| Summary: | Steep rise of parton densities in the limit of small parton momentum fraction <i>x</i> poses a challenge for describing the observed energy-dependence of the total and inelastic proton-proton cross sections <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>σ</mi> <mrow> <mi>p</mi> <mi>p</mi> </mrow> <mrow> <mi>tot</mi> <mo>/</mo> <mi>inel</mi> </mrow> </msubsup> </semantics> </math> </inline-formula>: considering a realistic parton spatial distribution, one obtains a too-strong increase of <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>σ</mi> <mrow> <mi>p</mi> <mi>p</mi> </mrow> <mrow> <mi>tot</mi> <mo>/</mo> <mi>inel</mi> </mrow> </msubsup> </semantics> </math> </inline-formula> in the limit of very high energies. We discuss various mechanisms which allow one to tame such a rise, paying special attention to the role of parton-parton correlations. In addition, we investigate a potential impact on model predictions for <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>σ</mi> <mrow> <mi>p</mi> <mi>p</mi> </mrow> <mi>tot</mi></msubsup></semantics></math></inline-formula>, related to dynamical higher twist corrections to parton-production processes.
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