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Pion-nucleon sigma commutator

Journal Article · · Phys. Rev., D; (United States)
The reason for the large discrepancy in the magnitude of the ..pi..N sigma commutator sigma (..pi..N) obtained from different analyses is discussed using a dynamical theory of the ..pi..N amplitude. With sigma (..pi..N) approx. 25 MeV this theory reproduces reasonably well both the experimental S-wave phase shifts at low energies and the amplitudes C/sup(/sup +/)(..nu.. = 0, - 4m/sub ..pi..//sup 2/ < or approx. = t < or = 0) determined by Langbein and others. In contrast to this value, various authors find sigma (..pi..N) approx. 65 MeV when the sigma commutator is evaluated using the method of Cheng and Dashen, in which sigma (..pi..N) is determined from the C/sup(/sup +/) amplitude at ..nu.. = 0, t = 2m/sub ..pi..//sup 2/. To have confidence in the results of such an analysis it is essential to know the true upper bound on the uncertainties of the amplitude, particularly because of the existence of a zero of C/sup(/sup +/) (0,t) in the neighborhood of t = 2m/sub ..pi..//sup 2/. Since these are unknown at present it cannot be established whether sigma (..pi..N) approx. 25 MeV is incompatible with the Cheng-Dashen-type calculations. Thus the discrepancy in the magnitude of the sigma commutator may be only apparent. We point out, however, that only the value sigma (..pi..N) approx. 25 MeV is consistent with both the experimental data and the constraints of the dynamical theory.
Research Organization:
Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
OSTI ID:
6361716
Journal Information:
Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 18:11; ISSN PRVDA
Country of Publication:
United States
Language:
English