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

In this paper, we investigate the differential cross sections of the inclusive jet and dijet productions of the ZEUS collaboration data at the center 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 double unintegrated parton distribution functions, i.e., UPDFs and DUPDFs, respectively. The \textsc{KaTie} event generator is used to calculate the differential cross section with the UPDFs, while for the input DUPDFs the calculations are directly performed by evaluating the corresponding matrix elements. We check the effect of choosing the different implementation of angular or strong ordering constraints using the UPDFs and the corresponding DUPDFs of Kimber-Martin-Ryskin (KMR) and the leading-order (LO) and next-to-leading-order (NLO) Martin-Ryskin-Watt (MRW) approaches. The impacts of choosing virtualities $k^2 = k_t^2$ or $k^2 = {k_t^2\over {(1-z)}}$ in the differential cross section predictions for the ZEUS experimental data are also investigated. 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 the KMR and LO-MRW UPDFs and DUPDFs are reasonably close to each other and in general 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 overshoot the inclusive jet experimental data.