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Interpretation of the measurements of total, elastic and diffractive cross sections at LHC

Recently at LHC one has obtained measurements of the total, elastic and diffractive cross sections in pp collisions at very high energy. The total cross section is in good agreement with predictions based on a leading behavior σ_{tot} (s) \propto (\ln s/s_0)^2, on the other hand the elastic cross section is lower than most expectations and the diffractive cross section is higher. It is remarkable that the ratio (σ_{el} + σ_{diff})/σ_{tot} calculated combining the results of the TOTEM and ALICE detectors is 0.495^{+0.05}_{-0.06}, very close to the maximum theoretically allowed value of 1/2 known as the Miettinen Pumplin bound. In this work we discuss these results using the frameworks of single and multi--channel eikonal models, and outline the main difficulties for a consistent interpretation of the data.