[en] elastic scattering ; pomeron ; analytic S matrix
[en] We consider simple-pole descriptions of soft elastic scattering for pp, (p) over barp, pi(+/-)p and K(+/-)p. We work at t and s small enough for rescatterings to be effectively absorbed in a simple-pole parametrization, and allow for the presence of a hard Pomeron. After building and discussing an exhaustive dataset, we show that simple poles provide an excellent description of the data in the region -0.5 GeV2<= t <= -0.1 GeV2, 6 GeV <= root s <= 63 GeV. We show that new form factors have to be used, and get information on the trajectories of the soft and hard Pomerons.