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Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all high energy region, the behavior of observables in the LHC collisions in the range $sqrt{s}$ = 2.76 - 14 TeV is discussed. Similarly to the case of 7 TeV data, the proposed amplitudes give excellent description of the preliminary 8 TeV data. We discuss the expected energy dependence of the observable quantities, and present predictions for the experiments at 2.76, 13 and 14 TeV.
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With analytical representation for the pp scattering amplitudes introduced and tested at lower energies, a description of high precision is given of the $dsigma/dt$ data at $sqrt{s}$= 13 TeV for all values of the momentum transfer, with explicit identification of the real and imaginary parts. In both $t$ and $b$ coordinates the amplitudes have terms identified as of non-perturbative and perturbative nature, with distinction of their influences in forward and large $|t|$ ranges and in central and peripheral regions respectively. In the forward range, the role of the Coulomb-nuclear interference phase is investigated. The energy dependence of the parameters of the amplitudes are reviewed and updated, revealing a possible emergence of a peculiar behavior of elastic and inelastic profiles in b-space for central collisions, which seems to be enhanced quickly at higher energies. Some other models are also briefly discussed in comparison, including the above mentioned behavior in b-space.
Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all energy region, the behavior of observables in the LHC collisions in the range $sqrt{s}$= 2.76 - 14 TeV is discussed. Similarly to the case of 7 TeV data, the proposed amplitudes give excellent description of the preliminary 8 TeV data. We discuss the expected energy dependence of the observable quantities, and present predictions for the experiments at 2.76, 13 and 14 TeV.
Exact analytical forms of solutions for Dispersion Relations for Amplitudes and Dispersion Relations for Slopes are applied in the analysis of pp and $rm {p bar p}$ scattering data in the forward range at energies below $sqrt(s)approx 30 GeV$. As inputs for the energy dependence of the imaginary part, use is made of analytic form for the total cross sections and for parameters of the $t$ dependence of the imaginary parts, with exponential and linear factors. A structure for the $t$ dependence of the real amplitude is written, with slopes $B_R$ and a linear factor $rho-mu_R t$ that allows compatibility of the data with the predictions from dispersion relations for the derivatives of the real amplitude at the origin. A very precise description is made of all $dsigma/dt$ data, with regular energy dependence of all quantities. It is shown that a revision of previous calculations of total cross sections, slopes and $rho$ parameters in the literatures is necessary, and stressed that only determinations based on $dsigma/dt$ data covering sufficient $t$ range using appropriate forms of amplitudes can be considered as valid.
Elastic scattering data gained for proton-proton collisions at high energies are being analyzed at the present practically only with the help of purely phenomenological mathematical models. And the question exists whether in the impact parameter plane the elastic processes may be interpreted as central or peripheral. From realistic point of view the peripherality should be preferred and one may expect that nucleon dimensions should manifest in some way in elastic data. It will be demonstrated that the elastic pp data at the energy of 53 GeV in the interval |t| from (0., 4.) [GeV^2] may be interpreted well as the superposition of mutual collisions of two internal structures with maximal external dimensions; the approximate dimensions and frequencies of corresponding structures being established on the basis of measured elastic data.
We predict pp elastic differential cross sections at LHC at c.m. energy 14 TeV and momentum transfer range |t| = 0 - 10 GeV*2 in a nucleon-structure model. In this model, the nucleon has an outer cloud of quark-antiquark condensed ground state, an inner shell of topological baryonic charge (r ~ 0.44F) probed by the vector meson omega, and a central quark-bag (r ~ 0.2F) containing valence quarks. We also predict elastic differential cross section in the Coulomb-hadronic interference region. Large |t| elastic scattering in this model arises from valence quark-quark scattering, which is taken to be due to the hard-pomeron (BFKL pomeron with next to leading order corrections). We present results of taking into account multiple hard-pomeron exchanges, i.e. unitarity corrections. Finally, we compare our prediction of pp elastic differential cross section at LHC with the predictions of various other models. Precise measurement of pp elastic differential cross section at LHC by the TOTEM group in the |t| region 0 - 5 GeV*2 will be able to distinguish between these models.
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