Trimuons in SU(3) gauge models

We discuss models of weak interactions which can account for the recently observed μ^?μ^?μ⁺ events in v_μ reactions by allowing for the production of a new heavy neutral lepton and a new quark. One model is based on an SU(3) × U(1) gauge theory in shich the left-handed leptons are classified in anti-triplets. The second model catagorizes the leptons in an octet in accord with the more restrictive SU(3) weak gauge theory.     

Ghost-free non-Abelian gauge theory: renormalization and gauge-invariance

Although it has been known for a long time that the special case n^μA_μ = 0 for an axial gauge of a vector field A_μ, characterized by a direction n_μ, is free from the peculiar loop complications inherent in all other known gauges of non-Abelian gauge theories, practical use of this ghost-free gauge has often met with some reserve. The reasons were always difficulties in the development of the theoretical formalism, all of which can be traced back to a singularity at n^μp_μ = 0 where p is some four-momentum. This paper, which is a sequel to an earlier one by one of the authors, is intended to show that within the functional integration formalism a consistent field theory can be developed. Here we first prove the gauge invariance of the renormalized theory, allowing for the presence of an arbitrary number of scalar and fermion fields with spontaneous symmetry breaking. Then it is shown that all on-shell elements for the physical S-matrix between properly selected physical sources are independent of n_μ (gauge invariant) and so are the renormalized masses.     

Vacuum copies and perturbation theory in the 't hooft-veltman gauge of QED

The 't Hooft-Veltman gauge condition ?_μA_μ + A_μ² = 0 gives a version of quantum electrodynamics with many similarities to Yang-Mills theory, including the presence of Gribov gauge-fixing ambiguities. We exhibit and discuss some properties of a family of copies of the vacuum, emphasizing their bearing on perturbation theory and the choice of a vacuum state. It is shown that in a general gauge theory, the same perturbation series results from expanding about any gauge-copy of the vacuum.     

A new unified theory with right-handed currents and proton stability

A unified vector-like gauge theory based on SU(6) is proposed, where the proton stability is achieved with reasonable lepto-quark massemeasurable in the decay K_L⁰→μe. We predict the existence of a long-lived messon decaying into Pe^?.     

Spinor theory of general relativity without elementary gravitons

We propose a generally covariant and locally Lorentz invariant theory of a Majorana spinor field ψ_μ^α. Our theory has no elementary spin-2 quanta, but does reproduce Einstein's general relativity as a classical solution. We compare this situation to the possibility of finding classical monopoles in a gauge theory, even though no such elementary object is introduced at the outset.     

Proton decay induced by instantons inSU(5) grand unification

Instantons infinitesimally turned out of theSU _c (3) subspace of spontaneously brokenSU(5) gauge theory induce a baryon number violating interaction proportional 1/μ _X ² like heavy vector boson exchange, but with a different tensor structure.     

Quantum phase transitions in cascading gauge theory

We study N=1 supersymmetric SU(K+P)×SU(K) cascading gauge theory of Klebanov et al. (2000) [1] and [2] on R×S³ at zero temperature, and at the origin of the baryonic branch. A radius of S³ sets a compactification scale μ. An interplay between μ and the strong coupling scale Λ of the theory leads to an interesting pattern of quantum phases of the system. For μ?μχSB=1.240467(8)Λ the vacuum state of the theory is chirally symmetric. At μ=μχSB the theory undergoes the first-order transition to a phase with spontaneous breaking of the chiral symmetry. We further demonstrate that the chirally symmetric state of cascading gauge theory becomes perturbatively unstable at scales below μc=0.950634(5)μχSB. Finally, we point out that for μ<1.486402(5)Λ the stress-energy tensor of cascading gauge theory can source inflation of a closed Universe.     

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.     

Perturbative QED in terms of gauge invariant fields

A formulation of QED using only gauge invariant fields acting on a physical state space is discussed. The fields are the electromagnetic tensor F_μν and a non-local electron field ψ_f depending on a quadruple {f^μ} of auxiliary functions. The f-ambiguity is physically meaningful: the f^μ contain information on the asymptotic configuration of the electromagnetic field accompanying charged particles. Equations of motion are introduced and solved perturbatively, in the sense that expressions for the Wightman functions of the theory are derived. No information on the commutation relations between the basic fields is needed.     

Chemical potentials in gauge theories

One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter A₀=const (A_μ is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories.     

Weak correction to the muon magnetic moment in a gauge model

The weak correction, a_μ^w, to the anomalous magnetic moment of the muon is calculated in an SU(2) ? U(1) ? U(1) gauge model of weak and electromagnetic interactions. The R_ξ gauge is used and Ward-Takahashi indentities are utilized eliminating all ξ-dependence before the loop integration is performed. a_μ^w,expt places no constraint on the mass of one of the neutral vector mesons, which may be arbitrarily small.     

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.     

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.     

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.     

VII. Difficulties in fixing the gauge in non-Abelian gauge theories

Some problems arising from the use of the Coulomb gauge in SU(2) Yang-Mills theory are discussed. It is shown that: i) the transversality condition does not fix the gauge uniquely (Gribov ambiguity); ii) there exist physical configurations that cannot be described by a continuous A_μ in the Coulomb gauge.     

Limitations on the existence of massless composite states

Massless particles represented by the fields with mixed spinor indices of SL(2,C) are generally shown to be forbidden in covariant field theory under the assumptions of positivity and covariiance alone. This remains true also in gauge theory (in which a negative metric appears) as far as the particles are gauge invariant. This in particular implies that any dynamical “gauge-type particle” (such as vector A_μ, Rarita-Schwinger ψ_μ etc.) cannot appear unless the system has a corresponding local invariance from the outset.     

Gauge invariance and renormalization

The renormalization of Abelian and non-Abelian local gauge theories is discussed. It is recalled that whereas Abelian gauge theories are invariant to local c-number gauge transformations δA_μ(x) = ?_μ,…, with □Λ = 0, and to the operator gauge transformation δA_μ(x) = ?_μφ(x), …, δφ(x) = α^?1?·A(x), with □φ = 0, non-Abelian gauge theories are invariant only to the operator gauge transformations $\text{δA}{}_{\mathrm{\mu }}\text{(x) ～}\textcolor{red}{}{}_{\mathrm{\mu }}\text{C(x)}$, …, introduced by Becchi, Rouet and Stora, where

_μ is the covariant derivative matrix and C is the vector of ghost fields. The renormalization of these gauge transformation is discussed in a formal way, assuming that a gauge-invariant regularization is present. The naive renormalized local non-Abelian c-number gauge transformation $\text{δA}{}_{\mathrm{\mu }}\text{(x) = (Z}{}_1\text{/Z}{}_3\text{)gA}{}_{\mathrm{\mu }}\text{(x) ×}\text{Λ}\text{(x)+?}{}_{\mathrm{\mu }}\text{Λ}\text{(x)}$, …, is never a symmetry transformation and is never finite in perturbation theory. Only for $\text{Λ}\text{(x) = (Z}{}_3\text{/Z}{}_1\text{)L}$ with L finite constants or for $\text{Λ}\text{(x) = Ω}\text{z}\text{?}{}_3\text{C(x)}$ with Ω a finite constant does it become a finite symmetry transformation, where $\text{z}\text{?}{}_3$ is the ghost field renormalization constant. The renormalized non-Abelian Ward-Takahashi (Slavnov-Taylor) identities are consequences of the invariance of the renormalized gauge theory to this formation. It is also shown how the symmetry generators are renormalized, how photons appear as Goldstone bosons, how the (non-multiplicatively renormalizable) composite operator A_μ × C is renormalized, and how an Abelian c-number gauge symmetry may be reinstated in the exact solution of many asymptotically fr ee non-Abelian gauge theories.     

Quarks and leptons

We review the physics of quarks and leptons within the framework of gauge theories for the weak and electromagnetic interactions. The Weinberg-Salam SU(2) × U(1) theory is used as a “reference point” but models based on larger gauge groups, especially SU(2)_L × SU(2)_R × U(1), are discussed. We distinguish among thre “generations” of fundamental fermions: The first generation (e^?, ν_e, u, d), the second generation (μ^?, ν_μ, c, s) and the third generation (τ^?, ν_τ, t, b). For each generation we discuss the classification of all fermions, the charged and neutral weak currents, possible right-handed currents, parity and CP-violation, fermion masses and Cabibbo-like angles and related problems. We review theoretical ideas as well as experimental evidence, emphasizing open theoretical problems and possible experimental tests. The possibility of unifying the weak, electromagnetic and strong interactions in a grand unification scheme is reviewed. The problems and their possible solutions are presented, generation by generation, but a brief subject-index (following the table of contents) enables the interested reader to follow any specific topic throughout the three generations.