Possibility of linearly rising total cross sections in ln s

The increase of the pp and K/sup +/p total cross sections has been discovered at CERN and Serpukhov respectively. As for pi /sup +or-/p scattering, no trace of the growth of total cross sections is yet observed. However, from the standpoint of the dual absorption model, which works well for the forward elastic scattering of pi /sup +or-/p and K/sup +or-/p at p/sub L/<or approximately=20 GeV/c, it is expected that the 'diffractive' part of the pi /sup +or-/p total cross sections also increases with energy. These increments of the pp, K/sup +/p and pi /sup +or-/p total cross sections may have a common physical origin. (11 refs).