Energy Dependence of the Ratio of the Elastic-to-Total Cross Sections for Proton—Proton and Antiproton—Proton Collisions

Abstract

The paper presents the phenomenological analysis of the energy dependence for the ratio of elastic to total cross section in proton-proton and antiproton-proton scattering. The analytic functions based on the study of low-and high-energy experimental data for various scattering parameters provide the quantitative description of energy dependence of the ratio with statistically acceptable qualities in wide range of collision energy √ s ≥ 3 GeV in the case of the separate datasets for pp, pp collisions and at √ s ≥ 5 GeV for the joined experimental data ensemble. Based on the fit results the estimations are derived for the ratio of elastic to total cross section in pp scattering at various √ s up to energy frontier √ s = 10 PeV which can be useful for present and future hadron colliders as well as for cosmic ray measurements at ultra-high energies. The indication is observed for onset of the asymptotic region at √ s 5 − 10 PeV for the ratio of cross sections under consideration.

Global Characteristics of the Medium Produced in Ultra-High Energy Cosmic Ray Collisions

“…It should be noted that analytic functions given below were obtained on the basis of the Standard Model (SM) without invoking any hypothesis concerning contributions from physics beyond it. The justification of the approach for ultra-high energy domain can be found elsewhere [2].…”

Optical Theorem, Crossing Property and Derivative Dispersion Relations: Implications on the Asymptotic Behavior of $σ_{tot}(s)$ and $ρ(s)$

“…The analytic functions deduced within various hypotheses (Table I, II) and numerical fit results (Table IV, VI) allow the phenomenological projections for the terms of the wide set G of global scattering parameters and its derivative quantities, in particular, for energies O(100 TeV) and higher. The main features for such predictions are described in detail elsewhere [25,34]. Simultaneous fit results obtained for database DB20 1 + (Table IV) allow predictions for the joined set G since DB20 1 + is one of the most complete databases considered here and, on the other hand, this database satisfies the general requirements used in the formation of databases.…”

“…That can be considered as indirect evidence in favor of the range for √ s a , derived with help of the condition for a/ε. Some numerical values for estimates of global scattering parameters are shown in Table VII for pp in the energy range from the nominal √ s of the LHC up to the high boundary of the PeV domain √ s = 10 PeV based on the detailed analysis above and the reasons discussed elsewhere [25,34]. The fitted results for DB20 1 + at √ s min = 5…”

“…3 The energy values for the measured σ pp tot and σ pp tot are considered close if P ∆ ≡ |P 1 − P 2 | ≤ 0.02 GeV or P 1 and P 2 coincide within errors, where P i is the laboratory momentum for the term G i 1 , i = 1, 2. On can note that the first condition for the closeness of P 1 and P 2 was previously used in [34]. The relative fraction of the pairs (σ pp tot , σ pp tot ) with finite P ∆ is 64.8% and almost all of such measurements are at √ s < 3.63 GeV.…”

“…Detailed analysis of the ratio of the elastic-to-total cross sections for pp and pp collisions [34] as well as the approach of the partonic disks [35] allow only the indication √ s a ∼ 5 − 10 PeV. Consideration of some other signatures of the "truly asymptotic regime" within Regge-eikonal model [22] results in much more conservative estimation for s a , in particular, the onset of the asymptotic regime can be expected in grand unified theory (GUT) energy domain in order of magnitude, i.e.…”