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In the present paper, we check and study the validity of the \textsc{KaTie}parton level event generator, by calculating the inclusive electron-proton (ep)dijet and the Proton-proton (p-p) Drell-Yan electron-pair productionsdifferential cross sections in the $k_t$- and collinear factorizationframeworks. The Martin-Ryskin-Watt (MRW) unintegrated parton distributionfunctions (UPDFs) are used as the input UPDFs. The results are compared withthose of ZEUS ep inclusive dijet and ATLAS p-p Drell-Yan electron-pairproductions, experimental data. The \textsc{KaTie} parton level event generatorcan directly calculate the cross sections in the $k_t$-factorization framework.It is noticed that the lab to the Breit transformation in this generator is notcorrectly implemented by its author, so the produced output does not cover theep ZEUS experimental data in which the mentioned transformation is applied. Byfixing the above transformation in the \textsc{KaTie} generator code, we couldappropriately produce the ep inclusive dijet differential cross section, incomparison with those of ZEUS data. It is also shown that the MRW at the NLOlevel, with the angular ordering constraint can successfully predict the ATLASp-p Drell-Yan data. Finally, as it is expected, we conclude that the$k_t$-factorization is an appropriate tool for the small longitudinal partonmomenta and high center of mass energies, with respect to the collinear one.

A validity check of the KATIE parton level event generator in the $k_t$-factorization and collinear frameworks