We calculate inclusive hadrons production in $pA$ collisions in the small-$x$ saturation formalism at one-loop order. The differential cross section is written into a factorization form in the coordinate space at the next-to-leading order, while the naive form of the convolution in the transverse momentum space does not hold. The rapidity divergence with small-$x$ dipole gluon distribution of the nucleus is factorized into the energy evolution of the dipole gluon distribution function, which is known as the Balitsky-Kovchegov equation. Furthermore, the collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final state hadron are factorized into the splittings of the associated parton distribution and fragmentation functions, which allows us to reproduce the well-known Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation. The hard coefficient function, which is finite and free of divergence of any kind, is evaluated at one-loop order.

• Received 29 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.054005