Complete set of electromagnetic corrections to the nucleon mass in the Nambu-Jona-Lasinio model

We show how to derive the complete set of electromagnetic corrections to the Nambu-Jona-Lasinio (NJL) model of the nucleon. Our results enable an accurate estimate of the electromagnetic contribution to the neutron-proton mass difference within this model. At the same time, our procedure demonstrates the way to calculate the complete set of meson corrections to the NJL model that maintains chiral symmetry.Comment: Contribution to Proceedings, KEK-Tanashi International Symposium on Physics of Hadrons and Nuclei, 14-17 December 1998, Tokyo, Japan, to be published in Nuclear Physics A. 5 pages, revtex, epsf, 2 postscript figures. Minor addition to last figure, typos correcte

Generalized parton distributions for dynamical equation models

We show how generalized parton distributions (GPDs) can be determined in the case where hadrons are described in terms of their partonic degrees of freedom through solutions of dynamical equations. We demonstrate our approach on the example of two-quark bound states described by the Bethe-Salpeter equation, and three-quark bound states described by three- and four-dimensional Faddeev-like equations. Within the model of strong interactions defined by the dynamical equations, all possible mechanisms contributing to the GPDs are taken into account, and all GPD sum rules are satisfied automatically. The formulation is general and can be applied to determine generalized quark distributions, generalized gluon distributions, transition GPDs, nucleon distributions in nuclei, etc. Our approach is based on the gauging of equations method.Comment: 23 pages, 9 figures, revtex4, feynm

Covariant three-body equations in phi^3 field theory

We derive four-dimensional relativistic three-body equations for the case of a field theory with a three-point interaction vertex. These equations describe the coupled 2->2, 2->3, and 3->3 processes, and provide the means of calculating the kernel of the 2->2 Bethe-Salpeter equation. Our equations differ from all previous formulations in two essential ways. Firstly, we have overcome the overcounting problems inherent in earlier works. Secondly, we have retained all possible two-body forces when one particle is a spectator. In this respect, we show how it is necessary to also retain certain three-body forces as these can give rise to (previously overlooked) two-body forces when used in a 2->3 process. The revealing of such hidden two-body forces gives rise to a further novel feature of our equations, namely, to the appearance of a number of subtraction terms. In the case of the piNN system, for example, the NN potential involves a subtraction term where two pions, exchanged between the nucleons, interact with each other through the pi-pi t-matrix. The necessity of an input pi-pi interaction is surprising and contrasts markedly with the corresponding three-dimensional description of the piNN system where no such interaction explicitly appears. This illustrates the somewhat unexpected result that the four-dimensional equations differ from the three-dimensional ones even at the operator level.Comment: 33, FIAS-R-22

Gauge invariant reduction to the light-front

The problem of constructing gauge invariant currents in terms of light-cone bound-state wave functions is solved by utilising the gauging of equations method. In particular, it is shown how to construct perturbative expansions of the electromagnetic current in the light-cone formalism, such that current conservation is satisfied at each order of the perturbation theory.Comment: 12 pages, revtex

Comment on "Nucleon form factors and a nonpointlike diquark"

Authors of Phys. Rev. C 60, 062201 (1999) presented a calculation of the electromagnetic form factors of the nucleon using a diquark ansatz in the relativistic three-quark Faddeev equations. In this Comment it is pointed out that the calculations of these form factors stem from a three-quark bound state current that contains overcounted contributions. The corrected expression for the three-quark bound state current is derived.Comment: 6 pages, 1 figure, revtex, eps

Implementing PCAC in Nonperturbative Models of Pion Production

Traditional few-body descriptions of pion production use integral equations to sum the strong interactions nonperturbatively. Although much physics is thereby included, there has not been a practical way of incorporating the constraints of chiral symmetry into such approaches. Thus the traditional few-body descriptions fail to reflect the underlying theory of strong interactions, QCD, which is largely chirally symmetric. In addition, the lack of chiral symmetry in the few-body approaches means that their predictions of pion production are in principle not consistent with the partial conservation of axial current (PCAC), a fact that has especially large consequences at low energies. We discuss how the recent introduction of the ``gauging of equations method'' can be used to include PCAC into traditional few-body descriptions and thereby solve this long standing problemComment: Contribution to Proceedings, 1st Asia-Pacific Conference on Few-Body Problems in Physics, Noda/Kashiwa, Japan, 23-28 August 1999, to be published by Springer-Verlag as "Few-Body Systems Supplement". 7 pages, revtex, epsf, 3 Postscript figure

In-matter three-body problem

We formulate three-dimensional equations for the finite temperature in-matter three-body problem. Our approach takes into account the full infinite series for the effective pair-interaction kernel, so that all possible two-body sub-processes allowed by the underlying Hamiltonian are retained.Comment: 5 pages, contribution to The 16th National Congress 2005 - Australian Institute of Physic