Asymptotic regime for hadron-hadron diffractive collisions at ultrahigh energies

Using the pre-LHC and LHC data for $\pi p$ and $pp$ diffractive collisions we study the ultrahigh energy asymptotic regime in the framework of the black disk picture. The black disk picture, being constrained by the s-channel unitarity condition and the $t$-channel analyticity, gives rather definite predictions for diffractive processes increasing with the energy. To deal with the data, we consider the Dakhno-Nikonov eikonal model which predicts a growth of the $\ln^2s$ type for total and elastic cross sections and $(\tau={\bf q}_\perp^2\ln^2s)$-scaling for diffractive scattering and diffractive dissociation of hadrons. According to the calculations, ultrahigh energy asymptotic characteristics of diffractive and total cross sections are universal, and this results in the asymptotic equality of cross sections for all types of hadrons. We estimate the energy scale of the asymptotics in different processes. The manifestation of the asymptotic regime in hadron fragmentation reactions is discussed.