we neglect the $(1-Dx)$ factor, i.e. we take $D=0$. We have checked that we get no improvement when $D$ is a free parameter. Next, in some cases the fits are not sensitive enough to uniquely determine the three remaining free parameters. In these cases we fix $A$ or $a$ at some plausible value (these are marked with a star in Table \[tab:params\]). Actually, besides the initial condition parameters $N$, $A$, $a$, $D$ we have also the boundary values of kinematic parameters $x_{A}$, $k_{T}$ (c.f. (\[eq:HEN\_fact\_2\])), which – to certain extent – are free parameters as well. We set them as follows. First, in order to be in an accordance with the assumptions leading to (\[eq:HEN\_fact\_2\]) we imply the cut $x_{A}<x_{B}$. Next, for all scenarios we set $x_{A\,\mathrm{min}}=0.0001$. For the model with the DGLAP correction we set $x_{A\,\mathrm{max}}=1.0$ while for the others we set $x_{A\,\mathrm{max}}=0.4$. Further we use $k_{T\,\mathrm{min}}=1\,\mathrm{GeV}$ for DGLAP models and $k_{T\,\mathrm{min}}=0.1\,\mathrm{GeV}$ for the others. Finally, we use $k_{T\,\mathrm{max}}=100\,\mathrm{GeV}$ for exponential initial condition and $k_{T\,\mathrm{max}}=400\,\mathrm{GeV}$ for the others. The last comment concerns the hard scale choice: in all fits we have used the average $p_{T}$ of the jets.

![The $p_{T}$ spectra of the central jet calculated using the best 