We compute the tree level cross section for gluon-gluon elastic scattering taking into account a dynamical gluon mass, and show that this mass scale is a natural regulator for this subprocess cross section. Using an eikonal approach in order to examine the relationship between this gluon-gluon scattering and the elastic pp andpp channels, we found that the dynamical gluon mass is of the same order of magnitude as the ad hoc infrared mass scale m 0 underlying eikonalized QCD-inspired models. We argue that this correspondence is not an accidental result, and that this dynamical scale indeed represents the onset of nonperturbative contributions to the elastic hadron-hadron scattering. We apply the eikonal model with a dynamical infrared mass scale to obtain predictions for σ pp,pp tot , ρ pp,pp , slope B pp,pp , and differential elastic scattering cross section dσp p /dt at Tevatron and CERN-LHC energies.

By means of empirical fits to the differential cross section data on pp andpp elastic scattering, above 10 GeV (center-of-mass energy), we determine the eikonal in the momentum -transfer space (q 2 -space). We make use of a numerical method and a novel semi-analytical method, through which the uncertainties from the fit parameters can be propagated up to the eikonal in the q 2 -space. A systematic study of the effect of the experimental information at large values of the momentum transfer is developed and discussed in detail. We present statistical evidence that the imaginary part of the eikonal changes sign in the q 2 -space and that the position of the zero decreases as the energy increases; after the position of the zero, the eikonal presents a minimum and then goes to zero through negative values. We discuss the applicability of our results in the phenomenological context, outlining some connections with nonperturbative QCD. A short review and a critical discussion on the main results concerning "model-independent" analyses are also presented.PACS. 13.85.Dz Elastic scattering -13.85.-t Hadron-induced high-energy interactions

We discuss some formal and fundamental aspects related with the replacement of integral dispersion relations by derivative forms, and their practical uses in high energy elastic hadron scattering, in particular $pp$ and $\bar{p}p$ scattering. Starting with integral relations with one subtraction and considering parametrizations for the total cross sections belonging to the class of entire functions in the logarithm of the energy, a series of results is deduced and our main conclusions are the following: (1) except for the subtraction constant, the derivative forms do not depend on any additional free parameter; (2) the only approximation in going from integral to derivative relations (at high energies) concerns to assume as zero the lower limit in the integral form; (3) the previous approximation and the subtraction constant affect the fit results at both low and high energies and therefore, the subtraction constant can not be disregarded; (4) from a practical point of view, for single-pole Pomeron and secondary reggeons parametrizations and center-of-mass energies above 5 GeV, the derivative relations with the subtraction constant as a free fit parameter are completely equivalent to the integral forms with finite (non-zero) lower limit. A detailed review on the conditions of validity and assumptions related with the replacement of integral by derivative relations is also presented and discussed.Comment: Revised version, 30 pages, 16 eps-figures, elsart.cls (included), to appear in Nucl Phys.

Abstract. Based on the behavior of the elastic scattering data, we introduce an almost model-independent parametrization for the imaginary part of the scattering amplitude, with the energy and momentum transfer dependences inferred on empirical basis and selected by rigorous theorems and bounds from axiomatic quantum field theory. The corresponding real part is analytically evaluated by means of dispersion relations, allowing connections between particle-particle and particle-antiparticle scattering. Simultaneous fits to proton-proton and antiproton-proton experimental data in the forward direction and also including data beyond the forward direction, lead to a predictive formalism in both energy and momentum transfer. We compare our extrapolations with predictions from some popular models and discuss the applicability of the results in the normalization of elastic rates that can be extracted from present and future accelerator experiments (Tevatron, RHIC and LHC).PACS. 13.85.Dz Elastic scattering -13.85.-t Hadron-induced high-energy interactions

A forward amplitude analysis on pp andpp elastic scattering above 5 GeV is presented. The dataset includes the recent high-precision TOTEM measurements of the pp total and elastic (integrated) cross-sections at 7 TeV and 8 TeV. Following previous works, the leading high-energy contribution for the total cross-section (σtot) is parametrized as ln γ (s/s h ), where γ and s h are free real fit parameters. Singly-subtracted derivative dispersion relations are used to connect σtot and the rho parameter (ρ) in an analytical way. Different fit procedures are considered, including individual fits to σtot data, global fits to σtot and ρ data, constrained and unconstrained data reductions. The results favor a rise of the σtot faster than the log-squared bound by Froissart and Martin at the LHC energy region. The parametrization for σtot is extended to fit the elastic cross-section (σ el ) data with satisfactory results. The analysis indicates an asymptotic ratio σ el /σtot consistent with 1/3 (as already obtained in a previous work). A critical discussion on the correlation, practical role and physical implications of the parameters γ and s h is presented. The discussion confronts the 2002 prediction of σtot by the COMPETE Collaboration and the recent result by the Particle Data Group (2012 edition of the Review of Particle Physics). Some conjectures on possible implications of a fast rise of the proton-proton total cross-section at the highest energies are also presented.