Title: Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity-I
Abstract: It is shown first that any scattering amplitude satisfying fixed transfer dispersion relations for −t 0 <t≤0 is in fact analytic in the topological product |t|<R×s in the cut plane with cutss=C+λ,s=−t−μ+C′, λ, μ≥0.R is some fixed number. For the pion-pion case,R=4μ2 where μ is the pion mass. For pion-pion scattering the domain is extended further by using elastic unitarity. The region of validity of dispersion relations is a certain domain in thet-plane, which contains in particular the real segmentt=-28μ2 tot=4μ2. The fixed energy sections of the amplitude for not too high energies contain part of the Mandelstam cuts. In particular in the elastic region the analyticity domain of the absorptive part contains part of the Mandelstam double-spectral function. The domain thus obtained is not yet a natural domain both from the pure analytic completion point of view and from the unitarity condition. The investigation is being continued.