Checks of asymptotia in pp elastic scattering at LHC

We parametrize TOTEM data for the elastic differential pp cross section at s=7TeV in terms of two exponentials with a relative phase. We employ two previously derived sum rules for pp elastic scattering amplitude in impact parameter space to check whether asymptotia has been reached at the LHC. A detailed study of the TOTEM data for the elastic differential cross section at s=7TeV is made and it is shown that, within errors, the asymptotic sum rules are satisfied at LHC. We propose to use this parametrization to study forthcoming higher energy data.