Analytical representation for amplitudes and differential cross section of pp elastic scattering at 13 TeV

With analytical representation for the pp scattering amplitudes introduced and tested at lower energies, a description of high precision is given of the $$d\sigma /dt$$ d σ / d t data at $$\sqrt{s}= 13$$ s = 13 TeV for all values of the momentum transfer, with explicit identification of the real and imaginary parts. In both t and b coordinates the amplitudes have terms identified as of non-perturbative and perturbative nature, with distinction of their influences in forward and large |t| ranges and in central and peripheral regions respectively. In the forward range, the role of the Coulomb-nuclear interference phase is investigated. The energy dependence of the parameters of the amplitudes are reviewed and updated, revealing a possible emergence of a peculiar behavior of elastic and inelastic profiles in b-space for central collisions, which seems to be enhanced quickly at higher energies. Some other models are also briefly discussed in comparison, including the above mentioned behavior in b-space.