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

TL;DR

This paper demonstrates that the Froissart bound, which limits the growth of proton cross-sections, is compatible with a self-similar model of TMDPDFs, ensuring theoretical consistency in high-energy physics.

Contribution

It shows the compatibility of Froissart bound with a self-similar model of TMDPDFs, linking fundamental bounds with parton distribution models.

Findings

Froissart bound constrains TMDPDF growth at high energies.

Self-similar model aligns with the logarithmic growth limit.

Theoretical consistency between bounds and TMD models is established.

Abstract

Froissart Bound implies that the total proton-proton cross-section (or equivalently structure function) cannot rise faster than the logarithmic growth $\log^2 s \sim \log^2 (1/x)$, where \textit{s} is the square of the center of mass energy and \textit{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.