TMD cross-section factorization for dijet production at the EIC

We use soft collinear effective theory (SCET) to study a dijet production process in deep-inelastic-scattering (DIS), measuring the imbalance of the two hard probes in the Breit frame. In order to achieve factorization of the transverse momentum dependent (TMD) cross-section, we need to introduce a new soft function that we calculate at one-loop, regulating rapidity divergencies with the #delta#-regulator. We use consistency relations with heavy meson pair production in DIS to extend the anomalous dimension of the dijet soft function to three loops. We also provide phenomenological discussion and plots for this process, which is expected to be measured at the future EIC. The study of these processes could provide new knowledge of the TMD gluon distributions, to which they are sensitive. (author)