Investigation of the Z boson production via hadron–hadron collisions in the $$k_t$$ k t and $$(z, k_t)$$ ( z , k t ) -factorization frameworks

Abstract

Abstract In this paper, we study the Z boson production via the proton–proton (p–p) collisions within the $$k_t$$ k t and $$(z, k_t)$$ ( z , k t ) -factorization frameworks, using the Martin–Ryskin–Watt (MRW) unintegrated parton distribution functions (UPDFs) and the double unintegrated parton distribution functions (DUPDFs), respectively. For calculation of the differential cross section (DCS) within the $$k_t$$ k t -factorization ( $$k_t$$ k t is the partonic transverse momentum), the KATIE parton level event generator is used, while for the $$(z, k_t)$$ ( z , k t ) -factorization, the DCS is directly computed. Up to the tree level partonic next-to-leading order (NLO) are included, beside the inclusion of branching ratios, in our calculation. It should be noted that Martin, Ryskin and Watt are originally calculated the same process, i.e., the Z boson production, within the $$(z, k_t)$$ ( z , k t ) -factorization framework, while including only the lowest order tree level partonic sub-process. However, the present report extends their work from two perspectives. First, the additional sub-processes are included, second, for the processes up to the next-to-leading order (NLO), a direct calculation by considering the final state leptons is imposed. Finally, we compare our results with the $$13\; TeV$$ 13 T e V data of the ATLAS, LHCb, CMS collaborations, the corresponding collinear factorization predictions and the Modarres, et al. reports. Our p–p DCS calculations show that the $$k_t$$ k t and $$(z, k_t)$$ ( z , k t ) -factorizations frameworks give relatively the same behavior in the central rapidity regions. While at the large rapidity regions, the $$(z, k_t)$$ ( z , k t ) -factorization, predicts the p–p DCS closer to the experimental data with respect to those of $$k_t$$ k t -factorization framework.