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 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 ϕ ( t ) functions of pp and p p ¯ collisions directly from the data. Surprisingly, notable qualitative differences in B(t) for pp and for p 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.

CERN 1211 Geneva 23 Switzerland

Department of Astronomy and Theoretical Physics Lund University 223 62 Lund Sweden

EKU KRC Mátrai út 36 Gyöngyös 3200 Hungary

MTA WIGNER FK POB 49 Budapest 114 1525 Hungary

Nuclear Physics Institute ASCR 25068 Řež Czech Republic

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