2004/04/23 by F. J. Yndurain, Yndurain, F. J.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #hep-ph
paper · pdf · doi:10.48550/arxiv.hep-ph/0404204
Plain TeX. Dedicated to Prof. Yuri Simonov in his 70th birthday
arxiv created 2004/04/23 · arxiv updated 2009/12/01
We show that a generalized Regge behaviour, Im F(s,t)≃ Φ(t)(log s/s)ν(t)(s/s)αP(t), \rm for |t|<|t0|, s→∞ where Φ(t)≃ ebt, 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 σ\rm tot(s)<(\rm Const.)×log s/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/s)log2s\overs1log7/2 s/s2, a good fit is obtained to ππ, πN, KN and NN cross sections from c.m. kinetic energy E\rm 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.