  A prescription is presented to construct manifestly gauge invariant
tree-level scattering amplitudes with one or two off-shell initial-state gluons
for processes with arbitrary particles in the final state, which allows for
calculations that are efficient and easy to automate. These scattering
amplitudes are relevant for factorization schemes beyond collinear
factorization that allow the gluons entering the partonic cross section to have
non-vanishing transversal momentum components.
