Gauge independent methods for threshold corrections in grand unification

The off-shell gauge independent effective action proposed by Vilkovisky and DeWitt (VDEA) as well as the “physical” mass-shell momentum subtraction (MMOM) scheme permit the observation of threshold effects of the “running” quantities in grand unification right through the thresholds in a manifestly gauge independent manner. In our present work we establish the coincidence not only between VDEA and MMOM, but also with Weinberg's “effective gauge theory” (EGT) approach, which to one loop order shares the gauge indepencence of VDEA and MMOM. Numerical results are presented for the minimalSU(5) values of the unification mass and of the Weinberg angle in all three schemes. The results of our careful analysis represent an a posteriori justification of previous calculations which were based upon subtraction schemes lacking manifest gauge independence. Moreover, we interpret our results as positive evidence for the physical relevance of the VDEA. We also list the complete one-loop results for massive two-point functions of the gauge bosons in the Landau-DeWitt gauge, to which the VDEA boils down in Yang-Mills theories.     

Cosmological constant from gauge fields on extra dimensions

We present a new model of dark energy which could explain the observed accelerated expansion of our Universe. We show that a five-dimensional Einstein–Yang–Mills theory defined in a flat Friedmann–Robertson–Walker universe compactified on a circle possesses degenerate vacua in four dimensions. The present Universe could be trapped in one of these degenerate vacua. With the natural requirement that the size of the extra dimension could be of the GUT scale or smaller, the energy density difference between the degenerate vacua and the true ground state can provide us with just the right amount of dark energy to account for the observed expansion rate of our Universe.     

Gauge coupling unification with extra dimensions and correction due to higher dimensional operators

We study the gauge coupling unification with extra dimensions. We take into account corrections due to the higher dimensional operators. We show the prediction of ₃(M_Z) is sensitive to such corrections, even if cΦ/M=O(0.01). We also discuss the b−τ Yukawa unification.     

Searching for family-number conserving neutral gauge bosons from extra dimensions

Previous studies have shown how the three generations of the Standard Model fermions can arise from a single generation in more than four dimensions and how off-diagonal neutral couplings arise for gauge-boson Kaluza-Klein recurrences. These couplings conserve family number in the leading approximation. While an existing example, built on a spherical geometry, suggests a high compactification scale, we conjecture that the overall structure is generic and work out possible signatures at colliders compatible with rare decays data.     

Grand unification in higher dimensions

We have recently proposed an alternative picture for the physics at the scale of gauge coupling unification, where the unified symmetry is realized in higher dimensions but is broken locally by a symmetry breaking defect. Gauge coupling unification, the quantum numbers of quarks and leptons and the longevity of the proton arise as phenomena of the symmetrical bulk, while the lightness of the Higgs doublets and the masses of the light quarks and leptons probe the symmetry breaking defect. Moreover, the framework is extremely predictive if the effective higher dimensional theory is valid over a large energy interval up to the scale of strong coupling. Precise agreement with experiments is obtained in the simplest theory—SU(5) in five dimensions with two Higgs multiplets propagating in the bulk. The weak mixing angle is predicted to be sin²θ_w=0.2313±0.0004, which fits the data with extraordinary accuracy. The compactification scale and the strong coupling scale are determined to be and , respectively. Proton decay with a lifetime of order is expected with a variety of final states such as e⁺π⁰, and several aspects of flavor, including large neutrino mixing angles, are understood by the geometrical locations of the matter fields. When combined with a particular supersymmetry breaking mechanism, the theory predicts large lepton flavor violating μ→e and τ→μ transitions, with all superpartner masses determined by only two free parameters. The predicted value of the bottom quark mass from Yukawa unification agrees well with the data. This paper is mainly a review of the work presented in hep-ph/0103125, hep-ph/0111068, and hep-ph/0205067 [1], [2] and [3].     

Localizing gravity in extra dimensions

We argue that a certain distribution of matter in higher dimensions can provide the correct behavior of gravity in four dimensions. Some explicit examples illustrating the idea are considered.     

Getting to the top with extra dimensions

The prospect of large extra dimensions and an effective theory of gravity at around a TeV has interesting experimental consequences. In these models, the Kaluza–Klein modes interact with Standard Model particles and these interactions lead to testable predictions at present and planned colliders. We investigate the effect of virtual exchanges of the spin-2 Kaluza–Klein modes in the production cross-section of pairs at the Tevatron and the LHC and find that the cross-section can be an effective probe of the large extra dimensions. This enables us to put bounds on the effective low-energy scale.     

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).     

Reconsidering extra time-like dimensions

In this study we reconsider the phenomenological problems related to tachyonic modes in the context of extra time-like dimensions. First we reconsider a lower bound on the size of extra time-like dimensions and improve on the conclusion in the literature. Next we discuss the issues of spontaneous decay of stable fermions through tachyonic decays and disappearance of fermions due to tachyonic contributions to their self-energies. We find that the tachyonic modes due to extra time-like dimensions are less problematic than the tachyonic modes in the usual 4-dimensional setting because the most troublesome Feynman diagrams are forbidden once the conservation of momentum in the extra time-like dimensions is imposed.     

GIMPs from extra dimensions

We study a scalar field theory in a flat five-dimensional setup, where a scalar field lives in a bulk with a Dirichlet boundary condition, and give an implementation of this setup to the Froggatt–Nielsen (FN) mechanism. It is shown that all couplings of physical field of the scalar with the all brane localized standard model particles are vanishing while realizing the usual FN mechanism. This setup gives the scalar a role as an only Gravitationally Interacting Massive Particle (GIMP), which is a candidate for dark matter.     

On finite lattice corrections to gauge field thermodynamics

We consider the ideal gas limit of lattice Yang-Mills with fermions. Recently, such a system has been considered in great detail in the literature. We discuss possible finite lattice corrections to the energy density of the quarks and gluons due to the constraint of the quark-gluon gas being in colour singlet state. In the case of pure Yang-Mills theory at finite temperature, we find that Monte Carlo data agree very well with the asymptotically free gluon gas being a colour singlet. In the presence of quarks, in the quenched approximation, we find that Monte Carlo data seem to agree with a distribution where the quarks themselves form a colour singlet.     

The Higgs in large extra dimensions

Transverse (submillimeter) and longitudinal (TeV) extra dimensions can help in dealing with the Higgs hierarchy problem. On the one hand large transverse dimensions can lower the fundamental scale of quantum gravity from the Planck scale to the TeV range. On the other hand longitudinal dimensions can provide genuine extra-dimensional symmetries (higher dimensional gauge symmetry and/or supersymmetry) to protect the Higgs mass against ultraviolet sensitivity. In this article we review recent developments along these directions. To cite this article: K. Benakli, M. Quirós, C. R. Physique 4 (2003).     

Leading temperature corrections to Fermi-liquid theory in two dimensions

We calculate the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependences of the spin components of the scattering vertex, the Landau function, and the spin susceptibility are found to be linear. T-linear terms in the effective mass and in the "charge-sector" quantities are found to cancel to second order in the interaction, but the cancellation is argued not to be generic. The connection with previous studies of the 2D Fermi-liquid parameters is discussed.     

Merging gauge coupling constants without grand unification

The merging of the running coupling constants of the weak, strong, and electromagnetic fields does not require the unification of these gauge fields at high energy. It can, in fact, be the property of a general fermionic system in which gauge bosons are not fundamental.