Exact treatment of dispersion relations in pp and p\=p elastic scattering

Based on a study of the properties of the Lerch's transcendent, exact closed forms of dispersion relations for amplitudes and for derivatives of amplitudes in pp and p\=p scattering are introduced. Exact and complete expressions are written for the real parts and for their derivatives at $t=0$ based on given inputs for the energy dependence of the total cross sections and of the slopes of the imaginary parts. The results are prepared for application in the analysis of forward scattering data of the pp and p\=p systems at all energies, where exact and precise representations can be written.Comment: 23 pages, 1 figur

Elastic amplitudes studied with the LHC measurements at 7 and 8 TeV

Recent measurements of the differential cross sections in the forward region of pp elastic scattering at 7 and 8 TeV show precise form of the $t$ dependence. We propose a detailed analysis of these measurements including the structures of the real and imaginary parts of the scattering amplitude. A good description is achieved, confirming in all experiments the existence of a zero in the real part in the forward region close to the origin, in agreement with the prediction of a theorem by A. Martin, with important role in the observed form of $d\sigma/dt$. Universal value for the position of this zero and regularity in other features of the amplitudes are found, leading to quantitative predictions for the forward elastic scattering at 13 TeV.Comment: 22 pages, 17 figures and 4 table

Photon and Pomeron -- induced production of Dijets in pppp, pApA and AAAA collisions

In this paper we present a detailed comparison of the dijet production by photon -- photon, photon -- pomeron and pomeron -- pomeron interactions in $pp$, $pA$ and ${\rm AA}$ collisions at the LHC energy. The transverse momentum, pseudo -- rapidity and angular dependencies of the cross sections are calculated at LHC energy using the Forward Physics Monte Carlo (FPMC), which allows to obtain realistic predictions for the dijet production with two leading intact hadrons. We obtain that \gamma \pom channel is dominant at forward rapidities in $pp$ collisions and in the full kinematical range in the nuclear collisions of heavy nuclei. Our results indicate that the analysis of dijet production at the LHC can be useful to test the Resolved Pomeron model as well as to constrain the magnitude of the absorption effects.Comment: 11 pages, 6 figures, 1 table. Improved and enlarged version published in European Physical Journal