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We describe the main features of recent LHC data on elastic pp scatteringthrough a simple parametrization to the amplitude, inspired by a model proposedby Barger and Phillips in 1973, comprising of two exponentials with a relativephase. Despite its simplicity, this parameterization reproduces two essentialaspects of the elastic differential cross section, the well known precipitousdescent in the forward direction and a sharp `dip' structure. To include acomplete description of data sets near -t=0, we correct the originalparametrization. We examine two possibilities, the presence of the two-pionthreshold singularity or a multiplicative factor reflecting the proton formfactor. We find good descriptions of LHC7 and ISR data in either case. The formfactor model allows simple predictions for higher energies through asymptotictheorems and asymptotic sum rules in impact parameter space. We presentpredictions for this model at higher LHC energies, which can be used to testwhether asymptotia is reached. The black disk limit in this model is seen to bereached only for energies near 10^6 TeV.

Elastic pp scattering from the optical point to past the dip: an empirical parametrization from ISR to LHC