  We consider light-like Wilson loops with hexagonal geometry in the planar
limit of N=4 Super-Yang-Mills theory. Within the Operator-Product-Expansion
framework these loops receive contributions from all states that can propagate
on top of the colour flux tube sourced by any two opposite edges of the loops.
Of particular interest are the two-particle contributions. They comprise
virtual effects like the propagation of a pair of scalars, fermions, and
gluons, on top of the flux tube. Each one of them is thoroughly discussed in
this paper. Our main result is the prediction of all the twist-2 corrections to
the expansion of the dual 6-gluons MHV amplitude in the near-collinear limit at
finite coupling. At weak coupling, our result was recently used by Dixon,
Drummond, Duhr and Pennington to predict the full amplitude at four loops. At
strong coupling, it allows us to make contact with the classical string
description and to recover the (previously elusive) AdS(3) mode from the
continuum of two-fermion states. More generally, the two-particle contributions
serve as an exemplar for all the multi-particle corrections.
