Forward Hadron Productions in Proton-Proton Collisions in Small-$x$ Formalism

Understand

Employing the so-called hybrid formalism, we calculate the cross section of inclusive hadron production in proton-proton collisions at forward rapidity in small-$x$ formalism at one-loop order.

• For the case of hadron production at forward rapidity, we can uses collinear parton distributions for projectile proton and $k_\perp$ dependent gluon distribution for target proton.
• We show that collinear divergences associated with initial and final state parton radiations are renormalized into parton distributions and fragmentation functions in terms of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation, respectively.
• Furthermore, rapidity divergence can be absorbed into the wave function of target proton which gives rise to the well-known Balitsky-Fadin-Kuraev-Lipatov equation.