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On the Generalized πN Potential A New Representation from Fixed‐ t Dispersion Relations
Author(s) -
Steiner F.
Publication year - 1970
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19700180103
Subject(s) - representation (politics) , amplitude , convergence (economics) , dispersion (optics) , mathematics , energy (signal processing) , dispersion relation , phase (matter) , statistical physics , physics , mathematical analysis , quantum mechanics , statistics , politics , political science , law , economics , economic growth
Starting from a recent paper [ 13 ] we derive a new representation of the left‐hand cut contribution for the πN system. This representation makes it possible to calculate the generalized πN potential accurately from phase shifts and high energy models, because it contains only the imaginary parts of the partial wave amplitudes in the physical region. The analytic properties, the region of convergence and the physical content of this representation is discussed. We propose to use this left‐hand cut contribution in bootstrap calculations, because it is more reliable than the approximate expressions which have been used in previous papers. – The left‐hand cut contributions are calculated and compared with the nucleon and Δ (1236) approximation for the ƒ 0+ (−) , ƒ 1− (−) , ƒ − (1+)and ƒ − (2−)partial wave amplitudes.