Pion--nucleon sigma-commutator. [S waves, phase shift, amplitudes]

Technical Report · Fri Jul 01 04:00:00 EDT 1977

DOI:https://doi.org/10.2172/7211677· OSTI ID:7211677

Banerjee, M. K.; Cammarata, J. B.

The reasons for the large discrepancies in the magnitude of the ..pi..N sigma-commutator, sigma(..pi..N), obtained by several authors are discussed using dynamic theory of the ..pi..N scattering amplitude. With sigma(..pi..N) approximately 25 MeV this theory reproduces reasonably well both the experimental S-wave phase shifts at low energies and the amplitudes C approximately/sup(+)/(..nu..=0,t less than or equal to 0) determined by Langbein. In the method of Cheng and Dashen the value of sigma(..pi..N) is obtained from these amplitudes by extrapolation to t = 2m/sup 2//sub ..pi../. A study of the experimental D-wave ''scattering lengths'' implies that the coefficient of the term quadratic in t in the Hoehler expansion of C approximately/sup(+)/(0,t) is negative. Adding such a term to the results of the S-wave theory will tend to improve the agreement for C approximately/sup (+)/(0,t less than or equal to 0). These results suggest that the large ''world value'' sigma(..pi..N) = 65 +- 5 MeV obtained using the Cheng-Dashen method is a consequence of errors in the extrapolation of amplitudes to the unphysical point ..nu.. = 0, t = 2m/sup 2//sub ..pi../. Only the smaller value sigma(..pi..N) approximately 25 MeV appears to be consistent with the experimental data and theoretical constraints.

• Research Organization: Maryland Univ., College Park (USA). Dept. of Physics and Astronomy
• DOE Contract Number: EY-76-S-05-5126
• OSTI ID: 7211677
• Report Number(s): ORO-5126-16
• Country of Publication: United States
• Language: English

Related Subjects

645206* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions
Baryon No. = 1-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
COMMUTATORS
CURRENT COMMUTATORS
D WAVES
ERRORS
HADRON-HADRON INTERACTIONS
INTERACTIONS
MATHEMATICAL OPERATORS
MESON-BARYON INTERACTIONS
MESON-NUCLEON INTERACTIONS
PARTIAL WAVES
PARTICLE INTERACTIONS
PHASE SHIFT
PION-NUCLEON INTERACTIONS
QUANTUM OPERATORS
S WAVES
SCATTERING AMPLITUDES
SCATTERING LENGTHS