Crossing symmetry and infrared safety of quark-antiquark annihilation to all orders

The question of the degree of infrared (IR) safety of the Bloch-Nordsieck cross-section for quark-antiquark annihilation at high energy is reconsidered by using crossing symmetry. It is argued that this symmetry guarantees that the IR divergent part of the relevant scattering amplitudes is invariant under the inversion of the (anti)quark velocity β in the centre-of-mass frame, i.e., under β→β−1. Employing this consequence of the crossing symmetry, a fairly simple explanation is given of why the power suppression factor O((1−β2)2) of IR divergences extends from two- to all-loops order in the strong-coupling expansion, once it is known that the logarithmic term ln(1−β2) is absent from the IR divergent part of the cross-section.