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, a 0 0. 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 a 0 0: (0.28 ± 0.09) μ − and (0.25 ± 0.08) μ − for the two methods respectively, consistent with other recent determinations from K e4 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 a 0 0: (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.