The Pomeron and Odderon in elastic, inelastic and total cross sections at the LHC

A simple model for elastic diffractive hadron scattering, reproducing the dip-bump structure is used to analyze PP and $\bar PP$ scattering. The main emphasis is on the delicate and non-trivial dynamics in the dip-bump region, near t=-1 GeV$^2$. The simplicity of the model and the expected smallness of the absorption corrections enables one the control of various contributions to the scattering amplitude, in particular the interplay between the C-even and C-odd components of the amplitude, as well as their relative contribution, changing with s and t. The role of the non-linearity of the Regge trajectories is scrutinized. The ratio of the real to imaginary parts of the forward amplitude, the ratio of elastic to total cross sections and the inelastic cross section are calculated. Predictions for the LHC energy region, where most of the exiting models will be either confirmed or ruled out, are presented.Comment: 16 pages, 13 figures. Small correction. To be published in the International Journal of Modern Physics

The soft and the hard pomerons in hadron elastic scattering at small t

We consider simple-pole descriptions of soft elastic scattering for pp, pbar p, pi+ p, pi- p, K+ p and K- p. We work at t and s small enough for rescatterings to be neglected, and allow for the presence of a hard pomeron. After building and discussing an exhaustive dataset, we show that simple poles provide an excellent description of the data in the region - 0.5 GeV^2 < t < -0.1 GeV^2, 6 GeV<sqrt(s)< 63 GeV. We show that new form factors have to be used, and get information on the trajectories of the soft and hard pomerons.Comment: 27 pages, 9 figures, LaTeX. A few typos fixed, and references correcte

Elastic scattering of hadrons

Colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high energies, elastic scattering contributes considerably (18-25%) to the total cross section. Its share first decreases and then increases at higher energies. Small-angle scattering prevails at all energies. Some characteristic features are seen that provide informationon the geometrical structure of the colliding particles and the relevant dynamical mechanisms. The steep Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoulders and dips, and then by a power-law drop. Results from various theoretical approaches are compared with experimental data. Phenomenological models claiming to describe this process are reviewed. The unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power-law, hard parton scattering regime under high momentum transfer. Data on the interference of the Coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering nuclear amplitude. The real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude (the so-called overlap function) at nonforward transferred momenta are also discussed. Problems related to the scaling behavior of the differential cross section are considered. The power-law regime at highest momentum transfer is briefly described.Comment: 72 pages, 11 Figures; modified Physics-Uspekhi 56 (2013)

Local nuclear slope and curvature in high energy pppp and p‾p\overline{p}p elastic scattering

The local nuclear slope $B(s,t) = {d \over d t} (\ln {d\sigma_n (s,t)\over dt})$ is reconstructed from the experimental angular distributions with a procedure that uses overlapping $t$-bins, for an energy that ranges from the ISR to the $S\bar ppS$ and the Tevatron. Predictions of several models of ($p,p$) and ($\bar p,p$) elastic scattering at high energy are tested in $B(s,t)$ at small $|t|$. Only a model with two-components Pomeron and Odderon gives a satisfactory agreement with the (non fitted) slope data, in particular for the evolution of $B(s,t)$ with $s$ as a function of $t$ in $\bar pp$ scattering. This model predicts a similar behavior for $pp$ and $\bar pp$ scattering at small $|t|$. A detailed confirmation for $pp$ collisions would be expected from RHIC