Mass Matrices in E6 Unification

We study a supersymmetric E6 grand unified model in which the SU(5) 5^* components are twisted in the third generation 27. Supplementing the adjoint Higgs field to a model analyzed previously, we calculate the mass matrices for the up and down quarks and charged leptons. Although the number of free parameters is less than that of observables, an overall fitting to the observed masses and mixing angles is shown to be possible. Most notably, we find two novel, parameter-independent relations between the lepton 2-3 mixing angle and the quark masses and CKM mixing angles that are in good agreement with the large lepton mixing recently observed.Comment: 33 pages, 5 figures, typos correcte

Fate of Vector Dominance in the Effective Field Theory

We reveal the full phase structure of the effective field theory for QCD, based on the hidden local symmetry (HLS) through the one-loop renormalization group equation including quadratic divergences. We then show that vector dominance (VD) is not a sacred discipline of the effective field theory but rather an accidental phenomenon peculiar to three-flavored QCD. In particular, the chiral symmetry restoration in HLS model takes place in a wide phase boundary surface, on which the VD is realized nowhere. This suggests that VD may not be valid for chiral symmetry restoration in hot and/or dense QCD.Comment: 4 pages, 3 figures. One reference added. Minor modification to shorten the manuscript. This is the version to appear in Physical Review Letter

Proving the Low Energy Theorem of Hidden Local Symmetry

Based on the Ward-Takahashi identity for the BRS symmetry, we prove to all orders of the loop expansion the low energy theorem of hidden local symmetry for the vector mesons (KSRF (I) relation) in the $U(N)_{\rm L}$ $\times$ $U(N)_{\rm R}$ / $U(N)_{\rm V}$ nonlinear chiral Lagrangian.Comment: 12 pages, LaTeX, DPNU-93-01/KUNS-117

Exact shock solution of a coupled system of delay differential equations: a car-following model

In this paper, we present exact shock solutions of a coupled system of delay differential equations, which was introduced as a traffic-flow model called {\it the car-following model}. We use the Hirota method, originally developed in order to solve soliton equations. %While, with a periodic boundary condition, this system has % a traveling-wave solution given by elliptic functions. The relevant delay differential equations have been known to allow exact solutions expressed by elliptic functions with a periodic boundary conditions. In the present work, however, shock solutions are obtained with open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure

Dynamical Gauge Boson and Strong-Weak Reciprocity

It is proposed that asymptotically nonfree gauge theories are consistently interpreted as theories of composite gauge bosons. It is argued that when hidden local symmetry is introduced, masslessness and coupling universality of dynamically generated gauge boson are ensured. To illustrate these ideas we take a four dimensional Grassmannian sigma model as an example and show that the model should be regarded as a cut-off theory and there is a critical coupling at which the hidden local symmetry is restored. Propagator and vertex functions of the gauge field are calculated explicitly and existence of the massless pole is shown. The beta function determined from the $Z$ factor of the dynamically generated gauge boson coincides with that of an asymptotic nonfree elementary gauge theory. Using these theoretical machinery we construct a model in which asymptotic free and nonfree gauge bosons coexist and their running couplings are related by the reciprocally proportional relation.Comment: 19 pages, latex, 6 eps figures, a numbers of corrections are made in the tex

Solvable Optimal Velocity Models and Asymptotic Trajectory

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic trajectory'' to determine $T$ and $v_B$ (the backward velocity of the pattern), the global parameters associated with vehicles' collective motion in a congested flow, in terms of parameters such as the sensitivity $a$, which appeared in the original coupled equations.Comment: 25 pages, 15 eps figures, LaTe

Hypercharge and baryon minus lepton number in E6

We study assignments of the hypercharge and baryon minus lepton number for particles in the $E_6$ grand unification model. It is shown that there are three assignments of hypercharge and three assignments of baryon minus lepton number which are consistent with the Standard Model. Their explicit expressions and detailed properties are given. In particular, we show that the $U(1)_{B-L}$ symmetry in $E_6$ cannot be orthogonal to the $SU(3)_R$ symmetry. Based on these investigations, we propose an alternative SU(5) grand unification model.Comment: 16 pages, JHEP3.cls, To appear in JHE

Gauge Coupling Unification in GUT with Anomalous U(1) Symmetry

We show that in the framework of grand unified theory (GUT) with anomalous $U(1)_A$ gauge symmetry, the success of the gauge coupling unification in the minimal SU(5) GUT is naturally explained, even if the mass spectrum of superheavy fields does not respect SU(5) symmetry. Because the unification scale for most realizations of the theory becomes smaller than the usual GUT scale, it suggests that the present level of experiments is close to that sufficient to observe proton decay via dimension 6 operators, $p\to e+\pi$.Comment: 4 pages, RevTeX, to appear in Phys.Rev.Let