  Planar N=4 super Yang-Mills appears to be integrable. While this allows to
find this theory's exact spectrum, integrability has hitherto been of no direct
use for scattering amplitudes. To remedy this, we deform all scattering
amplitudes by a spectral parameter. The deformed tree-level four-point function
turns out to be essentially the one-loop R-matrix of the integrable N=4 spin
chain satisfying the Yang-Baxter equation. Deformed on-shell three-point
functions yield novel three-leg R-matrices satisfying bootstrap equations.
Finally, we supply initial evidence that the spectral parameter might find its
use as a novel symmetry-respecting regulator replacing dimensional
regularization. Its physical meaning is a local deformation of particle
helicity, a fact which might be useful for a much larger class of
non-integrable four-dimensional field theories.
