  Wilson lines capture important features of scattering amplitudes, for example
soft effects relevant for infrared divergences, and the Regge limit. Beyond the
leading power approximation, corrections to the eikonal picture have to be
taken into account. In this paper, we study such corrections in a model of
massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit,
where the mass is generated through a Higgs mechanism. Using known three-loop
analytic expressions for the scattering amplitude, we find that the first power
suppressed term has a very simple form, equal to a single power law. We propose
that its exponent is governed by the anomalous dimension of a Wilson loop with
a scalar inserted at the cusp, and we provide perturbative evidence for this
proposal. We also analyze other limits of the amplitude and conjecture an exact
formula for a total cross-section at high energies.
