Analysis of pp and p̄p elastic scatterings based on theoretical bounds in high-energy physics: An update

Abstract

In a previous work a novel parametrization was proposed for the pp andpp total cross section. Here, results are presented for analysis updated with taken into account the recent data from accelerator experiments as well as from cosmic ray measurements. The analytic parameterizations suggested within axiomatic quantum field theory (AQFT) provide the quantitative description of energy dependence of global scattering observables with robust values of fit parameters. Based on the fit results the estimations are derived for the total cross section and the ρ parameter in elastic 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.

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

“…where ρ(s) ≡ ReF (s, 0)/ImF (s, 0) is the ratio of real to imaginary part of the amplitude in the forward direction. One can note that experimental data show |ρ(s)| 0.3 (0.2) at √ s 5 (3) GeV for pp (pp) collisions [4]. Therefore the limit in (7) is valid in wide energy ranges for both pp andpp scattering at accuracy level better than 0.1.…”

“…In the present work the ratio of the elastic cross section to the total cross section R e/t = σ el /σ tot (1) is studied in dependence on the collision energy for pp and pp collisions. For the first case the experimental sample for set of the global scattering parameters G pp ≡ {G i pp } 2 i=1 = {σ pp tot , σ pp el } based on the database from [3], for pp scattering experimental points for the corresponding set G pp are from [4].…”

“…In general the behavior of the σ tot in high energy domain can be qualitatively described as ∝ ln α ε for pp and pp collisions, where 0 < α ≤ 2, ε ≡ s/s 0 and s 0 = 1 GeV 2 . Such dependence appears in various approaches [3][4][5]. On the other hand the term ∝ ε −β suggested within axiomatic quantum field theory (AQFT) [6] allows us the reasonable description for the experimental data at low energies down to the √ s = 3 GeV [4,6].…”

“…Inner panel: the experimental points and fit curve in the narrow range √ s = 1.86 − 2.36 GeV near the low-energy boundary. Experimental data are from[3,4].…”

Three-quark force in p–p elastic scattering

“…In general, in the framework of this theory, a good agreement with the proton-proton elastic scattering differential cross section, total cross section σ t and the ratio ρ of real to imaginary parts of protonproton elastic scattering amplitude in the forward direction was obtained at FNAL and CERN-ISR energy [10][11][12][13][14]. A a e-mail: el_hamam@sci.asu.edu.eg similar fit with the experimental data of the same protonproton quantities at the same energy was obtained by using many different other approaches, for example, the eikonalization approach [15], Bialas-Bzdak model [16], axiomatic quantum field theory [17] and others [18][19][20][21][22].…”