Odderon and proton substructure from a model-independent Lévy imaging of elastic pp and pp¯ 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 pp¯ 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 ϕ(t) functions of pp and pp¯ collisions directly from the data. Surprisingly, notable qualitative differences in B(t) for pp and for pp¯ 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.