24 research outputs found
Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space
The scalar three-body Bethe-Salpeter equation, with zero-range interaction,
is solved in Minkowski space by direct integration of the four-dimensional
integral equation. The singularities appearing in the propagators are treated
properly by standard analytical and numerical methods, without relying on any
ansatz or assumption. The results for the binding energies and transverse
amplitudes are compared with the results computed in Euclidean space. A fair
agreement between the calculations is found.Comment: 10 pages, 2 figures, version accepted for publication in Phys. Lett.
Color-suppression of non-planar diagrams in bosonic bound states
We study the suppression of non-planar diagrams in a scalar QCD model of a
meson system in space-time dimensions due to the inclusion of the color
degrees of freedom. As a prototype of the color-singlet meson, we consider a
flavor-nonsinglet system consisting of a scalar-quark and a scalar-antiquark
with equal masses exchanging a scalar-gluon of a different mass, which is
investigated within the framework of the homogeneous Bethe-Salpeter equation.
The equation is solved by using the Nakanishi representation for the manifestly
covariant bound-state amplitude and its light-front projection. The resulting
non-singular integral equation is solved numerically. The damping of the impact
of the cross-ladder kernel on the binding energies are studied in detail. The
color-suppression of the cross-ladder effects on the light-front wave function
and the elastic electromagnetic form factor are also discussed. As our results
show, the suppression appears significantly large for , which supports
the use of rainbow-ladder truncations in practical nonperturbative calculations
within QCD.Comment: 12 pages, 7 figures. To appear in Physics Letters
Three-body bound states with zero-range interaction in the Bethe-Salpeter approach
The Bethe-Salpeter equation for three bosons with zero-range interaction is
solved for the first time. For comparison the light-front equation is also
solved. The input is the two-body scattering length and the outputs are the
three-body binding energies, Bethe-Salpeter amplitudes and light-front wave
functions. Three different regimes are analyzed: ({\it i}) For weak enough
two-body interaction the three-body system is unbound. ({\it ii}) For stronger
two-body interaction a three-body bound state appears. It provides an
interesting example of a deeply bound Borromean system. ({\it iii}) For even
stronger two-body interaction this state becomes unphysical with a negative
mass squared. However, another physical (excited) state appears, found
previously in light-front calculations. The Bethe-Salpeter approach implicitly
incorporates three-body forces of relativistic origin, which are attractive and
increase the binding energy.Comment: 13 pages, 7 figure
Bound state structure and electromagnetic form factor beyond the ladder approximation
We investigate the response of the bound state structure of a two-boson
system, within a Yukawa model with a scalar boson exchange, to the inclusion of
the cross-ladder contribution to the ladder kernel of the Bethe-Salpeter
equation. The equation is solved by means of the Nakanishi integral
representation and light-front projection. The valence light-front wave
function and the elastic electromagnetic form factor beyond the impulse
approximation, with the inclusion of the two-body current, generated by the
cross-ladder kernel, are computed. The valence wave function and
electromagnetic form factor, considering both ladder and ladder plus
cross-ladder kernels, are studied in detail. Their asymptotic forms are found
to be quite independent of the inclusion of the cross-ladder kernel, for a
given binding energy. The asymptotic decrease of form factor agrees with the
counting rules. This analysis can be generalized to fermionic systems, with a
wide application in the study of the meson structure.Comment: 19 pages, 6 figures, submitted to Phys. Lett.
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Longitudinal interferon-β effects in multiple sclerosis: differential regulation of IL-10 and IL-17A, while no sustained effects on IFN-γ, IL