Lévy imaging of elastic scattering and proton hollowness at 13 TeV

The shape of elastic differential cross section within and beyond the diffractive cone at 13 TeV $pp$ collision energy has been shown to be precisely described by the Lévy series expansion in whole available range of momentum transfers. This way, the crucial information about the real and imaginary parts of the elastic amplitude has been obtained resulting in precision reconstruction of the proton inelasticity profile. We have found that the profile function $P(b)$ undergoes a qualitative change at $\sqrt{s} \approx 7 $ TeV collision energy. At small values of the impact parameter $b$ a $P(b) \approx 1$ plateaux develops, which becomes depressed at larger energies, such that a shallow minimum is formed near $b = 0$. We have evaluated the corresponding error bar and found such a hotly debated proton hollowness (or ``black-ring'') effect with beyond 5$\sigma$ significance.