Proton structure and hollowness from Lévy imaging of pp elastic scattering

Abstract

The recently developed Lévy imaging method enables to extract an important physics information on hadron structure at high energies and ultra-low momentum transfers directly from elastic scattering data. In this work, we employ such a model-independent method to probe the internal structure of the proton and quantify its inelasticity profile in the impact parameter space emerging in proton-proton collisions at the highest available energy of √ s = 13 TeV. The inelasticity profile function and its error band for the proton and its substructure have been reconstructed at different energies and the proton hollowness (or "black-ring") effect with beyond 5σ significance has been found at 13 TeV.

Proton Holography Discovering Odderon from Scaling Properties of Elastic Scattering

“…A new possibility for phase reconstruction in elastic proton-proton scattering is based on our detailed analysis of elastic pp collisions data in the dip region at ISR and LHC energies [8,[22][23][24][25]. To support this conjecture, we present some qualitative considerations as well as the results of a model-independent study, and also discuss the currently known limitations of this promising new method.…”

“…These limiting cases were discussed for example in Appendices C and D of Ref. [22]. However, the observation of a diffractive minimum, followed by a diffractive maximum corresponds to the observation of an interference pattern, one of the conditions of phase reconstruction and holography.…”

“…Recently, we have discussed model-independent, whole −t range fits to the differential cross-section in Appendix A and B of Ref. [22] for pp and for pp elastic collisions, respectively. A closer inspection of these fits indicate that at the ISR energy range, the total cross-section is reproduced reasonably well, while the ρ 0 measurements are reproduced only in one case, at √ s = 44.7 GeV, within two standard deviations.…”

Lévy imaging of elastic scattering and proton hollowness at 13 TeV

“…The characteristics of the elastic amplitude, its both real and imaginary parts, carry a plenty of information about the inner proton structure, the proton profile in the impact parameter space and its energy dependence, as well as about the properties of QCD exchange interaction at low momentum transfers. In this work, we apply the recently developed model-independent Lévy imaging technique [1,2,3,4] for precision characterisation and extraction of relevant physics information about the proton structure and hence non-perturbative QCD directly from the available data on elastic cross sections at various energies. The results of our approach efficiently complement and provide an important guideline for the existing ongoing model-dependent efforts.…”

“…It corresponds to the Fourier-transform of a symmetric Lévy-stable source distribution [17]. This approximation with α = 0.9 gives a statistically acceptable description of pp elastic scattering at low-t at √ s = 23.5 GeV to 62.5 GeV, while at the LHC energies higher order Lévy expansion terms become relevant for description of the low-t behaviour [1]. At larger |t|, deviation of the data from the Lévy stable source distribution becomes even more pronounced in a vicinity of the dip-and-bump structure before turning back to a simple stretched exponential behaviour again (but with a different value of R) at large |t| beyond the secondary maximum.…”