It is shown that at sufficiently large $N_c$ for incident momenta which are much larger than the QCD scale, 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 $\log \mathbf{(}\log (N_c)\mathbf{)}/\log (N_c)$. A possible connection of this result to the Froissart-Martin bound is discussed.

• Received 10 April 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.262301