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The forthcoming p+Pb run at the LHC will provide crucial in formation on theinitial state effects of heavy ion collisions and on the gluon saturationphenomena. In turn, most of the saturation inspired phenomenology in heavy ioncollisions borrows substantial empiric information from the analysis of e+pdata, where abundant high quality data on the small-x kinematic region isavailable. Indeed, the very precise combined HERA data provides a testingground in which the relevance of novel QCD regimes, other than the successfullinear DGLAP evolution, in small-x inclusive DIS data can be ascertained. Wepresent a study of the dependence of the AAMQS fits, based on the runningcoupling BK non-linear evolution equations (rcBK), on the fitted dataset. Thisallows for the identification of the kinematical region where rcBK accuratelydescribes the data, and thus for the determination of its applicabilityboundary. It also set important constraints to the saturation models used tomodel the early stages of heavy ion collisions. Finally we compare the rcBKresults with NNLO DGLAP fits, obtained with the NNPDF methodology withanalogous kinematical cuts. Further, we explore the impact on LHC phenomenologyof applying stringent kinematical cuts to the low-x HERA data in a DGLAP fit.

Delineating the saturation boundary: linear vs non-linear QCD evolution from HERA data to LHC phenomenology