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 ( Φ³) 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 as precisely the scalar DGLAP kernel. Furthermore, the consistency of this result with an extended factorization hypothesis is investigated.