9 research outputs found
Confinement and the analytic structure of the one body propagator in Scalar QED
We investigate the behavior of the one body propagator in SQED. The self
energy is calculated using three different methods: i) the simple bubble
summation, ii) the Dyson-Schwinger equation, and iii) the Feynman-Schwinger
represantation. The Feynman-Schwinger representation allows an {\em exact}
analytical result. It is shown that, while the exact result produces a real
mass pole for all couplings, the bubble sum and the Dyson-Schwinger approach in
rainbow approximation leads to complex mass poles beyond a certain critical
coupling. The model exhibits confinement, yet the exact solution still has one
body propagators with {\it real} mass poles.Comment: 5 pages 2 figures, accepted for publication in Phys. Rev.
Multipole analysis of spin observables in vector meson photoproduction
A multipole analysis of vector meson photoproduction is formulated as a
generalization of the pseudoscalar meson case. Expansion of spin observables in
the multipole basis and behavior of these observables near threshold and
resonances are examined.Comment: 15 pages, latex, 2 figure
Feynman-Schwinger representation approach to nonperturbative physics
The Feynman-Schwinger representation provides a convenient framework for the
cal culation of nonperturbative propagators. In this paper we first investigate
an analytically solvable case, namely the scalar QED in 0+1 dimension. With
this toy model we illustrate how the formalism works. The analytic result for
the self energy is compared with the perturbative result. Next, using a
interaction, we discuss the regularization of various divergences
encountered in this formalism. The ultraviolet divergence, which is common in
standard perturbative field theory applications, is removed by using a
Pauli-Villars regularization. We show that the divergence associated with large
values of Feynman-Schwinger parameter is spurious and it can be avoided by
using an imaginary Feynman parameter .Comment: 26 pages, 9 figures, minor correctio
QCD Evolution Equations: Numerical Algorithms from the Laguerre Expansion
A complete numerical implementation, in both singlet and non-singlet sectors,
of a very elegant method to solve the QCD Evolution equations, due to Furmanski
and Petronzio, is presented. The algorithm is directly implemented in x-space
by a Laguerre expansion of the parton distributions. All the leading-twist
distributions are evolved: longitudinally polarized, transversely polarized and
unpolarized, to NLO accuracy. The expansion is optimal at finite x, up to
reasonably small x-values (), below which the convergence of
the expansion slows down. The polarized evolution is smoother, due to the less
singular structure of the anomalous dimensions at small-x. In the region of
fast convergence, which covers most of the usual perturbative applications,
high numerical accuracy is achieved by expanding over a set of approximately 30
polynomials, with a very modest running time.Comment: 30 pages, 13 figure
Quark-Antiquark Bound States within a Dyson-Schwinger Bethe-Salpeter Formalism
Pion and kaon observables are calculated using a Dyson-Schwinger
Bethe-Salpeter formalism. It is shown that an infrared finite gluon propagator
can lead to quark confinement via generation of complex mass poles in quark
propagators. Observables, including electromagnetic form factors, are
calculated entirely in Euclidean metric for spacelike values of bound state
momentum and final results are extrapolated to the physical region.Comment: Minor typographical corrections. Accepted for publication in Nucl.
Phys.
Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction
A path-integral approach for delta-function potentials is presented.
Particular attention is paid to the two-dimensional case, which illustrates the
realization of a quantum anomaly for a scale invariant problem in quantum
mechanics. Our treatment is based on an infinite summation of perturbation
theory that captures the nonperturbative nature of the delta-function bound
state. The well-known singular character of the two-dimensional delta-function
potential is dealt with by considering the renormalized path integral resulting
from a variety of schemes: dimensional, momentum-cutoff, and real-space
regularization. Moreover, compatibility of the bound-state and scattering
sectors is shown.Comment: 26 pages. The paper was significantly expanded and numerous equations
were added for the sake of clarity; the main results and conclusions are
unchange
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