3 research outputs found
On coupled-channel dynamics in the presence of anomalous thresholds
We explore a general framework to treat coupled-channel systems in the presence of overlapping left- and right-hand cuts as well as anomalous thresholds. Such systems are studied in terms of a generalized potential, where we exploit the known analytic structure of t- and u-channel forces as the exchange masses approach their physical values. Given an approximate generalized potential the coupled-channel reaction amplitudes are defined in terms of nonlinear systems of integral equations. For large exchange masses, where there are no anomalous thresholds present, conventional N=D methods are applicable to derive numerical solutions to the latter. At a formal level a generalization to
the anomalous case is readily formulated by use of suitable contour integrations with amplitudes to be evaluated at complex energies. However, it is a considerable challenge to find numerical solutions to
anomalous systems set up on a set of complex contours. By suitable deformations of left-hand and right-hand cut lines we manage to establish a framework of linear integral equations defined for real
energies. Explicit expressions are derived for the driving terms that hold for an arbitrary number of channels. Our approach is illustrated in terms of schematic three-channel systems. It is demonstrated
that despite the presence of anomalous thresholds the scattering amplitude can be represented in terms of three phase shifts and three inelasticity parameters, as one would expect from the coupled-channel
unitarity condition
A coupled-channel system with anomalous thresholds and unitarity
We consider the isospin one-half example system, with coupled channels in the
partial wave, chosen such that various phenomena that come with the opening of
an anomalous threshold can be illustrated in a step-wise procedure by a
suitable variation of up, down and strange quark masses. We use a set of LEC in
the chiral Lagrangian that were adjusted to a large set of Lattice QCD results.
The six phase shifts and inelasticity parameters are presented for various
choices of the pion mass. For a pion mass of 150 MeV there are no anomalous
thresholds encountered. The small change from 150 MeV to 145 MeV pion mass
causes a dramatic impact of the anomalous threshold on the phase shifts.Comment: 11 pages, 4 figure
Triangle and box diagrams in coupled-channel systems from the chiral Lagrangian
We perform an analysis of triangle- and box-loop contributions to the
generalized potential in the scattering of Goldstone bosons off the J^P= 0^-
and 1^- charmed mesons. Particular emphasis is put on the use of on-shell mass
parameters in such contributions in terms of a renormalization scheme that
ensures the absence of power-counting violating terms. This is achieved with a
systematically extended set of Passarino--Veltman basis functions, that leads
to manifest power-counting conserving one-loop expressions and avoids the
occurrence of superficial kinematical singularities. Compact expressions to
chiral order three and four are presented that are particularly useful in
coding such coupled-channel systems. Our formal results are generic and prepare
analogous computations for other systems, like meson-baryon scattering from the
chiral Lagrangian.Comment: 58 pages, 7 figures and 2 tables, minor corrections and extension