The general behavior of NLO unintegrated parton distributions based on the single-scale evolution and the angular ordering constraint

To overcome the complexity of generalized two hard scale (kt,μ) evolution equation, well known as the Ciafaloni, Catani, Fiorani and Marchesini (CCFM) evolution equations, and calculate the unintegrated parton distribution functions (UPDF), Kimber, Martin and Ryskin (KMR) proposed a procedure based on (i) the inclusion of single-scale (μ) only at the last step of evolution and (ii) the angular ordering constraint (AOC) on the DGLAP terms (the DGLAP collinear approximation), to bring the second scale, kt into the UPDF evolution equations. In this work we intend to use the MSTW2008 (Martin et al.) parton distribution functions (PDF) and try to calculate UPDF for various values of x (the longitudinal fraction of parton momentum), μ (the probe scale) and kt (the parton transverse momentum) to see the general behavior of three-dimensional UPDF at the NLO level up to the LHC working energy scales (μ2). It is shown that there exits some pronounced peaks for the three-dimensional UPDF(fa(x,kt)) with respect to the two variables x and kt at various energies (μ). These peaks get larger and move to larger values of kt, as the energy (μ) is increased. We hope these peaks could be detected in the LHC experiments at CERN and other laboratories in the less exclusive processes.