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arXiv · 1401.4327

Self-similarity and the Froissart bound

Akbari Jahan·D. K. Choudhury
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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.

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Akbari Jahan, D. K. Choudhury. 2014-01-17. Self-similarity and the Froissart bound. https://doi.org/10.1103/physrevd.89.014014

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