Solution of the dispersion relations for the πN-scattering amplitudes by the method of Padé approximants

• Published in: Nuclear physics. B 1972-06, Vol.42, p.541-557
• Main Authors: Fil'kov, L.V., Palyushev, B.B.
• Format: Article
• Language: English
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(72)90497-X

The [1, 1] Padé approximant is used in order to obtain a solution of the dispersion relations for the πN-scattering amplitude. The dispersion relations are constructed with one subtraction for the amplitude A (+) and without subtraction for all the other amplitudes. There is one free parameter (β) only, connected with the t-channel contribution. The results obtained for s, p and d waves with isospin T= 1 2 and T= 3 2 are in satisfactory agreement with experiment in quite a large energy region (except the P 13 wave). The results of the calculations do not change very much if one neglects the contribution of the t-channel ( β=0). The partial S l± (2 t) matrix analysis in the region below the threshold of πN-scattering indicates the existence of antibound states in the P 33 wave with effective masses of 900 and 955 MeV and in the P 11 wave with an effective mass of1010 MeV.