Determination of the pion-nucleon coupling constant and s-wave scattering lengths

Presently available values of D/sub +or-/, the real parts of the pi /sup +or-/p elastic scattering amplitudes in the forward direction in the laboratory frame, obtained by extrapolation of experimental data to the forward direction, have been fitted up to a pion lab. kinetic energy of 2 GeV using forward dispersion relation. A substantial number of data points have to be discarded to obtain a reasonable goodness of fit. Above 300 MeV the values of D/sub +or-/ obtained from the CERN phase shift analysis are strongly favoured compared with those from the Saclay analysis. The final results for the pion-nucleon coupling constant and s-wave scattering lengths are: 10/sup 3/f/sup 2 /=76.3+or-2.0, 10/sup 3/D/sub +/( mu )=-102.4+or-5.2, 10/sup 3/D/sub - /( mu )=104.8+or-5.4, 10/sup 3/(a/sub 1/-a/sub 3/)=270.6+or-11.3, 10 /sup 3/(a/sub 1/+2a/sub 3/)=3.1+or-8.0. The errors quoted take account of experimental uncertainties and also attempt to include systematic errors arising from the unphysical continuum and from the very high energy region. Coulomb barrier corrections have not been included. The results are compared with other determinations of the same quantities and their implications discussed. (47 refs).