Infrared structure of pp $\to$ 2 jets at NNLO: the gluon channel

We use the antenna subtraction method to isolate the infrared singularities present in QCD scattering amplitudes at next-to-next-to-leading order. In particular, infrared singularities due to double-real radiation and real-virtual radiation are subtracted from the QCD matrix elements using antenna functions which are then integrated analytically and added to the double-virtual contribution. Here we consider two-jet production at NNLO at hadron colliders and construct subtraction terms for the double-real and real-virtual channels that describe the single and double unresolved configurations of the pure gluon scattering matrix elements. In all singular regions we show numerically that the subtraction terms correctly approximate the matrix elements and demonstrate that upon integration they contribute to the cancellation of all infrared poles when combined with one and two-loop matrix elements.