Correlations between total cross sections and slopes

We investigate correlations between the total cross section and the slope of the elastic differential cross section for proton-proton and antiproton-proton scattering at the highest energies. Based on the empirical behavior of these quantities as function of the energy, we select two different analytical parametrizations connecting them, and obtain the correlations through fits to the experimental data available. We present and discuss practical uses of extrapolations and interpolations of the results. In the former case we refer to the estimation of the proton-proton total cross sections from the proton-air cross sections (obtained from cosmic-ray experiments), and in the later case, we critically discuss the recent measurement of the slope parameter at the BNL RHIC at 200 GeV by the pp2pp Collaboration