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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 $Q_s^2/k_\perp^2$, in which the collinear factorization result corresponds to the leading term. At high transverse momentum, the subleading correction terms are insignficant, whereas at low $p_\perp$, 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 $α_s$ when we use exact kinematics, as opposed to the approximate kinematics in previous work. With this matching, we can describe the experimental data from RHIC very well at high $p_\perp$.