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In this paper, we investigate the differential cross sections of theinclusive jet and dijet productions of the ZEUS collaboration data at thecenter of mass energies of $\sim 300\;GeV$ and $ 319\;GeV$ using the $k_t$ and$(z,k_t)\textrm{-factorizations}$ with the different unintegrated and doubleunintegrated parton distribution functions, i.e., UPDFs and DUPDFs,respectively. The \textsc{KaTie} event generator is used to calculate thedifferential cross section with the UPDFs, while for the input DUPDFs thecalculations are directly performed by evaluating the corresponding matrixelements. We check the effect of choosing the different implementation ofangular or strong ordering constraints using the UPDFs and the correspondingDUPDFs of Kimber-Martin-Ryskin (KMR) and the leading-order (LO) andnext-to-leading-order (NLO) Martin-Ryskin-Watt (MRW) approaches. The impacts ofchoosing virtualities $k^2 = k_t^2$ or $k^2 = {k_t^2\over {(1-z)}}$ in thedifferential cross section predictions for the ZEUS experimental data are alsoinvestigated. It is observed that, as one should expect, the applications of$(z,k_t)\textrm{-factorization}$ is better than the$k_t\textrm{-factorization}$ framework for the predictions of high virtuality$Q^2$ with respect to the ZEUS collaboration data, and also the results of theKMR and LO-MRW UPDFs and DUPDFs are reasonably close to each other and ingeneral can describe the data. It is also observed that only in the case of$k_t$-factorization, the inclusion of Born level makes our results to overshootthe inclusive jet experimental data.

Inclusive jet and dijet productions using $k_t$ and $(z,k_t)\textrm{-factorizations}$ versus ZEUS collaboration data