Comments on high-energy total cross sections in QCD

Abstract

We discuss how hadronic total cross sections at high energy depend on the details of QCD, namely on the number of colours Nc and the quark masses. We find that while a “Froissart”-type behaviour σtot∼Blog2⁡s 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 O(Nc0) at large Nc, and we discuss a bound for B which does not become singular in the Nf=2 chiral limit, unlike the Froissart–Łukaszuk–Martin bound. Keywords: Total cross sections, QCD, Nonperturbative approach