an explicit arguments were given that this is the case for dilute-dense collisions (actually the arguments hold for so-called “hybrid” factorization – see also below). Moreover it is known from the CGC approach that at really small $x$, i.e. in the saturation regime, the cross sections cannot be described by just dipoles (averages of two Wilson lines), but also higher correlators are needed [@Dominguez:2012ad], what violates the ordinary logic of factorization. However, for the case of back-to-back dijet production in dilute-dense collisions a generalized factorization has been proposed [@Dominguez:2011wm]; that is, the cross section can be given in terms of hard factors and certain universal pieces. Recently, these results were improved to the case of imbalanced dijets [@Kotko:2015ura]. In particular, when the imbalanced transverse momentum is of the order of transverse momenta of the jets the HEF for dijet production can be derived from the dilute limit of the CGC approach.

In the present work we shall constrain ourselves to dijet production in p-p collisions in the linear regime, as the kinematics we are interested in (and where the data exist) do not allow to develop the saturation region. We want to utilize most of the phase space covered by 