  Using the formalism of the light-cone wave function in perturbative QCD
together with the hybrid factorization, we compute the cross-section for three
particle production at forward rapidities in proton-nucleus collisions. We
focus on the quark channel, in which the three produced partons -- a quark
accompanied by a gluon pair, or two quarks plus one antiquark -- are all
generated via two successive splittings starting with a quark that was
originally collinear with the proton. The three partons are put on-shell by
their scattering off the nuclear target, described as a Lorentz-contracted
"shockwave". The three-parton component of the quark light-cone wave function
that we compute on this occasion is also an ingredient for other interesting
calculations, like the next-to-leading order correction to the cross-section
for the production of a pair of jets.
