Extension of the axiomatic analyticity domain: pion-nucleon scattering

Summary  Starting from analyticity in the topological product of the cuts-plane and the circle ¦t¦μ 2 and using unitarity several times, the domain of validity of fixed-t dispersion relations for elastic πN scattering is extended to a larger domainD πn which is shown to contain the negative real axis fromt=0 to the «inelastic point»t=−18.0μ2. Thus, as in meson-meson scattering, the only reason which prevents one from continuing further to the left, is our lack of knowledge about possibly occurring singularities above inelastic threshold. Using also a recent result of Bessis and Glaser, the best domain is found to be the intersection of the large Lehmann ellipse fors=(M+2μ)2 with the large Lehmann ellipse fors=(M+2μ)2+8μ(M+μ). In the elastic region the analyticity domain of the absorptive part extends to the border of the Mandelstam support. Partial-wave amplitudes are found to be analytic in two disconnected regions which touch the circle ¦s¦=M 2−μ 2 from inside and outside ins=M 2−μ 2.