The total cross section for proton-proton interactions at the FCC

TL;DR

This paper estimates the possible range of total proton-proton cross sections at the Future Circular Collider using dispersion relations and theoretical models, providing bounds for future experimental and theoretical work.

Contribution

It introduces a method to estimate lower and upper bounds of $\sigma_{tot}$ at FCC-hh energies using dispersion relations and $ln^{2}(s)$ evolution, and discusses intermediate models.

Findings

Lower limit based on dispersion relations and LHC data.

Upper limit derived from $ln^{2}(s)$ growth model.

Discussion of models within the estimated bounds.

Abstract

The lower and upper limits of the total cross section ($\sigma_{tot}$) at the projected FCC-hh have been estimated. A lower limit has been estimated using dispersion relations in combination with recent LHC data of $\sigma_{tot}$ and the $\rho$-parameter. The upper limit has been estimated using the standard $ln^{2}(s) $ evolution of $\sigma_{tot}$. Some models giving values in between those limits are also discussed.