integral over $d^{2}k_{TB}$ gives helicity sum for $B$ partons on one hand, and the integrated (collinear) PDF on the other $\int dk_{B}^{2}\,\mathcal{F}_{a^{*}/B}\left(x_{B},k_{TB}\right)=f_{a}\left(x_{B}\right)$. Thus, the final formula for the factorization model reads $$\begin{gathered}
d\sigma_{AB\rightarrow2j}=\int d^{2}k_{TA}\int\frac{dx_{A}}{x_{A}}\,\int\frac{dx_{B}}{x_{B}}\,\sum_{b}\\
\mathcal{F}_{g^{*}/A}\left(x_{A},k_{T A},\mu\right)\, f_{b}\left(x_{B},\mu\right)\, d\hat{\sigma}_{g^{*}b\rightarrow2j}\left(x_{A},x_{B},k_{T A},\mu\right),\label{eq:HEN_fact_2}\end{gathered}$$ where we have included the hard scale dependence not only in the collinear PDFs $f_{b}$, but in the UGD as well. Such a dependence turns out to be important for certain exclusive observables involving a hard scale (e.g. large $p_{T}$ of jets; see e.g. [@vanHameren:2014ala]). We note, that when the final states become well separated in rapidity, i.e. when the central jet lies in the opposite hemisphere to the forward jet we start to violate our condition $x_{A}\ll x_{B}$ and different approach should be used. The factorization formula (\[eq:HEN\_fact\_2\]) resembles the linearized approach of [@Dominguez:2011wm] but it extends beyond the correlation limit as here the hard sub-processes have injected a nonzero $k_{T}$. As mentioned before, the formula (\[eq:HEN\_fact\_2\]) has been recently derived from the CGC approach in [@Kotko:2015ura].

Small *x* evolution equations  {#sec:evolution_eqs}
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Let us now discuss the evolution equations for UGDs which were used in our fits. As described in the preceding section we concentrate on linear evolution equations. 