2,542 research outputs found
On The Ladder Bethe-Salpeter Equation
The Bethe-Salpeter (BS) equation in the ladder approximation is studied
within a scalar theory: two scalar fields (constituents) with mass
interacting via an exchange of a scalar field (tieon) with mass . The BS
equation is written in the form of an integral equation in the configuration
Euclidean -space with the kernel which for stable bound states is a
self-adjoint positive operator. The solution of the BS equation is formulated
as a variational problem. The nonrelativistic limit of the BS equation is
considered. The role of so-called abnormal states is discussed. The analytical
form of test functions for which the accuracy of calculations of bound state
masses is better than 1% (the comparison with available numerical calculations
is done) is determined. These test functions make it possible to calculate
analytically vertex functions describing the interaction of bound states with
constituents. As a by-product a simple solution of the Wick-Cutkosky model for
the case of massless bound states is demonstrated
Glueball as a bound state in the self-dual homogeneous gluon field
Using a simple relativistic QFT model of scalar fields we demonstrate that
the analytic confinement (propagator is an entire function in the complex
--plane) and the weak coupling constant lead to the Regge behaviour of the
two-particle bound states. In QCD we assume that the gluon vacuum is realized
by the self-dual homogeneous classical field which is the solution of the
Yang-Mills equations. This assumption leads to analytical confinement of quarks
and gluons. We extract the colorless two-gluon state from the QCD
generating functional in the one-gluon exchange approximation. The mass of this
bound state is defined by the Bethe-Salpeter equation. The glueball mass is
for if the gluon condensate is
.Comment: 3 pages. Parallel talk given at the 5rd International Conference on
Quark Confinement and the Hadron Spectrum (Confinement V), Gargnano, Italy,
September 10-14, 2002. To appear in the proceeding
Dimer-atom scattering between two identical fermions and a third particle
We use the diagrammatic -matrix approach to analyze the three-body
scattering problem between two identical fermions and a third particle (which
could be a different species of fermion or a boson). We calculate the s-wave
dimer-atom scattering length for all mass ratios, and our results exactly match
the results of Petrov. In particular, we list the exact dimer-atom scattering
lengths for all available two-species Fermi-Fermi and Bose-Fermi mixtures. In
addition, unlike that of the equal-mass particles case where the three-body
scattering -matrix decays monotonically as a function of the outgoing
momentum, we show that, after an initial rapid drop, this function changes sign
and becomes negative at large momenta and then decays slowly to zero when the
mass ratio of the fermions to the third particle is higher than a critical
value (around 6.5). As the mass ratio gets higher, modulations of the
-matrix become more apparent with multiple sign changes, related to the
"fall of a particle to the center" phenomenon and to the emergence of
three-body Efimov bound states.Comment: 6 pages, 3 figures, and 2 table
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