Matching Collinear and Small-x Factorization Calculations for Inclusive Hadron Production in pA Collisions

Understand

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 $\alpha_s$ when we use exact kinematics, as opposed to the approximate kinematics in previous work.