Measuring the Weizsaecker-Williams distribution of linearly polarized gluons at an EIC through dijet azimuthal asymmetries

The production of a hard dijet with small transverse momentum imbalance in semi-inclusive DIS probes the conventional and linearly polarized Weizsaecker-Williams (WW) Transverse Momentum Dependent (TMD) gluon distributions. The latter, in particular, gives rise to an azimuthal dependence of the dijet cross-section. In this paper we analyze the feasibility of a measurement of these TMDs through dijet production in DIS on a nucleus at an Electron-Ion Collider. We introduce the MCDijet Monte-Carlo generator to sample quark-antiquark dijet configurations based on leading order parton level cross-sections with WW gluon distributions that solve the non-linear small-x QCD evolution equations. These configurations are fragmented to hadrons using PYTHIA, and final state jets are reconstructed. We report on background studies and on the effect of kinematic cuts introduced to remove beam jet remnants. We estimate that with an integrated luminosity of 20 fb^{-1}/A one can determine the distribution of linearly polarized gluons with a statistical accuracy of approximately 5%.