Composite photon and W^\pm, Z^0 vector bosons from a top-condensation model at fixed v = 247 GeV

Starting from the historical Fermi four-fermion low-energy effective electroweak interactions Lagrangian for the third generation of quarks, augmented by an NJL type interaction responsible for dynamical symmetry breaking and heavy quark mass generation, and fixing the scalar (Higgs) field v.e.v. at v = 247 GeV, we show that: (1) heavy quark bound states Q\bar Q with quantum numbers of the W^\pm bosons exist for arbitrarily weak (positive) vector coupling G_F, so long as the quark mass is sufficiently large; (2) a massive composite neutral vector boson (Z^0) appears; (3) a massless composite parity-conserving neutral vector boson (\gamma) appears, the composite Higgs-Kibble ghosts decouple from the quarks and other particles, the longitudinal components of the vector boson propagators vanish, as G_F \to G_F^expt = 1/(\sqrt2 v^2), which also implies that the cutoff \Lambda \to \infty. Thus, the Fermi interaction model is equivalent to a locally gauge invariant theory but with definite values of coupling constants and masses. The model discussed here was chosen for illustrative purposes and is not equivalent to the Standard Model.Comment: 9 pages, 1 eps figur

Bound state in the vector channel of the extended Nambu--Jona-Lasinio model at fixed f_\pi

We show that, as a consequence of fixing f_\pi = 93 MeV: (1) a bound state pole in the J^P = 1^- scattering amplitude of the ENJL model exists for arbitrarily weak (positive) vector coupling G_2 so long as the constituent quark mass is sufficiently large; (2) there is a bound state for any quark mass when G_2 \geq 0.6/(8 f_\pi^2); (3) this bound state becomes massless at G_2 = 1/(8 f_\pi^2) and a tachyon for G_2 exceeding it. We show by way of an example that the model has no trouble fitting the \rho meson mass simultaneously with other observables.Comment: 9 pages, 2 (eps) figures, to appear in PL

U_A(1) symmetry breaking, scalar mesons and the nucleon spin problem in an effective chiral field theory

We establish a relationship between the scalar meson spectrum and the $U_A (1)$ symmetry-breaking 't Hooft interaction on one hand and the constituent quark's flavor-singlet axial coupling constant $g_{A, Q}^{(0)}$ on the other, using an effective chiral quark field theory. This analysis leads to the new sum rule $g_{A, Q}^{(0)}[m_{\eta '}^{2} + m_{\eta}^{2} - 2 m_{K}^{2} ]\simeq - m_{f_{0}^{'}}^{2} - m_{f_{0}}^{2} + 2 m_{K_{0}^{*}}^{2}$, where $\eta^{'}, \eta, K$ are the observed pseudoscalar mesons, $K_{0}^{*}$ is the strange scalar meson at 1430 MeV and $f_{0}, f_{0}^{'}$ are "the eighth and the ninth" scalar mesons. We discuss the relationship between the constituent quark flavor-singlet axial coupling constant $g_{A, Q}^{(0)}$ and the nucleon one $g_{A, N}^{(0)}$ (``nucleon's spin content'') in this effective field theory. We also relate $g_{A, Q}^{(0)}$, as well as the flavour-octet constituent quark axial coupling constant $g_{A, Q}^{(1)}$ to vector and axial-vector meson masses in general as well as in the tight-binding limit.Comment: 16 pages, 3 figures, RevTex, to appear in Nucl.Phys.

A Comment on General Formulae for Polarization Observables in Deuteron Electrodisintegration and Linear Relations

We establish a simple, explicit relation between the formalisms employed in the treatments of polarization observables in deuteron two-body electrodisintegration published by Arenh\"ovel, Leidemann, and Tomusiak in Few-Body Systems {\bf 15}, 109 (1993) and the results of the present authors published in Phys.~Rev.~C {\bf 40}, 2479 (1989). We comment on the overlap between the two sets of results.Comment: 9 pages, no figure

Reply to Comment on "Hara's theorem in the constituent quark model"

In the preceding Comment it is alleged that a "hidden loophole" in the proof of Hara's theorem has been found, which purportedly invalidates the conclusions of the paper commented upon. I show that there is no such loophole in the constituent quark model, and that the "counterexample" presented in the Comment is not gauge invariant.Comment: 5 pages, reply to lanl e-print hep-ph/970923

Linear Sigma model in the Gaussian wave functional approximation II: Analyticity of the S-matrix and the effective potential/action

We show an explicit connection between the solution to the equations of motion in the Gaussian functional approximation and the minimum of the (Gaussian) effective potential/action of the linear $\Sigma$ model, as well as with the N/D method in dispersion theory. The resulting equations contain analytic functions with branch cuts in the complex mass squared plane. Therefore the minimum of the effective action may lie in the complex mass squared plane. Many solutions to these equations can be found on the second, third, etc. Riemann sheets of the equation, though their physical interpretation is not clear. Our results and the established properties of the S-matrix in general, and of the N/D solutions in particular, guide us to the correct choice of the Riemann sheet. We count the number of states and find only one in each spin-parity and isospin channel with quantum numbers corresponding to the fields in the Lagrangian, i.e. to Castillejo-Dalitz-Dyson (CDD) poles. We examine the numerical solutions in both the strong and weak coupling regimes and calculate the Kallen-Lehmann spectral densities and then use them for physical interpretation.Comment: 14 pages, 4 ps figures, to appear in Nucl. Phy

Goldstone Theorem in the Gaussian Functional Approximation to the Scalar ϕ4\phi^{4} Theory

We verify the Goldstone theorem in the Gaussian functional approximation to the $\phi^{4}$ theory with internal O(2) symmetry. We do so by reformulating the Gaussian approximation in terms of Schwinger-Dyson equations from which an explicit demonstration of the Goldstone theorem follows directly.Comment: 11 page