Richard J. Jacob

Determinations of the πNσ term and s-wave scattering lengths☆

Abstract Determinations of the σ term and s-wave scattering lengths for pion-nucleon scattering are made using interior dispersion relations. The result for the σ term is obtained by extrapolating to the Cheng-Dashen point in only one variable. It is completely independent of the pion-nucleon coupling constant and insensitive to d and f waves in the resonance region. The use of interior dispersion relations allows a series of s-wave scattering length determinations to be made. It is observed that data at intermediate scattering angles gives more consistent results than data near the forward or backward directions, lending further support to the σ term calculation which utilizes only interior angle information.

The I = 0, s-wave ππ scattering length☆

Abstract Interior dispersion relations are applied to πN scattering amplitudes to extract the I = 0, s-wave ππ scattering length, a00. Two methods are used, the second of which also incorporates known ππ scattering phase shifts. We have used the πN amplitude analysis of Pietarinen and obtained values of a00: (0.28 ± 0.09)μ− and (0.25 ± 0.08)μ− for the two methods respectively, consistent with other recent determinations from Ke4 and πN → ππN data. The 1971 πN phase-shift analysis of Ahmehed and Lovelace was also used successfully in the first method to obtain the value a00: (0.15 ± 0.14)μ−, consistent with the above. The second method was found to be ineffective in the face of relatively unsmooth discrepancy functions obtained from the Ahmehed-Lovelace phase shifts.

Sum rules from boundary dispersion relations

Abstract Sum rules for inelastic reactions are derived from boundary dispersion relations. If sufficient data or a model is available for the amplitude in the direct channel, then these sum rules provide a means of studying the dynamics in the cross channel. The convergence of these sum rules is investigated, assuming they can be saturated with narrow-width resonances, and rough estimates of the coupling constants of cross-channel exchanges for the photoproduction of pseudoscalar mesons are obtained.