Herman J. Munczek

Gauge covariant fermion propagator in quenched, chirally symmetric quantum electrodynamics

Abstract We discuss the chirally symmetric solution of the massless, quenched, Dyson-Schwinger equation for the fermion propagator in three and four dimensions. The solutions are manifestly gauge covariant. We consider a gauge covariance constraint on the fermion-gauge-boson vertex, which motivates a vertex Ansatz that both satisfies the Ward identity when the fermion self-mass is zero and ensures gauge covariance of the fermion propagator.

Infrared effects on the axial gauge quark propagator

Abstract The axial gauge quark propagator is studied when only the most singular infrared part of the gluon propagator is retained in the Dyson-Schwinger equation. With a new representation for the quark-gluon vertex a simple configuration space propagator and a momentum space form valid for all values of the gauge variable n · p are obtained. The propagator has no poles. The effective potential is minimized when there is no chiral symmetry breaking.

qq̄ bound states in the Bethe‐Salpeter formalism

We review a relativistic and chirally symmetric framework used recently to calculate the spectrum of pseudoscalar, vector, and scalar meson bound states for light as well as heavy quarks. We outline a more systematic procedure for this calculation by introducing a well defined truncation of the infinite set of integral equations needed for a fully self‐consistent solution of all the propagators, vertices, and kernels.

Phenomenology of dynamical symmetry breaking in QCD

A consistent treatment of the QCD quark propagator and quark-antiquark bound state equations is presented which follows the Nambu and Jona-Lasinio approach to the discussion of chiral symmetry breaking. An expression is obtained for the dynamical, momentum dependent, mass. In the approximation used here the dynamical mass is determined byM0, its value at zero momentum, and by the strong coupling constant αs and bare quark massm0. In the limiting case of no explicit chiral symmetry breaking. i.e.,m0=0, this expression coincides in form with the one obtained by Chang and Chang in their renormalization-group analysis. In this limit chiral symmetry remains broken and we show the explicit appearance of a Nambu-Goldstone pion. A consistent calculation of the pseudoscalar, scalar and vector meson masses gives values ofm0, αs andM0 well in step with other estimates. This makes possible a calculation offπ, the pion decay constant, in reasonable agreement with experiment.

On the validity of approximations for the calculation of the pion decay constant

Abstract We examine the accuracy of the Pagels-Stokar formula for the calculation of the pion decay constant fπ in comparison to the more elaborate treatment involving the solution of the ladder Bethe-Salpeter equation. By using the gluon propagator model of K.-I. Aoki, M. Bando, T. Kugo, M.G. Mitchard and H. Nakatani we find that the Pagels-Stokar formula overestimates the pion decay constant by two to three times. This result is in agreement with our previous conclusions regarding other phenomenologically reasonable models of the gluon propagator. We argue that in their study of the calculation of the pion decay constant, Aoki et al. arrive at a positive conclusion concerning the validity of the Pagels-Stokar formula because of their use of approximated solutions to the ladder Schwinger-Dyson and Bethe-Salpeter equations and their incorrect assumption that these approximate solutions respect the axial Ward identify.

Scalars and Pseudoscalars in Non-linear Chiral Dynamics Based on QCD

The 1/N expansion of quantum chromodynamics (QCD) has recently been advocated as a guide to the construction of the effective, hadronic chiral-Lagrangian, including the consequences of the U (1) axial anomaly [1– 4]. We extend the standard non-linear chiral Lagrangian approach and include non-linearly transforming scalar fields In addition to the usuπal pseudoscalars. We thereby obtain a low-energy effective Lagrangian which incorporates both the usual PCAC and U (1) anomaly constraints and the new (for non-linear lagrangians) SU(3) breaking effects due to the scalar field vacuum expectation values. FK/Fπ ≠ 1 follows naturally in our approach, for example.

Generalized gauge for the weak interaction and the. delta. I = 1/2 rule. [Sp(4)XU(1) group, current-current interaction, heavy leptons, triangle aromalie cancellation]

We show that the local gauge group Sp(4) x U(1) can be adopted to obtain the standard results for the effective lowest-order weak interaction but with a ..delta..I = 1/2 nonleptonic current-current interaction. Some other features of our model are the presence of heavy leptons, the cancellation of triangle anomalies between leptons and quarks if the latter carry charm and color, and, at least in one version, the presence of two extra quarks with the same charge as u and c. (AIP)