Searching for extremely high-energy behavior from accelerator-energy regions

We use rich information on πp total cross sections below N(∼10 GeV) in addition to high-energy data in order to discriminate whether these cross sections increase like logν or log2ν 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 σtot(+) above 7 GeV in terms of high-energy parameters constrained by these two FESR. We have shown from this analysis that the log2ν behavior are preferred to the logν behavior. We also propose to search for p-bar p, pp total cross sections at extremely high-energy from accelerator-energy regions using the similar technique. (author)