  A factorization algorithm for a patron shower model based on the evolution of
momentum distributions proposed in a previous work is studied. The scaling
violation of initial state parton distributions is generated using parton
showers to an accuracy of the next-to-leading logarithmic (NLL) order of
quantum chromodynamics (QCD) using the information from only splitting
functions and initial parton distributions at some fixed low energy. In the
algorithm proposed in this paper, the total momentum of the initial state
partons is conserved in any factorization scheme for mass singularities. As an
example, the scaling violation of the parton distributions and the transverse
momentum distributions due to initial state parton radiation are calculated
with the jet calculs scheme.
