SIDIS at small $x$ at next-to-leading order: Gluon contribution

We calculate the contribution of gluons to single inclusive hadron production at next-to-leading order (NLO) accuracy in deep inelastic scattering (DIS) at small $x$ using the color glass condensate formalism. It is shown that the only divergence present is the standard collinear divergence, which is absorbed into scale evolution of quark-hadron fragmentation function. Our calculations are performed at finite $N_c$ and we provide general finite $N_c$ expressions for the structure of Wilson lines appearing in inclusive dihadron and single hadron production cross sections. We also comment on how one can obtain rapidity distribution of hadron multiplicities from our results.

Figure 1

The real corrections $i{\mathcal{A}}_1^a,\dots ,i{\mathcal{A}}_4^a$. The arrows on Fermion lines indicate Fermion number flow, whereas all momenta flow to the right. The thick solid line indicates multiple scatterings from the target.