The total nucleon-nucleon cross section at large N_c

TL;DR

This paper derives a large N_c limit for the total nucleon-nucleon cross section, showing it becomes momentum-independent and scales with log-squared of N_c, with potential links to the Froissart-Martin bound.

Contribution

It provides a theoretical prediction for the nucleon-nucleon cross section at large N_c, extending understanding of QCD in this regime.

Findings

Cross section becomes momentum-independent at large N_c.

Total cross section scales as log^2(N_c).

Results connect to the Froissart-Martin bound.

Abstract

It is shown that at sufficiently large $N_c$ for incident momenta which are much larger than the QCD, the total nucleon-nucleon cross section is independent of incident momentum and given by $\sigma^{\rm total}=2 \pi \log^2(N_c) / (m^2_{\pi})$. This result is valid in the extreme large $N_c$ regime of $\log(N_c) \gg 1$ and has corrections of relative order $\log (\log(N_c))/\log(N_c)$. A possible connection of this result to the Froissart-Martin bound is discussed.