2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/41428We propose to use rich informations on pi p total cross sections below N=10 GeV in order to investigate whether these cross sections increase like log nu or log2 nu at high energies. A finite-energy sum rule (FESR) which is derived in the spirit of the P' sum rule as well as the n=1 moment FESR have been required to constrain the high-energy parameters. We then searched for the best fit of pi p total cross sections above 70 GeV in terms of high-energy parameters constrained by these two FESR. We can conclude that our analysis strongly favours the log2 nu behaviors satisfying the Froissart unitarity bound.Talk presented at Moriond conf. 2002. 4 pages, 1 eps figure, uses moriond.styHigh Energy Physics - Phenomenologytext