The total nucleon-nucleon cross section at large N_c

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 ${\sigma }^{\mathrm{total}}=2\pi {\log }^2(N_c)/(m_{\pi }^2)$. 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.

Comments: 4 pages