The Present Status of Pion-Nucleon Phase Shift Analysis

Abstract

Since the CERN (l) and the Saclay (2) phase shift analyses (1967–73), which discovered the most important nucleon resonances up to 2GeV mass, progress has been made in the methods for determining πN amplitudes and partial waves. Especially the problem of ambiguous solutions is understood (3, 14) and can be solved nowadays by using analyticity constraints together with isospin invariance (4). Also the experimental information on π±p → π ±p and π p → π °n differential cross sections and polarizations and on the π ±p total cross sections has considerably increased since 1973. At present two phase shift solutions are available which, apart from data, are also based on the information derived from the analytic properties of scattering amplitudes. The CMU-LBL group (5) worked in the lab. momentum range.4–2 GeV/c and is extending the investigations up to 3 GeV/c. The collaboration between the Karlsruhe group and E. Pietarinen from Helsinki (KH) resulted in a set of partial waves (6, 7) which runs from threshold to 10 GeV/c. Also fixed-t amplitudes in terms of an expansion developed by Pietarinen (8) are available in a t-range −lGev2 ≲ t ≤ ο. A new amplitude analysis (9) in the t-range |t| ≤.5 GeV2 and up to 200 GeV/c is in progress at Karlsruhe.