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On coupled-channel dynamics in the presence of anomalous thresholds

Lutz, Matthias F. M. ; Korpa, Csaba L. (2022):
On coupled-channel dynamics in the presence of anomalous thresholds. (Publisher's Version)
In: Physical Review D, 98 (7), American Physical Society, ISSN 2470-0010, e-ISSN 2470-0029,
DOI: 10.26083/tuprints-00012794,
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Item Type: Article
Origin: Secondary publication
Status: Publisher's Version
Title: On coupled-channel dynamics in the presence of anomalous thresholds
Language: English
Abstract:

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.

Journal or Publication Title: Physical Review D
Journal volume: 98
Issue Number: 7
Publisher: American Physical Society
Collation: 26 Seiten
Classification DDC: 500 Naturwissenschaften und Mathematik > 530 Physik
Divisions: 05 Department of Physics > Institute of Nuclear Physics
Date Deposited: 11 Mar 2022 13:19
Last Modified: 11 Mar 2022 13:19
DOI: 10.26083/tuprints-00012794
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-127946
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/12794
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