The present work is devoted to study the high-energy QCD events, such as the di-jet productions from proton–proton inelastic collisions at the LHC in the forward-center and the forward-forward configurations. This provides us with much valuable case study, since such phenomena can provide a direct glimpse into the partonic behavior of a hadron in a dominant gluonic region. We use the unintegrated parton distribution functions ( UPDF ) in the kt -factorization framework. The UPDF of Kimber et al. ( KMR ) and Martin et al. ( MRW ) are generated in the leading order ( LO ) and next-to-leading order ( NLO ), using the Harland-Lang et al. ( MMHT2014 ) PDF libraries. While working in the forward-center and the forward-forward rapidity sectors, one can probe the parton densities at very low longitudinal momentum fractions ( x ). Such a model computation can provide simpler analytic description of data with respect to existing formalisms such as perturbative QCD . The differential cross-section calculations are performed at the center of mass energy of 7 TeV corresponding to CMS collaboration measurement. It is shown that the gluonic jet productions are dominant and a good description of data as well as other theoretical attempts (i.e. KS -linear, KS -nonlinear and rcBK ) is obtained. The uncertainty of the calculations is derived by manipulating the hard scale of the processes by a factor of two. This conclusion is achieved, due to the particular visualization of the angular ordering constraint ( AOC ), that is incorporated in the definition of these UPDF .
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