Soft and hard Pomerons in hadron elastic scattering at small t

We consider simple-pole descriptions of soft elastic scattering for $pp$, p̄p, π^±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≤√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.