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Comments on high-energy total cross sections in QCD

We discuss how hadronic total cross sections at high energy depend on the details of QCD, namely on the number of colours $N_c$ and the quark masses. We find that while a "Froissart"-type behaviour $σ_{\rm tot}\sim B\log^2s$ is rather general, relying only on the presence of higher-spin stable particles in the spectrum, the value of $B$ depends quite strongly on the quark masses. Moreover, we argue that $B$ is of order ${\cal O}(N_c^0)$ at large $N_c$, and we discuss a bound for $B$ which does not become singular in the $N_f=2$ chiral limit, unlike the Froissart-Łukaszuk-Martin bound.