23,214 research outputs found
Variational Field Theoretic Approach to Relativistic Scattering
Nonperturbative polaron variational methods are applied, within the so-called
particle or worldline representation of relativistic field theory, to study
scattering in the context of the scalar Wick - Cutkosky model. Important
features of the variational calculation are that it is a controlled
approximation scheme valid for arbitrary coupling strengths, the Green
functions have all the cuts and poles expected for the exact result at any
order in perturbation theory and that the variational parameters are
simultaneously sensitive to the infrared as well as the ultraviolet behaviour
of the theory. We generalize the previously used quadratic trial action by
allowing more freedom for off-shell propagation without a change in the
on-shell variational equations and evaluate the scattering amplitude at first
order in the variational scheme. Particular attention is paid to the
-channel scattering near threshold because here non-perturbative effects can
be large. We check the unitarity of a our numerical calculation and find it
greatly improved compared to perturbation theory and to the zeroth order
variational results.Comment: 26 pages, Latex, 5 postscript figures embedded with epsf, submitted
to Nucl. Phys.
Onset of -nuclear binding in a pionless EFT approach
and bound states are explored in stochastic
variational method (SVM) calculations within a pionless effective field theory
(EFT) approach at leading order. The theoretical input consists of regulated
and contact terms, and a regulated energy dependent contact
term derived from coupled-channel models of the nucleon
resonance plus a regulated contact term. A self consistency procedure
is applied to deal with the energy dependence of the subthreshold
input, resulting in a weak dependence of the calculated -nuclear binding
energies on the EFT regulator. It is found, in terms of the scattering
length , that the onset of binding \eta\,^3He requires a minimal
value of Re close to 1 fm, yielding then a few MeV binding
in \eta\,^4He. The onset of binding \eta\,^4He requires a lower value of
Re, but exceeding 0.7 fm.Comment: v4 consists of the published Physics Letters B version [31] plus
Erratum ([30], Appendix A here); main results and conclusions remain intac
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