Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions

We study forward dijet production in dilute-dense hadronic collisions. By con- sidering the appropriate limits, we show that both the transverse-momentum-dependent (TMD) and the high-energy factorization formulas can be derived from the Color Glass Condensate framework. Respectively, this happens when the transverse momentum im- balance of the dijet system, kt, is of the order of either the saturation scale, or the hard jet momenta, the former being always much smaller than the latter. We propose a new formula for forward dijets that encompasses both situations and is therefore applicable re- gardless of the magnitude of kt. That involves generalizing the TMD factorization formula for dijet production to the case where the incoming small-x gluon is o�-shell. The deriva- tion is performed in two independent ways, using either Feynman diagram techniques, or color-ordered amplitudes.