  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.
