Matching collinear and small x factorization calculations for inclusive hadron production in pA collisions

We construct a theoretical framework to match the formulas for forward inclusive hadron productions in $pA$ collisions in the small x saturation formalism and collinear factorization. The small x calculation can be viewed as a power series in Qₛ²/k_⊥², in which the collinear factorization result corresponds to the leading term. At high transverse momentum, the subleading correction terms are insignificant, whereas at low p_⊥, the power corrections become important and the small x resummation is essential to describe the differential cross section. We show that the familiar collinear factorization calculation can smoothly match the results from small x factorization at next-to-leading order in αₛ when we use exact kinematics, as opposed to the approximate kinematics in previous work. With this matching, we can describe the experimental data from the RHIC very well at high p_⊥.