Odderon and proton substructure from a model-independent Lévy imaging of elastic $pp$ and $p\bar{p}$ collisions

We describe a new and model-independent Lévy imaging method of quality fits to the published datasets and reconstruct the amplitude of high-energy pp and $p\bar{p}$ elastic scattering processes. This method allows us to determine the excitation function of the shadow profile P(b), the elastic slope B(t) and the nuclear phase $\phi (t)$ functions of pp and $p\bar{p}$ collisions directly from the data. Surprisingly, notable qualitative differences in B(t) for pp and for $p\bar{p}$ collisions point towards an Odderon effect. As a by-product, we clearly identify the proton substructure with two different sizes at the ISR and LHC energies, that has striking similarity to a dressed quark (at the ISR) and a dressed diquark (at the LHC). We present model-independent results for the corresponding sizes and cross-sections for such a substructure for the existing data at different energies.