An empirical model for $pp$ scattering and geometrical scaling
  We present the result of an empirical model for elastic $pp$ scattering at LHC which indicates that the asymptotic black disk limit ${\cal R}=\sigel/\sigtot\rightarrow1/2$ is not yet reached and discuss the implications on classical geometrical scaling behavior. We propose a geometrical scaling law for the position of the dip in elastic $pp$ scattering which allows to make predictions valid both for intermediate and asymptotic energies. 
G. Pancheri, D.A. Fagundes, A. Grau and Yogendra N. Srivastava
hep-ph