Saturation and non-linear effects in diffractive processes

Through a direct implementation of the saturation regime resulting from the unitarity limit in the impact parameter representation, we explore various possibilities for the energy dependence of hadronic scattering. We show that it is possible to obtain a good description of the scattering amplitude from a hard pomeron provided one includes non-linear effects.Comment: Contribution to the XIth International Conference on Symmetry Methods in Physics (SYMPHYS-11), Prague, 21st to 24th June, 2004. 9 pages, 3 figures, uses icsm.cls (provided). Typos fixed in version

Comparison of different non-linear equations and corresponding unitarization schemes

Different forms of non-linear equations which mimic parton saturation in the non-perturbative regime are examined. These equations lead to corresponding unitarization schemes in the impact parameter representation of the hadron scattering amplitude. It is shown how specific properties of the non-linear equations reflect different features of the diffraction processes.Comment: 7 pages, 5 figures, needs PoS.cls and PoSlogo, contribution to the proceedings of the International Workshop on Diffraction in High-Energy Physics "DIFFRACTION 2006", Adamantas, Milos island, Greece, September 5 - 10, 200

An Analysis of the New LHC Data through the Dispersion Relations

We analyse the tension between the (indirect) measurements of the total cross section, and show the impact of various assumptions on the extraction of the parameters from the elastic scattering amplitude, with a special attention to the total cross section. In particular, the determination of the phase of the elastic scattering amplitude will play an important role, and we shall study it via dispersion relations. We shall also examine the origin of the dependence on momentum transfer of the slopes of the different parts of the scattering amplitude in different models. We shall also give the results of another similar analysis based on a Regge-trajectory approach for the hadron scattering amplitude.Comment: 5 page

Long-range potential and the fine structure of the diffraction peak

The possibility of oscillations in the differential elastic cross section of hadron scattering at small momentum transfer is studied. It is shown that string-like quark potentials at large distances can lead to such small oscillations, and an analysis of the experimental data at small $|t|$ allows the determination of the parameters of the potential.Comment: 6 pages, 6 figures, Talk presented at the International Workshop on Diffraction in High-Energy Physics, Otranto (Lecce, Italy), September 10-15, 201

Analytic properties of unitarization schemes

The analytic properties of the elastic hadron scattering amplitude are examined in the impact parameter representation at high energies. Different unitarization procedures and the corresponding non-linear equations are presented. Several unitarisation schemes are presented. They lead to almost identical results at the LHC.Comment: 7 pages, needs class cjpsuppl.cls (provided), to appear in the proceedings of the Advanced Studies Institute on Symmetries and Spin, SPIN-Praha-2006, Czech. J. Phys. 56 (2006

How precisely will the total cross section be measured at the LHC?

It is very likely that hadronic scattering will enter a new regime at the LHC, as the black-disk limit is reached. This will lead to a severe change in the t dependence of the real part and of the slope of the elastic scattering amplitude, and in turn this may bias the measurement of the total cross section. We examine this issue, and suggest new strategies to test the reliability of the total cross section measurements.Comment: 4 pages, 6 figure

Saturation effects in diffractive scattering at LHC energies

Unitarization schemes can be reduced to non-linear equations which saturate at small $b$ the evolution of the elastic amplitude with $s$, and which mimic parton saturation in the non-perturbative regime. These equations enable us to study the effect of saturation on total and elastic cross sections for various models, and to evaluate the uncertainties on $\sigma_{tot}$ and $\rho(s,t)$ at the LHC in the presence of a hard pomeron.Comment: 4 pages, 3 figures, report at XXXIII IHEP, Moscow, July 26 - August 2, 200