Electroweak Gauge Theory Research Articles

Higgs boson coupling as a probe of the sphaleron property

Sphaleron is a non-perturbative solution of electroweak gauge theories, which is crucially important for the scenario of electroweak baryogenesis. The sphaleron energy depends on details of the mechanism for the electroweak symmetry breaking. We find that in many of new physics models the deviation of the sphaleron energy from the prediction in the standard model is proportional to that of the triple Higgs boson coupling with opposite signs. This interesting relation would be useful to determine the sphaleron energy by measuring this couplings at future collider experiments.

New scalar contributions to the weak dipole moments of charged leptons

We calculate the contributions of new scalar particles to the weak anomalous dipoles moments in alternative electroweak gauge theories.

Gerald Stanford Guralnik

Gerald Stanford Guralnik

Fermi and the theory of weak interactions

The history of weak interactions starting with Fermi's creation of the beta decay theory and culminating in its modern avatar in the form of the electroweak gauge theory is described. Discoveries of parity violation, matter-antimatter asymmetry, W and Z bosons and neutrino mass are highlighted.

Octonionic Non-Abelian Gauge Theory

We have made an attempt to describe the octonion formulation of Abelian and non-Abelian gauge theory of dyons in terms of 2×2 Zorn vector matrix realization. As such, we have discussed the U(1) e ×U(1) m Abelian gauge theory and U(1)×SU(2) electroweak gauge theory and also the SU(2) e ×SU(2) m non-Abelian gauge theory in term of 2×2 Zorn vector matrix realization of split octonions. It is shown that SU(2) e characterizes the usual theory of the Yang Mill’s field (isospin or weak interactions) due to presence of electric charge while the gauge group SU(2) m may be related to the existence of ’t Hooft-Polyakov monopole in non-Abelian Gauge theory. Accordingly, we have obtained the manifestly covariant field equations and equations of motion.

The Origin of Matter

“If we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of Nature, we must regard it rather as an accident that the Earth (and presumably whole solar system), contains a preponderance of negative electrons and positive protons. . ..” This is a sentence in the Nobel Lecture given by Paul A. M. Dirac in 1933. 1) This is the first proposal for baryon-anti-baryon symmetric universe. However, astrophysical observations have ruled out the presence of antimatter in the present universe up to the scale of clusters of galaxies. If our universe indeed began baryon symmetric, those imbalances in numbers of baryons and anti-baryons must be generated by some physical processes in the early universe. I show, in this talk, that decays of the heavy (right-handed) Majorana neutrinos in the early universe generate the imbalances between baryon and anti-baryon numbers. The presence of super heavy (right-handed) Majorana neutrinos is an important prediction of unified theories beyond the standard model. An integration of the heavy Majorana neutrinos induces very small masses for neutrinos via the seesaw mechanism. 2) Thus, small neutrino masses is a reflection of unification at very high energy scale. It is quite natural to consider that the heavy Majorana neutrinos are produced thermally in the early universe. When the temperature of the universe cools down to the masses of the heavy Majorana neutrinos, the heavy neutrinos begin to decay into Higgs boson and lepton or Higgs boson and anti-lepton. The decay may produce the lepton-number asymmetry if CP invariance is violated in the decay processes. The CP invariance can be easily violated by phases in new complex Yukawa coupling of Higgs boson to the right-handed neutrinos and left-handed leptons. The decay processes can easily be out of thermal equilibrium. Thus, the decay processes of heavy Majorana neutrinos can satisfy three Sakharov conditions 3) for baryogenesis. This produced lepton-number asymmetry is converted into the baryon-number asymmetry in the present universe through non-perturbation effects of the electroweak gauge theory. 5) This is called “leptogenesis”. 4) I show that the neutrino masses observed in various neutrino-oscillation experiments are just in the range predicted by the thermal leptogenesis. 6)

Low-energy Theorems for Strongly Interacting W's and Z's in SU(2)L × SU(2)R × U(1)B–L

In this work, low energy theorems for gauge boson (GB) longitudinal modes of the SU(2)L × SU(2)R × U(1)B−L electroweak gauge theory are derived. These theorems are valid for energies in the domain of applicability of the Equivalence Theorem, and hold for all left-right symmetric models assuming that there are no extra contributions from light scalars to the scattering amplitudes.

Does the Higgs Mechanism Exist?

This paper explores the argument structure of the concept of spontaneous symmetry breaking in the electroweak gauge theory of the Standard Model: the so‐called Higgs mechanism. As commonly understood, the Higgs argument is designed to introduce the masses of the gauge bosons by a spontaneous breaking of the gauge symmetry of an additional field, the Higgs field. The technical derivation of the Higgs mechanism, however, consists in a mere reshuffling of degrees of freedom by transforming the Higgs Lagrangian in a gauge‐invariant manner. This already raises serious doubts about the adequacy of the entire manoeuvre. It will be shown that no straightforward ontic interpretation of the Higgs mechanism is tenable, since gauge transformations possess no real instantiations. In addition, the explanatory value of the Higgs argument will be critically examined.

Particle physics: a comprehensive introduction

1. The Particle Physics Program. 2. How to Calculate Amplitudes. 3. Scattering of Leptons and Photons. 4. Hadrons. 5. Isospin and Flavor SU(3), Accidental Symmetries. 6. The Constituent Quark Model. 7. The Full Color Gauge Theory. 8. Weak Interactions of Fermions. 9. Weak Mixing Phenomena. 10.The Electroweak Gauge Theory and Symmetry Breaking. 11. Large Cross Section Processes. 12. Scattering with Large Momentum Transfer. 13. Physics at Higher Energies. Appendix A. Conventions.

Leptogenesis in the Early Universe*

The presence of superheavy Majorana neutrinos is an important prediction of unified theories beyond the standard model. An integration of the heavy Majorana neutrinos induces very small masses for neutrinos via the seesaw mechanism. Thus, small neutrino masses is a reflection of a unification at very high energy scale.It is quite natural to consider that the heavy Majorana neutrinos are produced thermally in the early universe. Then, the heavy neutrinos begin to decay into Higgs and lepton, or Higgs and anti-lepton when the temperature of the universe cools down to the masses of heavy Majorana neutrinos. The decays of the heavy neutrinos may produce the lepton-number asymmetry if CP invariance is violated in the decay processes. This lepton-number asymmetry is converted into the baryon-number asymmetry in the present universe (leptogenesis) through nonperturbative effects of the electroweak gauge theory. We show, in this talk, that the neutrino masses suggested from atmospheric and solar neutrino-oscillation experiments are just in the range favorable for the thermal leptogenesis. With the aid of the observed neutrino masses we find that the thermal leptogenesis takes place at temperatures T ≳ 2 × 109 GeV.However, the above scenario suffers from the gravitino problem if one extends the standard model to the supergravity framework. This is because too many gravitinos are produced at the temperature required for the thermal leptogenesis and their decays destroy light elements created by the big-bang nucleosynthesis. We show that a leptogenesis via inflaton decay is an interesting alternative to the thermal leptogenesis. This scenario is free from the gravitino problem if the gravitino has a relatively large mass as m3/2 ≃ 3–6 TeV.The importance of neutrinoless double β decay experiments and measurement of CP violation in neutrino oscillation experiments is also emphasized to explain the present universe's baryon asymmetry.

Vacuum structure and high-energy scattering

This short review deals with the manifestations of the vacuum structure of non-Abelian gauge theories in high-energy scattering. Specifically, it concentrates on instanton-induced hard scattering processes, both in the electroweak gauge theory and in QCD. Soft scattering processes in QCD and their connection to models of semi-hard vacuum fluctuations are also briefly discussed.

On the lattice construction of electroweak gauge theory

Based on the Ginsparg-Wilson relation, a gauge invariant formulation of electroweak SU(2) × U(1) gauge theory on the lattice is considered. If the hypercharge gauge coupling is turned off in the vacuum sector of the U(1) gauge fields, the theory consists of four left-handed SU(2) doublets and it is possible, as in vector-like theories, to make the fermion measure defined globally in all topological sectors of SU(2). We then try to incorporate U(1) gauge field, following Lüscher's reconstruction theorem. The global integrability condition is proved for “gauge loops” in the space of the U(1) gauge fields with arbitrary SU(2) gauge field fixed in the background. For “non-gauge loops”, however, the proof is given so far only for the classical SU(2) instanton backgrounds.

ON THE STRUCTURE OF PHYSICAL SPACE

In this paper we develop a theory based on the postulate that the environment where physical phenomena take place is the space of four complex parameters of the linear group of transformations. Using these parameters as fundamental building blocks we construct ordinary space–time and the internal space. Lorentz invariance is built in the definition of external space, while the symmetry of the internal space, S(1)×SU(2) results as a consequence of the identification of the external coordinates. Thus, special relativity and the electroweak interaction symmetry ensue from the properties of the basic building blocks of physical space. Since internal and external space are derived from a common structure, there is no need to bring into the theory any additional hypothesis to account for the microscopic nature of the internal space, nor to introduce symmetry breaking mechanisms that would normally be required to force a splitting of the internal and external symmetries. As an outcome of the existence of a basic structure underlying the external space–time, the weak and electromagnetic coupling constants are not independent and the Weinberg weak mixing angle is derived from the theory. In this new theory, there is an interrelationship between external and internal transformations, which leads to the quantization of electric charge. Finally we conclude that the electroweak gauge theory can be regarded as a consequence of Einstein's general theory of relativity. The proposed theory represents an extension of the normally accepted theory and includes it as a particular case. This paper is an attempt to formulate a new framework in which the physical phenomena take place, and to explore some of its consequences.

One-loop leading logarithms in electroweak radiative corrections

We discuss the evaluation of the collinear single-logarithmic contributions to virtual electroweak corrections at high energies. More precisely, we proof the factorization of the mass singularities originating from loop diagrams involving collinear virtual gauge bosons coupled to external legs. We discuss, in particular, processes involving external longitudinal gauge bosons, which are treated using the Goldstone-boson equivalence theorem. The proof of factorization is performed within the 't Hooft--Feynman gauge at one-loop order and applies to arbitrary electroweak processes that are not mass-suppressed at high energies. As basic ingredient we use Ward identities for Green functions with arbitrary external particles involving a gauge boson collinear to one of these. The Ward identities are derived from the BRS invariance of the spontaneously broken electroweak gauge theory.

Sum rules for e+e− → W+W− helicity amplitudes from BRS invariance

BRS invariance of the electroweak gauge theory leads to relationships between amplitudes with external massive gauge bosons and amplitudes where some of these gauge bosons are replaced with their corresponding Nambu-Goldstone bosons. Unlike the equivalence theorem, these identities are exact at all energies. In this paper we discuss such identities which relate the process e + e − → W + W − to W ± χ ∓ and χ + χ − production. By using a general form factor decomposition for e + e − → W + W −, e + e − → W ± χ ∓ and e + e − → χ + χ −, amplitudes, these identities are expressed as sum rules among scalar form factors. Because these sum rules may be applied order by order in perturbation theory, they provide a powerful test of higher order calculations. By using additional Ward-Takahashi identities we find that the various contributions are divided into separately gauge-invariant subsets, the sum rules applying independently to each subset. After a general discussion of the application of the sum rules we consider the one-loop contributions of scalar-fermions in the Minimal Supersymmetric Standard Model as an illustration.

ELECTROWEAK VORTICES AND GAUGE EQUIVALENCE

Vortex configurations in the electroweak gauge theory are investigated. Two gauge-inequivalent solutions of the field equations, the Z and W vortices, have previously been found. They correspond to embeddings of the Abelian Nielsen-Olesen vortex solution into a U(1) subgroup of SU(2)×U(1). It is shown here that any electroweak vortex solution can be mapped into a solution of the same energy with a vanishing upper component of the Higgs field. The correspondence is a gauge equivalence for all vortex solutions except those for which the winding numbers of the upper and lower Higgs components add to zero. This class of solutions, which includes the W vortex, corresponds to a singular solution in the one-component gauge. The results, combined with numerical investigations, provide an argument against the existence of other vortex solutions in the gauge-Higgs sector of the Standard Model.

Vacuum of the electroweak gauge theory in a strong magnetic field in A heat bath

Expressions are obtained for the thermodynamic potential of a gas of electrically charged vector bosons in a magnetic field and the effective potential of the Weinberg-salam theory in a strong magnetic field in a heat bath. In the single-loop approximation, an estimate is obtained for the value of the critical temperatureTcr corresponding to the phase transition in the Weinberg-Salam theory in a magnetic field. It is shown that it is possible to determine correctly the total probability for production of aW+W− boson pair from the vacuum by an ultrastrong magnetic field in a heat bath, and an expression is obtained for this probability. It is argued that in the Weinberg-Salam theory the restoration of the spontaneously broken symmetry atT=0,B>B cr (1) is simultaneously accompanied by dynamical symmetry breaking of the theory.

Anomaly in SU(2/1) Electroweak Gauge Theory

Anomalies in an SU(2/1) electroweak gauge theory are studied by means of the path-integral method. We show that in such a gauge theory, the anomalies for axial vector current of leptonic fields vanish though one's for vector current remain. We also discuss the conditions which cancel the anomaly in the latter case.

Parity-violation effects on the Auger-electron emission from highly charged atomic ions.

Within the framework of standard electroweak gauge theory, parity-violation effects on the Auger emission from atomic ions are examined. Highly charged ions are prime candidates due to their simple atomic structure and large electroweak charge. To be specific, the Auger decay of the 2[ital s][sup 2] [ital J]=0 level in U[sup 90+] is analyzed. In QED, the polarization-asymmetry parameter is identically zero. It is found that neutral-current mixing of the 2[ital s][sup 2] [ital J]=0 and 2[ital s]2[ital p] [ital J]=0 levels yields a polarization asymmetry of 10[sup [minus]7].

PHENOMENOLOGICAL PARAMETER ANALYSIS OF A HIGGSLESS ELECTROWEAK GAUGE THEORY WITH INDUCED INTERACTIONS INCLUDED

The nonlinear version of the electroweak gauge theory (BESS model) is considered. It contains no physical Higgs particle but, instead, a further triplet of massive gauge bosons. Parameter bounds are derived which can be deduced from expected data of high precision experiments. The induced fermionic couplings which emerge due to the model’s nonrenormalizability are treated in a consistent way.