Do the pi N Total Cross Sections Increase Like log nu or log2 nu at High   Energies ?
  We 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. 
Keiji Igi (Kanagawa univ.) and Muneyuki Ishida (Tokyo Institute of   Tech)