge is carried out by using the Dirac bracket quantization procedure. The main results are: The translation of Dirac brackets into equal-time commutators is possible, without ambiguities, because of the absence of ordering problems. All equal-time commutators are compatible with constraints and gauge conditions holding as strong operator relations. All equal-time commutators are compatible with chromoelectric, chromomagnetic, and fermionic fields vanishing at spatial infinity. The colored gauge potentials A^0,a, A^1,a, and A^2,a are seen to develop a physically significant, although pure gauge, behavior at x³ = ± ∞, as required by the presence of a nontrivial topological content. Poincaré invariance is satisfied without introducing in the Hamiltonian “extra” quantum mechanical potentials. The determinant of the Faddeev-Popov matrix does not depend upon the field variables.     

Discriminating between Z′-boson effects and effects of anomalous gauge couplings in the double production of W ± bosons at a linear collider

The potential of the International Linear electron-positron Collider (ILC) for seeking, in the annihilation production of W ^±-boson pairs, signals induced by new neutral gauge bosons predicted by models belonging to various classes and featuring an extended gauge sector is studied. Limits that will be obtained at ILC for the parameters and masses of Z′ bosons are compared with present-day and future data from the Large Hadron Collider (LHC). The possibility of discriminating between the effects of Z-Z′ mixing and signals induced by anomalous gauge couplings (AGC) is demonstrated within theoretically motivated trilinear gauge models involving several free anomalous parameters. It is found that the sensitivity of ILC to the effects of Z-Z′ mixing in the process e ⁺ e ^? → W ⁺ W ^? and its ability to discriminate between these two new-physics scenarios, Z′ and AGC, become substantially higher upon employing polarized initial (e ⁺ e ^?) and final (W ^±) states.     

U(1)-invariant current forms

Let λ : U(1) → GL (V) be a linear representation. Lagrangians defined on J¹(T*M × V)whose universal current form is gauge invariant, are described in terms of gauge invariant Lagrangians and invariant functions on V. A characterization of gauge invariant Lagrangians depending on matter fields only, that is, L : J¹V → ?, is also obtained.     

Remark on the consistent gauge anomaly in supersymmetric theories

We present a direct field theoretical calculation of the consistent gauge anomaly in the superfield formalism, on the basis of a definition of the effective action through the covariant gauge current. The scheme is conceptually and technically simple and the gauge covariance in intermediate steps reduces calculational labors considerably. The resultant superfield anomaly, being proportional to the anomaly d^abc=trT^a{T^b,T^c}, is minimal without supplementing any counterterms. Our anomaly coincides with the anomaly obtained by Marinković as the solution of the Wess–Zumino consistency condition.     

Extension to velocity dependent gauge transformations

In previous papers it was shown that in phase space a generator of gauge transformations for a singular Lagrangian \(L(q,\dot q)\) is given byG[ε^α]=ε _k ^α φ _α ^k (q,p,t) where φ _α ^k are first class constraints andG is subjected to a stationarity condition. A non-trivial extension from velocity (or momentum) independent gauge transformations to velocity dependent ones is realized, by replacing gauge functions ε^α(t) with momentum dependent functions ε^α(q,p,t), as long asG satisfies the stationarity condition. Inversely, it is proved in a classical framework that, within velocity dependent gauge transformations, all generators of gauge transformations can be expressed in terms of the linear combinations of φ _α ^k .     

QCD cascade model in deep inelastic scattering

We develop a new QCD cascade model for jets in deep inelastic scattering. We use the light-like axial gauge whose gauge vector is parallel to momentum of the initial parton so that only final partons cascade. Due to this feature we can generate events for any given virtualityQ ² andx _B =Q ²/2Pq.     

A theorem on electromagnetic properties of leptons

The following theorem is proven: Every lepton with the mass m, electric charge q and spin J belonging to any representation of a non-abelian gauge group must have the magnetic moment μ = qJm^?1, electric mean squared radius r² = qJ(J + 1)m^?2 and electric quadrupole moment Q = qJ(2J ? 1)m^?2 in the first order of the electromagnetic effects in an arbitrary renormalizable theory with the non-abelian gauge group symmetry which permits the validity of the Gerasimow-Drell-Hearn and Cabibbo-Radicati sum rules. The formula for the magnetic moment applies also for an abelian symmetry and remains valid even if the gauge symmetry is spontaneously broken.     

QCD calculations in the light-cone gauge

The non-singlet quark structure function is calculated in the leading logarithm approximation in an axial gauge with n² = 0, the light-cone gauge. The choice n² = 0 leads to a simple identity for loop integrals involving the extra n · k denominators. We compare the results graph by graph with both Feynman gauge QCD and a scalar gluon theory. The leading diagrams are the same “rainbow” diagrams as for the case of the scalar theory.The techniques are also applied to quark-quark scattering at large transverse momentum. The leading diagrams have the same dressed ladder-form factor structure.     

Corrections to the Zτ +τ− vertex in topcolor-assisted technicolor theory

We calculate the corrections to the Zτ⁺τ^? vertex in the one-family topcolor-assisted technicolor models without exact custodial symmetry contributed from the exchange of extended technicolor (ETC) sideways and diagonal gauge bosons and the topcolor gauge boson Z′. The precise measurements of the τ asymmetry parameter Aτ give strong constraint on the free parameters in the topcolor-assisted technicolor models.     

Bounds on the masses of neutral generation-changing gauge bosons

The existence of several generations of quarks and leptons suggests the possibility of a gauge symmetry connecting the different generations. The neutral gauge bosons of such a scheme would mediate rare processes such as K_L⁰→μ^±, K⁺→π⁺e^?π⁺, μN→eN and would contribute to ΔM(K_S⁰?K_L⁰). We study these and other processes within a simple theoretical framework and derive bounds involving the masses and coupling constants of the generation-changing gauge bosons and various generation-mixing angles. The lower bounds for the relevant masses lie in the 10–100 TeV region. Various remarks concerning the relevance of these bounds to currently popular theoretical ideas and to future experiments are presented.     

Infrared properties of two-loop,initial state spectator interactions in the Drell-Yan process

We use the light-cone axial gauge of proper-time ordered perturbation theory and study the soft-IR properties of the two-loop virtuals' diagrams considered by Bodwin, Brodsky and Lepage for ππ → μ⁺μ^- + X. It is shown that although the systematic summation over all possible spectator interactions removes the outside soft-IR divergences in the non-overlapping ladder Glauber diagrams, unphysical inside soft-IR divergences persist. So, in the light-cone axial gauge the on-shell Glauber region is not a gauge invariant concept which can be physically isolated from radiative corrections which non-trivially involve other diagrammatic regions. Due to gauge invariance it can be potentially misleading in eikonal phenomenologies based on perturbative QCD to assume an ad hoc inside soft-IR cutoff in analyzing possible non-abelian effects in multiple scatterings involving spectators.     

An analytic calculation of the weak field limit of the static color dielectric constant

We analyze the Dyson equation/Ward identity system for the axial gauge n · A = 0 gluon propagator Δ_μν(q)whenn · q = 0. The solution behaves like (q^?4 + (q²)^ν?1) for small q₂, and we are able to calculate the power ν analytically. It turns out to be 0.1737. This analytic calculation verifies our earlier numerical solutions to these equations. For static problems, n · q = 0 is the temporal gauge, and in this gauge the gluon propagator is directly related to the color dielectric constant. We can thus calculate the dielectric constant in the infrared limit.     

On the vacuum structure of an SU(2) Yang-Mills theory

By using a compactification of the spatial part R³ of Minkowski-space different from the one-point compactification to S³, we get a new classification of the vacua for an SU(2) gauge theory. It contains, besides the vacua arising in the S³ compactification, the Gribov vacua as new classes. We discuss the role of pseudoparticle solutions within this framework and comment on the problem of the Coulomb gauge degeneracy.     

Infrared instability of QCD at finite temperatures

The infrared behaviour of the transversal gluon propagator in QCD at T≠0 is investigated within the ghost-free axial gauge. The singularities found in this propagator for the momentum p ～ g²T remain for any choice of the gauge and indicate the infrared instability of QCD at finite temperatures.     

Gauge boson masses and lepton mixing inO(4)⊗U(1) gauge model

The Cabibbo angle is introduced as a mixing angle of the gauge bosonsW ^± andX ^± in anO(4)?U(1) gauge model. Masses of gauge bosons are calculated to beM _W=82 (input), \(M_z = \sqrt 2 M_W s\gamma = 130\) (γ is mixing angle, sin² γ=0.21),M _x=666, andM _Y=660, in units GeV. TheW _μ ^± andZ _μ ⁰ couple to the familiar charged and neutral currents, respectively. The effective neutrino oscillation angle is found to be the Cabibbo angle.     

Photon initiated reactions in the resonance region

A consistent picture of two body photon initiated reactions is achieved by implementing a resonance model in the s-channel compatible with duality and gauge invariance. Large real parts generated by contact terms to achieve gauge invariance appear in a well defined pattern. Their size explains hitherto puzzling reactions like γN → ?N, γN → ?^? and γN → ω^?, near their thresholds.     

Electromagnetism in terms of its two degrees of freedom

Electromagnetism is described in terms of two scalar gauge-invariant variables. The role of gauge freedom in the quantization process when A^μ(x) is written in momentum space appears as the indetermination of a two-dimensional space-like plane orthogonal to the (null) momentum k^μ plus a c-number arbitrary function. Duality rotations can naturally be described as the freedom to choose two orthonormal vectors in the two-dimensional space-like plane. The action written in terms of the two dynamical degrees of freedom is explicitly invariant under finite duality rotations and the associated Noether current is gauge invariant. Finally, we establish the equivalence for the Poisson bracket relations (PBR's) (based on equal time and equal null-time PBR for the two degrees of freedom) between A^μ(x) and A^ν(x′) for any gauge.