One particle cross section in the target fragmentation region: an explicit calculation in (φ³)₆

One particle inclusive cross sections in the target fragmentation region are considered and an explicit calculation is performed in (\phi^3)_6 model field theory. The collinear divergences can be correctly absorbed into a parton density and a fragmentation function but the renormalized cross section gets a large logarithmic correction as expected in a two scale regime. We find that the coefficient of such a correction is precisely the scalar DGLAP kernel. Furthermore the consistency of this result with an extended factorization hypothesis is investigated.