Hadronic total cross sections at high energy and the QCD spectrum

Abstract

We show how to obtain the leading energy dependence of hadronic total cross sections, in the framework of the nonperturbative approach to soft high-energy scattering based on Wilson-loop correlation functions, if certain nontrivial analyticity assumptions are satisfied. The total cross sections turn out to be of "Froissart" type, $\sigma_{\rm tot}^{(hh)}(s) \mathop\sim B\log^2 s$ for ${s \to \infty}$. We also discuss under which conditions the coefficient $B$ is universal, i.e., independent of the hadrons involved in the scattering process. In the most natural scenarios for universality, $B$ can be related to the stable spectrum of QCD, and is predicted to be $B_{\rm th}\simeq 0.22~{\rm mb}$, in fair agreement with experimental results. If we consider, instead, the stable spectrum of the quenched (i.e., pure-gauge) theory, we obtain a quite larger value $B^{(Q)}_{\rm th} \ge 0.42~{\rm mb}$, suggesting (quite surprisingly) large unquenching effects due to the sea quarks.