# Froissart bound and self-similarity based models of proton structure functions

## TL;DR

This paper explores how self-similarity models of proton structure functions can be compatible with the Froissart bound, which limits the growth of the structure function at high energies, and compares these models with recent experimental data.

## Contribution

The authors generalize previous self-similarity models to incorporate Froissart bound constraints and analyze their validity against recent HERA data and existing models.

## Key findings

- Froissart-compatible models can fit HERA data within limited x-Q^2 ranges.
- Models with logarithmic growth are more constrained than power-law models.
- Phenomenological validity of Froissart-compatible models is narrower than power-law models.

## 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. Compatibility of such behavior with the notion of self-similarity in a model of structure function suggested by us sometime back is now generalized to more recent improved self-similarity based models and compare with recent data as well as with the model of Block, Durand, Ha and McKay. Our analysis suggests that Froissart bound compatible self-similarity based models are possible with $\log^2 1/x$ rise in limited $x-Q^2$ ranges of HERA data, but their phenomenological ranges validity are narrower than the corresponding models having power law rise in $1/x$.