Proton-proton hollowness at the LHC from inverse scattering

Abstract

Parameterizations of the pp scattering data at the LHC collision energies indicate a hollow in the inelasticity profile of the pp interaction, with less absorption for head-on collisions than at a non-zero impact parameter. We show that some qualitatively unnoticed features may be unveiled by a judicious application of the inverse scattering problem in the eikonal approximation and interpre- tation within an optical potential model. The hollowness effect is magnifed in a 3D picture of the optical potential, and will presumably be enhanced at yet higher energies. Moreover, in 3D it sets in at much smaller energies than at the LHC. We argue that hollowness in the impact parameter is a quantum effect, relying on the build-up of the real part of the eikonal scattering phase and its possible passage through $\pi/2$. We also show that it precludes models of inelastic collisions where inelasticity is obtained by naive folding of partonic densities.Comment: 9 pages, 6 figures,expanded version with further discussion

Hollowness in pp and pp¯ scattering in a Regge model

“…We have also illustrated the criteria for its appearance. As shown in [17], the very existence of the hollowness phenomenon is quantum-mechanical in nature, as it invalidates folding constructions of the inelasticity profile, as used e.g. in Refs.…”

“…We recall that ours is a multi-energy analysis which includes both pp and pp within a Regge setup. The persistent occurrence of hollowness at the LHC can be traced to quantum mechanical interference effects which defy purely geometric models [17]. As we have already mentioned, our motivation to use the Regge approach is a realization of analytic properties, such as a fixed-t dispersion relation and crossing, which allows to fix the phase of the amplitude whose absolute value is determined from LHC data.…”

Hollowness in $pp$ Scattering at the LHC

“…Here we discuss the sensitivity of this hollowness feature on modeling of the phase of the elastic scattering amplitude as a function of the momentum transfer. In previous analyses [1,[8][9][10][11][12][13][14][15][16][17][18][19] this effect was not treated with sufficient attention.…”

“…In this contribution we focus on the aspects of the alleged hollowness effect in pp scattering not covered in our previous paper [1] and talks [2,3], where the basic concepts and further details of the presented analysis may be found. The recent TOTEM [4] and ATLAS (ALFA) [5] data for the differential elastic cross section for pp collisions at √ s = 7 TeV and √ s = 8 TeV [6,7] suggest a stunning behavior (impossible to explain on classical grounds), where more inelasticity in the reaction occurs when the protons collide at an impact parameter b of a fraction of a fermi, than for headon collisions.…”

“…Imaginary parts of the optical potential V (r) (a) and the on-shell optical potential W (r) (b), introduced in Refs [1,2],. plotted for parameterizations of ρ(t) from Eq.…”