Abstract
The ratios $\rho^{pp}_{\bar pp}(s)$ of the real to the imaginary part of forward elastic $pp$ and $\bar pp$ scattering amplitudes at very high energies are considered in the models with rising total cross-sections and its difference. It is shown from the dispersion relations for $pp$ and $\bar pp$ scattering amplitudes that in the Froissaron and Maximal Odderon approach the ratios do not vanish asymptotically and they have the opposite signs for $pp$ and $\bar pp$ scattering.
Highlights
It was proved in the paper [1] that the real part of the crossing-even elastic scattering amplitude has to be positive at s → ∞
(2) In order to make a conclusion about possible behavior of ρppppðsÞ at s → ∞ we should consider the most general case for odderon contribution allowed by the known restrictions on asymptotic properties of scattering pp and pp amplitudes
We consider here the real parts of crossing-even and crossing-odd pp and pp amplitudes which are dominated at high energy by pomeron and odderon contribution correspondingly
Summary
It was proved in the paper [1] that the real part of the crossing-even elastic scattering amplitude has to be positive at s → ∞. (1) The crossing odd component, odderon, for these amplitudes plays a very important role in observed differences in pp and pp cross sections and it is lively discussed in the old and recent papers devoted to phenomenological models [2]. (2) In order to make a conclusion about possible behavior of ρppppðsÞ at s → ∞ we should consider the most general case for odderon contribution allowed by the known restrictions on asymptotic properties of scattering pp and pp amplitudes. This is the goal of the present paper.
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