Regge models of the proton structure function with and without hard Pomeron: a comparative analysis

A comparative phenomenological analysis of Regge models with and without a hard Pomeron component is performed using a common set of recently updated data. It is shown that the data at small $x$ do not indicate explicitly the presence of the hard Pomeron. Moreover, the models with two soft-Pomeron components (simple and double poles in the angular momentum plane) with trajectories having intercept equal one lead to the best description of the data not only at $W>3$ GeV and at small $x$ but also at all $x\leq 0.75$ and $Q^{2}\leq 30000$ GeV$^{2}$.Comment: 21 pages, LaTeX2e, 4 eps figures, report number is added, some typos are correcte

Proton structure function. Soft and hard Pomerons

Regge models for proton structure function with and without a hard Pomeron contribution are compared with all available data in the region $W>3$ GeV, $Q^{2}\leq 3000$ GeV$^{2}$ and $x<0.75$. It is shown that the data do not support a hard Pomeron term in $\gamma^{*} p$ amplitude. Moreover, the data support the idea that the soft Pomeron, either is a double pole with $\alpha_{P}(0)=1$ in the angular momentum $j$-plane, or is a simple pole with $\alpha_{P}(0)=1+\epsilon$ where $\epsilon \ll 1$.Comment: 6 pages, LaTeX2e with elsart.sty, no figures. Talk given at the IX-th Blois Workshop on Elastic and Diffractive Scattering, Pruhonice near Prague, June, 2001, one reference is correcte

Rescattering corrections in elastic scattering

A detailed study of the rescattering series is performed within a model, using a generalized procedure of eikonalization and fitted to the $pp$ and $\bar pp$ elastic scattering data. We estimate and compare the various rescattering corrections to be added to the Born contribution in the amplitude. We find that their number is finite, whereas it increases with the energy and the transfer, like does their importance. In the domain where data exist, we find also that a correct computation must include, at least, all two- and three-Reggeon exchanges and some four- and five-Reggeon exchanges. Any approximation aiming to reduce this (large) number of exchange would be hazardous, especially when extrapolating. We extend our estimates in the domain of future experiments.Comment: LaTeX2e, 15 pages, 14 eps figure

Of Dips, Structures and Eikonalization

We have investigated several models of Pomeron and Odderon contributions to high energy elastic $pp$ and $\bar p p$ scattering. The questions we address concern their role in this field, the behavior of the scattering amplitude (or of the total cross-section) at high energy, and how to fit all high energy elastic data. The data are extremely well reproduced by our approach at all momenta and for sufficiently high energies. The relative virtues of Born amplitudes and of different kinds of eikonalizations are considered. An important point in this respect is that secondary structures are predicted in the differential cross-sections at increasing energies and these phenomena appear quite directly related to the procedure of eikonalizing the various Born amplitudes. We conclude that these secondary structures arise naturally within the eikonalized procedure (although their precise localization turns out to be model dependent). The fitting procedure naturally predicts the appearance of a zero at small $|t|$ in the real part of the even amplitude as anticipated by general theorems. We would like to stress, once again, how important it would be to have at LHC both $pp$ and $p \bar p$ options for many questions connected to the general properties of high energy hadronic physics and for a check of our predictions.Comment: 28 pages, LaTeX, 7 figure

Eikonalization and Unitarity Constraints

An extensive generalization of the ordinary and quasi-eikonal methods is presented for the $pp$ and $\bar pp$ elastic scattering amplitudes, which takes into account in a phenomenological way all intermediate multiparticle states involving the crossing even and crossing odd combinations of Reggeons. The formalism in this version involves a maximum of three parameters corresponding to the intermediate states which are possible in this configuration. The unitarity restriction is investigated and particular cases are discussed. An interesting result that emerges concerns the Odderon trajectory intercept: we find that unitarity dictates that this quantity {\it must} be below or equal unity unless a very peculiar equality exists between the coupling of the particles to the Pomeron and the Odderon.Comment: Latex2e, 22 pages, 4 eps figures included, version accepted for publication in Eur. Phys. J. C (some comments in Sect.2 and in Conclusion and one reference are added

Elastic pp and pˉp\bar pp scattering in the Modified Additive Quark Model

The modified additive quark model, proposed recently, allows to improve agreement of the standard additive quark model with the data on the $pp, \bar pp, \pi^{\pm} p, \gamma p$ and $\gamma \gamma$ total cross-sections, as well as on the ratios of real to imaginary part of $pp$ and $\bar pp$ amplitudes at $t=0$. Here, we extend this model to non forward elastic scattering of protons and antiprotons. A high quality reproduction of angular distributions at 19.4 GeV $\leq \sqrt{s}\leq$ 1800 Gev is obtained. A zero at small $|t|$ in the real part of even amplitude in accordance with a recently proved high energy general theorem is found.Comment: 14 pages, LaTeX2e, 4 eps figures. Revised version accepted for publication in European Physical Journal

The proton structure function and a soft Regge Dipole Pomeron: a test with recent data

A recently published soft Regge Dipole Pomeron model intended for all $x$ and $Q^2$ is proved to give a good agreement with (non fitted) recent HERA data from ZEUS (SVX95) on the protonstructure function $F_2^p(x,Q^2)$ at low $Q^2$ and low $x$. The model also reproduces (without fit) the recently estimated experimental derivatives ${\partial F_2^p\over\partial\ell n Q^2}$ and ${\partial \ell n F_2^p\over\partial\ell n (1/x)}$ in a wide $x$ and $Q^2$-region.Comment: 5 pages (LaTeX), 4 figures (Encapsulated PS

New possibilities of old soft pomeron in DIS

A traditional Regge model with a $Q^2$-independent Pomeron intercept closed (or equal) to one is constructed in order to describe the available data on the proton structure function. A Dipole Pomeron model which does not explicitly violate unitarity is developed and investigated. An excellent agreement with the 1209 data is found ($\chi^2/{dof}=1.11$) in the whole kinematical domain investigated by experiments. A comparison of the model with already existing ones is made. The $x-$, $Q^2-$slopes and the effective intercept are discussed as $Q^2$ and $x$ functions.Comment: 19 pages LaTeX, 10 eps figures included, one of figure captions is correcte