Grand Unification Equation

Physical Review D, 2002

We consider the scenario where all the couplings in the theory are strong at the cutoff scale, in the context of higher dimensional grand unified field theories where the unified gauge symmetry is broken by an orbifold compactification. In this scenario, the noncalculable correction to gauge unification from unknown ultraviolet physics is naturally suppressed by the large volume of the extra dimension, and the threshold correction is dominated by calculable contribution from Kaluza-Klein towers that gives the values for sin 2 θ w and α s in good agreement with low-energy data. The threshold correction is reliably estimated despite that the theory is strongly coupled at the cutoff scale. A 5d SU (5) model is presented as an example, where rapid d = 6 proton decay is avoided by putting the first generation matters in the 5d bulk.

Running coupling constants both of QED and QCD are studied in a heuristic way. We estimate two branches of the running coupling of the QCD, the first going from low to moderate energies, and the second running at high energies. The intercept of the high energy branch of QCD with the high energy curve of the QED-coupling is used, as a means to estimate the Grand Unification Theory (GUT) scale.

Physical Review D, 1993

We study the possibility of achieving low unification scale in a grand unification scheme based on the gauge group SU(16). Baryon number symmetry being an explicit local gauge symmetry here gauge boson mediated proton decay is absent. We present in detail a number of symmetry breaking patterns and the higgs field representations giving rise to the desired symmetry breakings and identify one chain giving low energy unification. These higgs field representations are constructed in such a way that higgs mediated proton decay is absent. At the end we indicate the very rich low energy physics obtainable from this model which includes quark-lepton un-unified symmetry and chiral color symmetry. In brief some phenomenological implications are also studied.

Physics Letters B, 1997

We investigate the possibility that unification occurs at strong coupling. We show that, despite the fact the couplings pass through a strong coupling regime, accurate predictions for their low energy values are possible because the couplings of the theory flow to infrared fixed points. We determine the low-energy QCD coupling in a favoured class of strong coupling models and find it is reduced from the weak coupling predictions, lying close to the experimentally measured value. We extend the analysis to the determination of quark and lepton masses and show that (even without Grand Unification) the infra-red fixed point structure may lead to good predictions for the top mass, the bottom to tau mass ratio and tan β. Finally we discuss the implications for the unification scale finding it to be increased from the MSSM value and closer to the heterotic string prediction.

Annals of Physics, 2003

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 sin 2 θ w = 0.2313± 0.0004, which fits the data with extraordinary accuracy. The compactification scale and the strong coupling scale are determined to be M c 5 × 10 14 GeV and M s 1 × 10 17 GeV, respectively. Proton decay with a lifetime of order 10 34 years is expected with a variety of final states such as e + π 0 , 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, 3].

1982

1997

Quantum cosmology may restrict the class of gauge models which unify electroweak and strong interactions. In particular, if one studies the normalizability criterion for the one-loop wave function of the universe in a de Sitter background one finds that the interaction of inflaton and matter fields, jointly with the request of normalizability at one-loop order, picks out non-supersymmetric versions of unified gauge models.

Modern Physics Letters A, 1993

We consider an alternative to conventional grand unified theories originally proposed by Maiani, Parisi and Petronzio, where owing to the existence of extra fermion generations at some intermediate scale, the gauge couplings become large at high energies. We first comment on how the non-supersymmetric version of this scenario is ruled out; we then consider the two-loop evolution of couplings in the supersymmetric extension of this scenario, and check whether such a scenario is feasible in the light of the precise values of couplings now available from LEP.

Eprint Arxiv Hep Ph 9411222, 1994

We discuss the basic idea of the Gauge-Yukawa Unification that is based on the principle of the reduction of couplings. This method of unification relies on the search of successful renormalization group invariant relations among couplings, which do not originate from symmetry principles. The predictive power of Grand Unified Theories can be increased by this method, predicting for instance values of the top quark mass consistent with the recent experimental data. The hope is that this unification attempt might shed further light on the origin of the Yukawa sector of the standard model.

viXra, 2014

This fault line which separates nuclear from particle physics is concisely captured by Jaffe and Witten when they state at page 3 of the "Yang-Mills and Mass Gap" problem [12] that: ".. . for QCD to describe the strong force successfully. .. It must have 'quark confinement,' that is, even though the theory is described in terms of elementary fields, such as the quark fields, that transform non-trivially under SU(3), the