Analytic models and forward scattering from accelerator to cosmic-ray energies

Abstract

Analytic models for hadron-hadron scattering are characterized by analytical parametrizations for the forward amplitudes and the use of dispersion relation techniques to study the total cross section ${\sigma }_{tot}$ and the $\rho$ parameter. In this paper we investigate four aspects related to the application of the model to $pp$ and $\bar{p}p$ scattering, from accelerator to cosmic-ray energies: 1) the effect of different estimations for ${\sigma }_{tot}$ from cosmic-ray experiments; 2) the differences between individual and global (simultaneous) fits to ${\sigma }_{tot}$ and $\rho$; 3) the role of the subtraction constant in the dispersion relations; 4) the effect of distinct asymptotic inputs from different analytic models. This is done by using as a framework the single Pomeron and the maximal Odderon parametrizations for the total cross section. Our main conclusions are the following: 1) Despite the small influence from different cosmic-ray estimations, the results allow us to extract an upper bound for the soft pomeron intercept: $1+\epsilon =1.094$; 2) although global fits present good statistical results, in general, this procedure constrains the rise of ${\sigma }_{tot}$; 3) the subtraction constant as a free parameter affects the fit results at both low and high energies; 4) independently of the cosmic-ray information used and the subtraction constant, global fits with the odderon parametrization predict that, above $\sqrt{s}\approx 70$ GeV, ${\rho }_{pp}(s)$ becomes greater than ${\rho }_{\bar{p}p}(s)$, and this result is in complete agreement with all the data presently available. In particular, we infer ${\rho }_{pp}=0.134\pm 0.005$ at $\sqrt{s}=200$ GeV and $0.151\pm 0.007$ at 500 GeV (BNL RHIC energies).

16 pages, 7 figures, aps-revtex, wording changes, corrected typos, to appear in Physical Review D

References in corpus (1)

• Benchmarks for the Forward Observables at RHIC, the Tevatron-run II and the LHC

Cited by in corpus (20)

• Total cross-section and rapidity gap survival probability at the LHC through an eikonal with soft gluon resummation
• Total Hadronic Cross Section and the Elastic Slope: An Almost Model-Independent Connection
• QCD effective charge and the structure function $F_2$ at small-$x$
• Critical analysis of derivative dispersion relations at high energies
• Soft Pomerons and the Forward LHC Data
• On the rise of proton-proton cross-sections at high energies
• Extrema bounds for the soft Pomeron intercept
• A study on analytic parametrizations for proton-proton cross-sections and asymptotia
• Meson Structure Functions in Valon Model
• Phenomenological analysis connecting proton-proton and antiproton-proton elastic scattering
• Non-perturbative QCD effects in forward scattering at LHC
• An analysis on extrema and constrained bounds for the soft Pomeron intercept
• Phenomenological Analysis of $pp$ and $\bar{p}p$ Elastic Scattering Based on Theoretical Bounds in High-Energy Physics
• An updated analysis on the rise of the hadronic total cross-section at the LHC energy region
• Total Hadronic Cross Section Data and the Froissart-Martin Bound
• Analysis of $pp$ and $\bar{p}p$ Elastic Scattering Based on Theoretical Bounds in High-Energy Physics: an Update
• A model of diffractive excitation in $pp$ collisions at high energies
• Odderon and Pomeron as Fractal Dimension in $pp$ and $\bar{p}p$ Total Cross Sections
• The small $x$ behavior of the gluon structure function from total cross sections
• Soft Pomeron in light of the LHC correlated data