Dihadron production in DIS at NLO: the real corrections

By using the formalism of the light-cone wave function along with the colour glass condensate effective theory, we consider next-to-leading order (NLO) corrections to the production of a pair of hadrons in electron-proton, or electron-nucleus, collisions at small Bjorken $x$. To the order of interest, the process involves the fluctuation of a virtual photon into a quark-antiquark pair, followed by the emission of a gluon from either the quark, or the antiquark. For the case of a virtual photon with transverse polarization, we compute the real NLO corrections, where the emitted gluon is present in the final state. We first compute the tree-level cross-section for the production of the quark-antiquark-gluon system and then deduce the real NLO corrections to dihadron production by integrating out the kinematics of the gluon. We verify in detail that, in the limit where the gluon is soft, our calculation reproduces the (real piece of the) B-JIMWLK evolution of the leading-order cross-section for quark-antiquark production. Similarly, in the limit where the gluon is collinear with its emitter, we recover the real terms in the DGLAP evolution of the fragmentation function. The virtual NLO corrections to dihadron production will be presented by one of us in a subsequent publication.