Analyticity and scaling property of pp and p\=p forward scattering amplitudes

We analyse the pp elastic scattering amplitudes using the recent LHC data, revisiting the model proposed by A. Martin based on analytic continuation and crossing symmetry. Introducing a new form for the scaling function we show that the data are consistent with the crossing symmetry of the scattering amplitudes at $\sqrt{s}= $ 7 and 8 TeV. The complex amplitude automatically obeys the constraints of dispersion relations and their derivatives. The real part reproduces the zero predicted by A. Martin, which is crucial to describe with precision the differential cross section in the forward direction at LHC energies. Since the free parameters of the model are energy independent, the analytical form of the amplitude leads to predictions for higher and asymptotic energies.