36 research outputs found
The Spin Structure of the qq Interaction and the Mass Spectra of Bound q\bar q Systems: Different Versions of the 3-Dimensional Reductions of the Bethe-Salpeter Equation
Bound q\bar q -systems are considered in the framework of three different
versions of the 3-dimensional reduction of the Bethe-Salpeter equation, all
having the correct one-body limit when one of the constituent quark masses
tends to infinity, and in the framework of the Salpeter equation. The spin
structure of confining qq interaction potential is taken in the form
x\gamma_{1}^{0}\gamma_{2}^{0}+(1-x)I_{1}I_{2}, with 0 \leq x \leq 1. The
problem of existence (nonexistence) of stable solutions of 3-dimensional
relativistic equations for bound q\bar q systems is studied for different
values of x from this interval. Some other aspects of this problem are
discussed.Comment: 10 pages, LaTeX-file (article.sty
Bound q\bar q Systems in the Framework of the Different Versions of the 3-Dimensional Reductions of the Bethe-Salpeter Equation
Bound q\bar q systems are studied in the framework of different 3-dimensional
relativistic equations derived from the Bethe-Salpeter equation with the
instantaneous kernel in the momentum space. Except the Salpeter equation, all
these equations have a correct one-body limit when one of the constituent quark
masses tends to infinity. The spin structure of the confining qq interaction
potential is taken in the form ,
with . At first stage, the one-gluon-exchange potential is
neglected and the confining potential is taken in the oscillator form. For the
systems (u\bar s), (c\bar u), (c\bar s) and (u\bar u), (s\bar s) a comparative
qualitative analysis of these equations is carried out for different values of
the mixing parameter x and the confining potential strength parameter. We
investigate: 1)the existence/nonexistence of stable solutions of these
equations; 2) the parameter dependence of the general structure of the meson
mass spectum and leptonic decay constants of pseudoscalar and vector mesons. It
is demonstrated that none of the 3-dimensional equations considered in the
present paper does simultaneously describe even general qualitative features of
the whole mass spectrum of q\bar q systems. At the same time, these versions
give an acceptable description of the meson leptonic decay characteristics.Comment: 22 pages, 5 postscript figures, LaTeX-file (revtex.sty
Stability in the instantaneous Bethe-Salpeter formalism: harmonic-oscillator reduced Salpeter equation
A popular three-dimensional reduction of the Bethe-Salpeter formalism for the
description of bound states in quantum field theory is the Salpeter equation,
derived by assuming both instantaneous interactions and free propagation of all
bound-state constituents. Numerical (variational) studies of the Salpeter
equation with confining interaction, however, observed specific instabilities
of the solutions, likely related to the Klein paradox and rendering (part of
the) bound states unstable. An analytic investigation of this problem by a
comprehensive spectral analysis is feasible for the reduced Salpeter equation
with only harmonic-oscillator confining interactions. There we are able to
prove rigorously that the bound-state solutions correspond to real discrete
energy spectra bounded from below and are thus free of any instabilities.Comment: 23 pages, 3 figures, extended conclusions, version to appear in Phys.
Rev.
Elastic Pion Scattering on the Deuteron in a Multiple Scattering Model
Pion elastic scattering on deuterium is studied in the KMT multiple
scattering approach developed in momentum space. Using a Paris wave function
and the same methods and approximations as commonly used in pion scattering on
heavier nuclei excellent agreement with differential cross section data is
obtained for a wide range of pion energies. Only for MeV and very
backward angles, discrepancies appear that are reminiscent of disagreements in
pion scattering on He, H, and He. At low energies the second order
corrections have been included. Polarization observables are studied in detail.
While tensor analyzing powers are well reproduced, vector analyzing powers
exhibit dramatic discrepancies.Comment: 25 pages LATEX and 9 postscript figures in a self-extracting uufile
archiv
Pion interaction with the trinucleon up to the eta production threshold
Pion elastic, charge exchange scattering and induced eta production on the
trinucleon systems are investigated in a coupled-channels approach in momentum
space with Fadeev wave functions. The channel is
included using an isobar model with S-, P-, and D-wave resonances. While the
coherent reactions like He(He can be reasonably well reproduced
up to =500 MeV, large discrepancies appear for the incoherent
processes, He(H and He(H at backward
angles and energies above -resonance. In the forward direction the
calculations underestimate the experimental measurements very
close to threshold but agreement with the data improves with increasing pion
energy. Predictions are made for the asymmetries of the various reactions on
polarized He.Comment: 40 pages, 12 figures (available from the authors), Mainz preprint
MKPH-T-92-1