Pion-Nucleon Scattering and Pion-Pion Interactions
Nov 15, 1962
26 pages
Published in:
- Phys.Rev. 128 (1962) 1881-1907
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Abstract: (APS)
Low energy s- and p-wave π−N scattering is analyzed by partial wave dispersion relations. From the experimental π−N phase shifts we derive the "discrepancies" in the physical energy region and on the crossed cut. We are able to separate the discrepancies into the short-range (≲0.2×10−13 cm) π−N interactions and the π−π contributions to π−N scattering. The π−π contributions found in this way satisfy several stringent tests which show the validity of our method for deriving and separating the π−π contributions.
The (+) charge combination of s- and p-wave π−N amplitudes yields considerable information about the T=0 π−π interaction at low energies. The T=0, J=0 π−π scattering is dominant, and we determine possible sets of the corresponding phase shift δ00. Several of our solutions for δ00 agree with recent solutions of the Chew-Mandelstam equations for π−π scattering. Comparison with the latter suggests that the π−π coupling parameter is λ=−0.18±0.05, and the π−π scattering length is a0=1.3±0.4 (in units where ℏ=μ=c=1). Other information, from the p+d and π+N→π+π+N experiments and from τ decay, is consistent with our proposed values of δ00.
The (-) charge combination of s- and p-wave π−N amplitudes gives information about the T=1, J=1 π−π interaction which is consistent with the observed ρ resonance. However in the T=1, case, complete prediction of our π−N results via the helicity amplitudes for π+π→N+N¯ is not yet satisfactory. Possible reasons for this are given.
The p-wave π−N interaction is separated into its constituent parts, and for example, it is seen that any attempt to determine the position of the (32, 32) resonance must include the T=0, J=0 π−π interaction. The extent to which our analysis depends on assuming charge independence is examined. We also discuss how our results can be regarded as a fairly good physical proof of the Mandelstam representation.References(48)
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