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∼Blog2s 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.
Highlights
The behaviour of hadronic total cross sections at high energy is one of the oldest puzzles of strong interactions
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
In a recent paper [31] we have argued, within the abovementioned nonperturbative approach [23,24,25,26,27,28,29,30] in Euclidean space [32,33], that hadron–hadron total cross sections at high energy behave like σtot ∼ B(1 − κ) log2 s ≤ 2B log2 s
Summary
The behaviour of hadronic total cross sections at high energy is one of the oldest puzzles of strong interactions. Martin bound [36,37,38], and only about 50–60% larger than the experimental value, resulting in a much more restrictive “Froissartlike” bound (which is satisfied by Bexp) It is part of the standard lore that hadronic total cross sections should be mostly governed by the “gluonic sector” of the theory, and this leads to expect that they could be described fairly accurately using the quenched approximation of QCD, i.e., pure SU (3). Since only the stable spectrum enters the maximisation (2), the crucial point is to understand how the stability of hadrons changes as the parameters are varied, and how this affects the overall scale of total cross sections This is precisely the purpose of this paper.
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