We re-examine the extraction of rho(s,t), the ratio of the real part to the imaginary part of the scattering amplitude, and of the spin-flip amplitude, from the existing experimental data in the Coulomb-hadron interference region. We show that it is
not possible to find reasonable assumptions about the structure of the scattering amplitude of proton-proton and proton-antiproton elastic scattering at high energy that would lead, in proton-antiproton scattering for 3.8 < p_L <6 GeV/c, to an agreement between data and an analysis based on dispersion relations.
We consider two well-known classes of unitarization of Born amplitudes of hadron elastic scattering. The standard class, which saturates at the black disk limit includes the standard eikonal representation, while the other class, which goes beyond th
e black-disk limit to reach the full unitarity circle, includes the U matrix. It is shown that the basic properties of these schemes are independent of the functional form used for the unitarisation, and that U matrix and eikonal schemes can be extended to have similar properties. A common form of unitarisation is proposed interpolating between both classes. The correspondence with different nonlinear equations are also briefly examined.
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 tur
n 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.
The problems linked with the extraction of the basic parameters of the hadron elastic scattering amplitude at the LHC are explored. It is shown that one should take into account the saturation regime which will lead to new effects at the LHC.
We critically re-examine the calculation of central production of dijets in quasi-elastic hadronic collisions. We find that the process is not dominated by the perturbative contribution, and discuss several sources of uncertainties in the calculation.
The analytic properties of the eikonal and U-matrix unitarization schemes are examined. It is shown that the basic properties of these schemes are identical. Both can fill the full circle of unitarity, and both can lead to standard and non-standard a
symptotic relations for the ratio of the elastic cross section to the total cross section. The relation between the phases of the unitarized amplitudes in each scheme is examined, and it is shown that demanding equivalence of the two schemes leads to a bound on the phase in the U-matrix scheme.
The problems linked to the extraction of the basic parameters of the hadron elastic scattering amplitude at the LHC are explored. The impact of the Black Disk Limit (BDL)$-$ which constitutes a new regime of the scattering processes - on the determination of these values is examined.
