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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.
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The following effects in the nearly forward (soft) region of the LHC are proposed to be investigated: 1) At small |t| the fine structure of the cone (Pomeron) shouldbe scrutinized: a) a break of the cone near $tapprox - 0.1 ~ GeV$^2, due to the two-pion threshold, and required by t-channel unitarity, is expected, and b) possible small-period oscillations between $t=0$ and the dip region. 2) In measuring the elastic $pp$ scattering and total $pp$ cross section at the LHC, the experimentalists are urged to treat the total cross section $sigma_t,$ the ratio $rho$, the forward slope $B$ and the luminosity ${cal L}$ as free arameters, and to publish model-independent results on ${dN/{dt}}.$ 3) Of extreme interest are the details of the expected diffraction minimum in the differential cross section. Its position, expected in the interval $0.4<-t<1$ GeV$^2$ at the level of about $10^{-2} {rm mb} cdot$ GeV$^{-2}div 10^{-1} {rm mb}cdot$ GeV$^{-2}$, cannot be predicted unambiguously, and its depth, i.e. the ratio of $dsigma/dt$ at the minimum to that at the subsequent maximum (about $-t=5 $GeV$^2$, which is about 5 is of great importance. 4) The expected slow-down with increasing $|t|$ of the shrinkage of the second cone (beyond the dip-bump), together with the transition from an exponential to a power decrease in $-t$, will be indicative of the transition from soft to hard physics. Explicit models are proposed to help in quantifying this transition. 5) In a number of papers a limiting behavior, or saturation of the black disc limit (BDL) was predicted. This controversial phenomenon shows that the BDL may not be the ultimate limit.
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.
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 consider possible saturation effects in the structure function $F_L$ at fixed W in HERA energy range and in $bbar b-$production at LHC energies in the framework of $k_T-$facrorization approach.
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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