Self-similarity and the Froissart bound

Abstract

The Froissart bound implies that the total cross section (or, equivalently, the structure function) cannot rise faster than the logarithmic growth of ${\ln }^2\left(\frac{1}{x}\right)$. In this work, we show that such a slow growth is not compatible with the notion of self-similarity. As a result, it calls for the modification of the defining transverse-momentum-dependent parton density function (TMD PDF) of a self-similarity based proton structure function $F_2\left(x,Q^2\right)$ at small \textit{x}. Using plausible assumptions, we obtain the Froissart saturation condition on this TMD PDF.

11 pages, 2 figures, 1 table

References in corpus (5)

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Cited by in corpus (3)

• Proton structure functions at low $x$: the Fractal distributions
• Froissart bound and self-similarity based models of proton structure functions
• An overview of scale invariance in proton structure with holographic insights