6 research outputs found
Unitarity and the Bethe-Salpeter Equation
We investigate the relation between different three-dimensional reductions of
the Bethe-Salpeter equation and the analytic structure of the resultant
amplitudes in the energy plane. This correlation is studied for both the
interaction Lagrangian and the system with -, -,
and -channel pole diagrams as driving terms. We observe that the equal-time
equation, which includes some of the three-body unitarity cuts, gives the best
agreement with the Bethe-Salpeter result. This is followed by other 3-D
approximations that have less of the analytic structure.Comment: 17 pages, 8 figures; RevTeX. Version accepted for publication in
Phys. Rev.
Relativistic Quantum Mechanics - Particle Production and Cluster Properties
This paper constructs relativistic quantum mechanical models of particles
satisfying cluster properties and the spectral condition which do not conserve
particle number. The treatment of particle production is limited to systems
with a bounded number of bare-particle degrees of freedom. The focus of this
paper is about the realization of cluster properties in these theories.Comment: 36 pages, Late
Solution of the Bethe-Salpeter equation for pion-nucleon scattering
A relativistic description of pion-nucleon scattering based on the
four-dimensional Bethe-Salpeter equation is presented. The kernel of the
equation consists of s- and u-channel nucleon and delta pole diagrams, as well
as rho and sigma exchange in the t-channel. The Bethe-Salpeter equation is
solved by means of a Wick rotation, and good fits are obtained to the s- and
p-wave phase shifts up to 360 MeV pion laboratory energy. The coupling
constants determined by the fits are consistent with the commonly accepted
values in the literature.Comment: 34 pages, RevTeX; 7 figures. Several references added, a few typos
corrected. Accepted for publication in Physical Review
What is the structure of the Roper resonance?
We investigate the structure of the nucleon resonance N^*(1440) (Roper)
within a coupled-channel meson exchange model for pion-nucleon scattering. The
coupling to pipiN states is realized effectively by the coupling to the sigmaN,
piDelta and rhoN channels. The interaction within and between these channels is
derived from an effective Lagrangian based on a chirally symmetric Lagrangian,
which is supplemented by well known terms for the coupling of the Delta isobar,
the omega meson and the 'sigma', which is the name given here to the strong
correlation of two pions in the scalar-isoscalar channel. In this model the
Roper resonance can be described by meson-baryon dynamics alone; no genuine
N^*(1440) (3 quark) resonance is needed in order to fit piN phase shifts and
inelasticities.Comment: 55 pages, 14 figure