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

Application of thermodynamics to driven systems

Application of thermodynamics to driven systems is discussed. As particular examples, simple traffic flow models are considered. On a microscopic level, traffic flow is described by Bando's optimal velocity model in terms of accelerating and decelerating forces. It allows to introduce kinetic, potential, as well as total energy, which is the internal energy of the car system in view of thermodynamics. The latter is not conserved, although it has certain value in any of two possible stationary states corresponding either to fixed point or to limit cycle in the space of headways and velocities. On a mesoscopic level of description, the size n of car cluster is considered as a stochastic variable in master equation. Here n=0 corresponds to the fixed-point solution of the microscopic model, whereas the limit cycle is represented by coexistence of a car cluster with n>0 and free flow phase. The detailed balance holds in a stationary state just like in equilibrium liquid-gas system. It allows to define free energy of the car system and chemical potentials of the coexisting phases, as well as a relaxation to a local or global free energy minimum. In this sense the behaviour of traffic flow can be described by equilibrium thermodynamics. We find, however, that the chemical potential of the cluster phase of traffic flow depends on an outer parameter - the density of cars in the free-flow phase. It allows to distinguish between the traffic flow as a driven system and purely equilibrium systems.Comment: 9 pages, 6 figures. Eur. Phys. J. B (2007) to be publishe

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

Chiral SU(3) dynamics and Λ\Lambda-hyperons in the nuclear medium

We present a novel approach to the density dependent mean field and the spin-orbit interaction of a $\Lambda$-hyperon in a nuclear many-body system, based on flavor-SU(3) in-medium chiral perturbation theory. The leading long-range $\Lambda N$-interaction arises from kaon exchange and from two-pion exchange with a $\Sigma$-hyperon in the intermediate state. The empirical $\Lambda$-nucleus potential depth of about $-28$MeV is well reproduced with a single cutoff scale, $\bar \Lambda = 0.7$GeV, effectively representing all short-distance (high-momentum) dynamics not resolved at scales characteristic of the nuclear Fermi momentum. This value of $\bar\Lambda$ is remarkably consistent with the one required to reproduce the empirical saturation point of isospin-symmetric nuclear matter in the same framework. The smallness of the $\Lambda$-nuclear spin-orbit interaction finds a natural (yet novel) explanation in terms of an almost complete cancellation between short-range contributions (properly rescaled from the known nucleonic spin-orbit coupling strength) and long-range terms generated by iterated one-pion exchange with intermediate $\Sigma$-hyperons. The small $\Sigma\Lambda$-mass difference figures prominently in this context.Comment: 9 pages, 4figure

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

The Pion Decay Constants and the Rho-Meson Mass at Finite Temperature in the Hidden Local Symmetry

We study the temperature dependence of the pion decay constant and rho-meson mass in the hidden local symmetry model at one loop. Using the standard imaginary time formalism, we include the thermal effect of rho meson as well as that of pion. We show that the pion gives a dominant contribution to the pion decay constant and rho-meson contribution slightly decreases the critical temperature. The rho-meson pole mass increases as T^4/m_\rho^2 at low temperature dominated by the pion-loop effect. At high temperature, although the pion-loop effect decreases the rho-meson mass, the rho-loop contribution overcomes the pion-loop contribution and rho-meson mass increases with temperature. We also show that the conventional parameter a is stable as the temperature increases.Comment: We added a comment on the correction to the rho-meson mass from the omega-pi loop. This is the final version to be published in Phys. Rev. D. 19 pages (LaTeX-RevTeX), 7 PostScript figure

Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur

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