Predictions of pp, pbar p total cross section and rho ratio at LHC and cosmic-ray energies

We propose to use rich informations on the pp, pbar p total cross sections sigma below N=10GeV in order to predict the total cross section and rho ratio at very high energies. Using the FESR as a constraint for high energy parameters, we search for the simultaneous best fit to the data points of sigma and rho ratio up to some energy (e.g., ISR, Tevatron) to determine the high-energy parameters. We then predict sigma and rho in the LHC and high-energy cosmic-ray regions. Using the data up to sqrt s=1.8TeV(Tevatron), we predict sigma^pp and rho^pp at the LHC energy(sqrt s=14TeV) as 106.3+-1.9 mb and 0.126+-0.004, respectively. The predicted values of sigma in terms of the same parameters are in good agreement with the cosmic-ray experimental data up to Plab = 10^(8--9)GeV