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

摘要

To overcome the complexity of generalized two hard scale ( k t , 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, k t 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 k t (the parton transverse momentum) to see the general behavior of three-dimensional UPDF at the NLO level up to the LHC working energy scales ( μ 2 ). It is shown that there exits some pronounced peaks for the three-dimensional UPDF ( f a ( x , k t ) ) with respect to the two variables x and k t at various energies ( μ ). These peaks get larger and move to larger values of k t , 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.