Monte Carlo modelling of NLO DGLAP QCD Evolution in the fully unintegrated form

Presently available perturbative QCD calculations combining hard process matrix element with the Parton Shower Monte Carlo programs feature hard process matrix element calculated often beyond the leading order (LO), that is including complete next-to-leading-order (NLO), or even next-to-next-to-leading-order (NNLO) corrections, while Parton Shower is only at the leading order (LO). We report here on a work in progress which demonstrate feasibility of constructing Parton Shower Monte Carlo (PSMC) featuring complete NLO corrections to QCD evolution with respect to the logarithm of the factorization scale. This effort presently covers non-singlet subset of Feynman diagrams contributing to the above QCD evolution. It should be stressed that our approach to the NLO QCD evolution is exclusive, that is giving insight into the fully unintegrated phase space. However, at the inclusive level our implementation agrees exactly with the standard inclusive picture of the NLO DGLAP evolution. Our new approach (after including NLO singlet diagrams) provides a complete method of combining the resummed and fixed order perturbative QCD calculations beyond the LO in a form suitable for the MC implementation, an alternative to the existing ones. First practical applications will include Monte Carlo generators for W/Z production processes in hadron-hadron colliders and lepton-hadron colliders.