Structure of forward pp and pp¯ elastic amplitudes at low energies

Abstract

Exact analytical forms of solutions for Dispersion Relations for Amplitudes and Dispersion Relations for Slopes are applied in the analysis of pp and pp scattering data in the forward range at energies below (s) ≈ 30 GeV. As inputs for the energy dependence of the imaginary part, use is made of analytic form for the total cross sections and for parameters of the t dependence of the imaginary parts, with exponential and linear factors. A structure for the t dependence of the real amplitude is written, with slopes BR and a linear factor ρ − µRt that allows compatibility of the data with the predictions from dispersion relations for the derivatives of the real amplitude at the origin. A very precise description is made of all dσ/dt data, with regular energy dependence of all quantities. It is shown that a revision of previous calculations of total cross sections, slopes and ρ parameters in the literature is necessary, and stressed that only determinations based on dσ/dt data covering sufficient t range using appropriate forms of amplitudes can be considered as valid.

The elastic differential pp cross-section at 13 TeV: an empirical model analysis

“…We stress that the asymptotic behaviour of the slope B(s) chosen above, differs from the usual ln(s) behaviour expected from Regge or Pomeron pole trajectories. Namely, in this empirical model, the slope in the forward region increases faster than a logarithm, in agreement with an earlier study by Ryskin and Shegelsky [15],[see, also [16], [17], [18] and predicting a higher energy behaviour as confirmed by the recent TOTEM observations at LHC13. In the following subsections, we shall apply this model to the recent TOTEM data, starting with the CNI region.…”

“…As we shall see below, this is due to their chosen parametrization of the nuclear amplitude in Eq. (18). For example, the form of the nuclear amplitude adopted in Eq.…”

Analytical representation for amplitudes and differential cross section of pp elastic scattering at 13 TeV

“…Unfortunately, the determination of the |t| = 0 quantities such as σ (s) and ρ(s) based purely on the bare data of PDG is not secure, because this inclusive data basis has not been not submitted to a selection and evaluation of consistency and quality [43]. Values of σ and ρ are not quantities directly measured, but rather are model dependent calculations, requiring identification of the imaginary and real parts of the amplitude, and in many cases the dσ/dt measurements are not sufficient in range and quality for these calculations.…”

Analytical representation for amplitudes and differential cross section of pp elastic scattering at 13 TeV

“…The determination of the |t| = 0 parameters σ(s) and ρ(s) using the very irregular data basis of PDG is not secure, because the data basis supported by PDG has not been not submitted to a selection and evaluation of consistency and quality [36]. Values of σ and ρ are not measured quantities, but rather are model dependent calculations, and in many cases the dσ/dt measurements are not sufficient for a proper determination.…”