Predictions of pp, pbar p total cross section and rho ratio at LHC and cosmic-ray energies based on duality

TL;DR

This paper uses duality principles and finite energy sum rules to analyze total cross sections and rho ratios in proton-proton and antiproton-proton scattering, predicting values at LHC and cosmic-ray energies that align with experimental data.

Contribution

It introduces a method combining duality and FESR constraints to discriminate high-energy behaviors of scattering cross sections, favoring a log squared growth model.

Findings

Predicted sigma(tot) at LHC: 106.3 mb with uncertainties

Predicted rho at LHC: 0.126 with uncertainties

Good agreement with cosmic-ray data up to Plab=10^9 GeV

Abstract

Based on duality, we previously proposed to use rich informations on pi p total cross sections below N=10GeV in addition to high-energy data in order to discriminate whether these cross sections increase like log nu or log2 nu at high energies. We then arrived at the conclusion that our analysis prefers the log2 nu behaviours. Using the FESR as a constraint for high energy parameters also for the pp, pbar p scattering, we search for the simultaneous best fit to the data points of sigma(tot) and rho ratio up to some energy (e.g., ISR, Tevatron) to determine the high-energy parameters. We then predict sigma(tot) and rho in the LHC and high-energy cosmic-ray regions. Using the data up to E=1.8TeV (Tevatron), we predict sigma(tot)pp and rho(pp) at the LHC energy (E=14TeV) as 106.3+- 5.1syst +- 2.4stat mb and 0.126 +- 0.007syst +- 0.004stat, respectively. The predicted values of sigma(tot) in terms of the same parameters are in good agreement with the cosmic-ray experimental data up to Plab = 10 (8--9) GeV.