Froissart Bound and Transverse Momentum Dependent Parton Distribution Functions (TMDPDF) with self-similarity

Froissart Bound implies that the total proton-proton cross-section (or equivalently structure function) cannot rise faster than the logarithmic growth ${\log }^{2}s\sim {\log }^2(1\mathrm{/}x)$, where $\mathit{\text{s}}$ is the square of the center of mass energy and $\mathit{\text{x}}$ is the Bjorken variable. In the present report, compatibility of such behavior will be shown in case of Transverse Momentum Dependent Parton Distributions Functions (TMDPDF) or TMDs for the model of proton based on self-similarity.