Scattering amplitudes at multi TeV energies

We show that a generalized Regge behaviour, Im F (s, t) ≃ Φ(t)(log s/ˆ s) ν(t) (s/ˆ s) α P (t) , for |t| < |t0|, s → ∞ where Φ(t) ≃ e bt , αP (t) ≃ αP (0) + α ′ P (0)t, and t0 is the first zero of αP (t), αP (t0) = 0, implies that the corresponding cross section is bounded by σtot(s) < (Const.) × log s/ˆ s. This growth, however, is not sufficient to fit the experimental cross sections. If, instead of this, we assume saturation of the improved Froissart bound, i.e., a behaviour Im F (s, 0) ≃ A(s/ˆ s) log 2 s s1 log 7/2 s/s2 , a good fit is obtained to ππ, πN , KN and N N cross sections from c.m. kinetic energy E kin ≃ 1 GeV to 30 TeV (producing a cross section of 108 ± 6 mb at LHC energy). This suggests that the Regge-type behaviour only holds for values of the momentum transfer very near zero.