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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>N</c:mi><c:mi>c</c:mi></c:msub></c:math> and we provide general finite <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>c</e:mi></e:msub></e:math> 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.