Gauge theory of a group of diffeomorphisms. III. The fiber bundle description

A new fiber bundle approach to the gauge theory of a group G that involves space‐time symmetries as well as internal symmetries is presented. The ungauged group G is regarded as the group of left translations on a fiber bundle G(G/H,H), where H is a closed subgroup and G/H is space‐time. The Yang–Mills potential is the pullback of the Maurer–Cartan form and the Yang–Mills fields are zero. More general diffeomorphisms on the bundle space are then identified as the appropriate gauged generalizations of the left translations, and the Yang–Mills potential is identified as the pullback of the dual of a certain kind of vielbein on the group manifold. The Yang–Mills fields include a torsion on space‐time.

Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincaré gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2+ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2+ and 2− particles of equal mass, as well as a massive pseudoscalar.

New physics in e(+)e(-) -> Z(gamma) at the ILC with polarized beams: explorations beyond conventional anomalous triple gauge boson couplings

One of the most-studied signals for physics beyond the standard model in the production of gauge bosons in electron-positron collisions is due to the anomalous triple gauge boson couplings in the Z(gamma) final state. In this work, we study the implications of this at the ILC with polarized beams for signals that go beyond traditional anomalous triple neutral gauge boson couplings. Here we report a dimension-8 CP-conserving Z(gamma)Z vertex that has not found mention in the literature. We carry out a systematic study of the anomalous couplings in general terms and arrive at a classification. We then obtain linear-order distributions with and without CP violation. Furthermore, we place the study in the context of general BSM interactions represented by e(+)e(-)Z(gamma) contact interactions. We set up a correspondence between the triple gauge boson couplings and the four-point contact interactions. We also present sensitivities on these anomalous couplings, which will be achievable at the ILC with realistic polarization and luminosity.

Gravitational rescue of minimal gauge mediation

Gravity mediated supersymmetry breaking becomes comparable to gauge mediated supersymmetry breaking contributions when messenger masses are close to the GUT scale. By suitably arranging the gravity contributions, one can modify the soft supersymmetry breaking sector to generate a large stop mixing parameter and a light Higgs mass of 125 GeV. In this kind of hybrid models, however, the nice features of gauge mediation like flavor conservation, etc. are lost. To preserve the nice features, gravitational contributions should become important for lighter messenger masses and should be important only for certain fields. This is possible when the hidden sector contains multiple (at least two) spurions with hierarchical vacuum expectation values. In this case, the gravitational contributions can be organized to be ``just right.'' We present a complete model with two spurion hidden sector where the gravitational contribution is from a warped flavor model in a Randall-Sundrum setting. Along the way, we present simple expressions to handle renormalization group equations when supersymmetry is broken by two different sectors at two different scales.

Role of polarization in probing anomalous gauge interactions of the Higgs boson

We explore the use of polarized e(+)/e(-) beams and/or the information on final state decay lepton polarizations in probing the interaction of the Higgs boson with a pair of vector bosons. A model independent analysis of the process e(+)e(-) -> f (f) over barH, where f is any light fermion, is carried out through the construction of observables having identical properties under the discrete symmetry transformations as different individual anomalous interactions. This allows us to probe an individual anomalous term independent of the others. We find that initial state beam polarization can significantly improve the sensitivity to CP-odd couplings of the Z boson with the Higgs boson (ZZH). Moreover, an ability to isolate events with a particular tau helicity, with even 40% efficiency, can improve sensitivities to certain ZZH couplings by as much as a factor of 3. In addition, the contamination from the ZZH vertex contributions present in the measurement of the trilinear Higgs-W (WWH) couplings can be reduced to a great extent by employing polarized beams. The effects of initial state radiation and beamstrahlung, which can be relevant for higher values of the beam energy are also included in the analysis.

The validity of the Adler-Bardeen theorem in the supersymmetric U(1) gauge model

Using the dimensional reduction regularization scheme, we show that radiative corrections to the anomaly of the axial current, which is coupled to the gauge field, are absent in a supersymmetric U(1) gauge model for both 't Hooft-Veltman and Bardeen prescriptions for γ5. We also discuss the results with reference to conventional dimensional regularization. This result has significant implications with respect to the renormalizability of supersymmetric models.

Surface waves in the presence of external high frequency fields

The system equations of a collisionless, unmagnetized plasma, contained in a box where a high frequency (HF) electric field is incident, are solved in the electrostatic approximation. The surface modes of the plasma in the semi-infinite and box geometry are investigated. In thi high frequency limit, the mode frequencies are not significantly changed by the HF field but their group velocities can be quite different. Two long wavelength low frequency modes, which are not excited in the absence of HF field, are found. These modes are true surface modes (decaying on one wavelength from the surface) unlike the only low frequency ion acoustic mode in the zero field case. In the short wavelength limit the low frequency mode occurs at omega i/ square root 2, omega i being the ion plasma frequency, as a result similar to the case of no HF field.

Renormalisation of the Fayet-Illiopoulos term in supersymmetric spontaneously broken U( 1) gauge theories

It is shown that the Fayet-Illiopoulos D term in N= 1 supersymmetric spontaneously broken U( 1) gauge theories may get one-loop corrections, even when trace U( 1) charges are zero. However, these corrections are only logarithmically divergent and hence do not affect the naturalness of the theory.

Technicolor

The need for reexamination of the standard model of strong, weak, and electromagnetic interactions is discussed, especially with regard to 't Hooft's criterion of naturalness. It has been argued that theories with fundamental scalar fields tend to be unnatural at relatively low energies. There are two solutions to this problem: (i) a global supersymmetry, which ensures the absence of all the naturalness-violating effects associated with scalar fields, and (ii) composite structure of the scalar fields, which starts showing up at energy scales where unnatural effects would otherwise have appeared. With reference to the second solution, this article reviews the case for dynamical breaking of the gauge symmetry and the technicolor scheme for the composite Higgs boson. This new interaction, of the scaled-up quantum chromodynamic type, keeps the new set of fermions, the technifermions, together in the Higgs particles. It also provides masses for the electroweak gauge bosons W± and Z0 through technifermion condensate formation. In order to give masses to the ordinary fermions, a new interaction, the extended technicolor interaction, which would connect the ordinary fermions to the technifermions, is required. The extended technicolor group breaks down spontaneously to the technicolor group, possibly as a result of the "tumbling" mechanism, which is discussed here. In addition, the author presents schemes for the isospin breaking of mass matrices of ordinary quarks in the technicolor models. In generalized technicolor models with more than one doublet of technifermions or with more than one technicolor sector, we have additional low-lying degrees of freedom, the pseudo-Goldstone bosons. The pseudo-Goldstone bosons in the technicolor model of Dimopoulos are reviewed and their masses computed. In this context the vacuum alignment problem is also discussed. An effective Lagrangian is derived describing colorless low-lying degrees of freedom for models with two technicolor sectors in the combined limits of chiral symmetry and large number of colors and technicolors. Finally, the author discusses suppression of flavor-changing neutral currents in the extended technicolor models.

Renormalisation of the Fayet-Illiopoulos term in supersymmetric spontaneously broken U( 1) gauge theories

It is shown that the Fayet-Illiopoulos D term in N= 1 supersymmetric spontaneously broken U( 1) gauge theories may get one-loop corrections, even when trace U( 1) charges are zero. However, these corrections are only logarithmically divergent and hence do not affect the naturalness of the theory.

Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Surface waves in the presence of external high frequency fields

The system equations of a collisionless, unmagnetized plasma, contained in a box where a high frequency (h.f.1 electric field is incident, are solved in the electrostatic approximation. The surface modes of the plasma in the semi-infinite and box geometry are investigated. In the high frequency limit, the mode frequencies are not significantly changed by the h.f. field but their group velocities can be quite different. Two long wavelength low frequency modes, which are not excited in the absence of h.f. field, are found. These modes are true surface modes (decaying on one wavelength from the surface) unlike the only low frequency ion acoustic mode in the zero field case. In the short wavelength limit the low frequency mode occurs at &/2, oi being the ion plasma frequency, a result similar to the case of no h.f. field.

Supersymmetric Solution Of Gauge Hierarchy Problem

Some recent developments with respect to the resolution of the gauge hierarchy problem in grand unified theories by supersymmetry are presented. A general argument is developed to show how global supersymmetry maintains the stability of the different mass-scales under perturbative effects.