Comments on high-energy total cross sections in QCD

TL;DR

This paper examines how high-energy hadronic total cross sections in QCD depend on parameters like the number of colors and quark masses, highlighting the conditions for Froissart-like behavior and bounds on the coefficient B.

Contribution

It provides a detailed analysis of the dependence of total cross section behavior on QCD parameters and proposes bounds on the coefficient B that remain finite in the chiral limit.

Findings

Froissart-like behavior is general given higher-spin stable particles.

The coefficient B depends strongly on quark masses.

B is of order N_c^0 at large N_c and has a non-singular bound in the chiral limit.

Abstract

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 $\sigma_{\rm tot}\sim B\log^2s$ 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-\L ukaszuk-Martin bound.