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Partial Wave Crossing Relations for Meson‐Baryon Scattering
Author(s) -
Steiner F.
Publication year - 1971
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.19710190302
Subject(s) - crossing , physics , partial wave analysis , level crossing , amplitude , ansatz , scattering amplitude , symmetry (geometry) , quantum electrodynamics , angular momentum , projection (relational algebra) , quantum mechanics , mathematical physics , mathematics , geometry , archaeology , algorithm , history
Three different types of relations for meson‐baryon partial wave amplitudes following from the s ↔ u crossing symmetry of the invariant amplitudes are investigated: i) the partial wave crossing relations directly derived from the s ↔ u crossing symmetry and the partial wave projection, ii) the partial wave crossing relations following from a combined use of s ↔ u crossing symmetry and analyticity, and iii) the crossing sum rules, which are a direct consequence of the s ↔ u crossing symmetry. The kernels entering the crossing relations i) and ii) are given in an analytic form, valid for arbitrary angular momentum. Their properties are studied in detail. By means of the partial wave crossing relations ii) it is demonstrated that u ‐channel exchange of a resonance leads to a resonance‐like behaviour of the partial wave amplitudes on the crossed physical cut. This phenomenon is described in terms of “pseudoresonances”. Finally the crossing sum rules iii) and their practical use are thoroughly discussed, and they are compared with the partial wave crossing relations i) and ii). Special attention is paid to the crossing symmetry constraints on the S ‐wave amplitudes. As a result of these investigations we present a crossing symmetric ansatz for these amplitudes which gives a more reliable parametrization than the usual effective range approximation.