Markovian MC simulation of QCD evolution at NLO level with minimum kT

We present two Monte Carlo algorithms of the Markovian type which solve the modified QCD evolution equations at NLO level. The modifications with respect to the standard DGLAP evolution concern the argument of the strong coupling constant, αS. We first analyze the z-dependent argument and then the kT-dependent one. The evolution time variable is identified with the rapidity. The two algorithms are tested to 0.05% precision level. We find that the NLO corrections in the evolution of the parton momentum distributions with kT-dependent coupling constant are of the order of 10 to 20%, and in the small-x region even up to 30%, with respect to the LO contributions.