Abstract
We comment on phase selection of the scattering amplitude, emphasizing that the elastic overlap function should have a central impact parameter profile at high energies and highlighting the role of the reflective scattering mode at the LHC energies. Emerging problems with the use of peripheral impact parameter dependence of the elastic overlap function are explicitly indicated. Their solution is an elimination of the phases connected to peripheral form of the elastic overlap function. Contrary, we adhere to a relative peripheral form of the inelastic overlap function with an additional new feature of a maximum at nonzero value of the impact parameter at the highest energies. Phenomenologically, the dynamics of hadron scattering is motivated by a hadron structure with a hard central core presence.
Highlights
Role of the scattering amplitude phasePhase of the elastic scattering amplitude plays an important role in physics interpretation of hadron scattering
It will be shown further that unitarity being combined with Mandelstam analyticity allows one to obtain a more stringent constraint for the profile of the elastic overlap function and, as a consequence, for the scattering amplitude phase
We address the problems related to a peripheral option for the elastic scattering in what follows
Summary
Phase of the elastic scattering amplitude plays an important role in physics interpretation of hadron scattering. The important role of the phase has been clearly demonstrated under analysis of the LHC experimental data obtained by the TOTEM Collaboration [1]. To this end, it is instrumental to address the elastic and inelastic overlap functions in order to limit choice of the phases suitable for further considerations and phenomenological analysis. Despite the explicit form of the phase dependence after elimination of peripheral distribution of the elastic scattering remains to be unknown and leave us with results of phenomenological models only, it allows one to reduce an arbitrariness under the phase selection in the data analysis [1]. The results come from a combined utilization of unitarity and analyticity in the region of large impact parameters
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